Daily Papers

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

In this work, we aim to develop an MLLM that understands and solves questions by learning to create each intermediate step of the reasoning involved till the final answer. To this end, we propose Collective Monte Carlo Tree Search (CoMCTS), a new learning-to-reason method for MLLMs, which introduces the concept of collective learning into ``tree search'' for effective and efficient reasoning-path searching and learning. The core idea of CoMCTS is to leverage collective knowledge from multiple models to collaboratively conjecture, search and identify effective reasoning paths toward correct answers via four iterative operations including Expansion, Simulation and Error Positioning, Backpropagation, and Selection. Using CoMCTS, we construct Mulberry-260k, a multimodal dataset with a tree of rich, explicit and well-defined reasoning nodes for each question. With Mulberry-260k, we perform collective SFT to train our model, Mulberry, a series of MLLMs with o1-like step-by-step Reasoning and Reflection capabilities. Extensive experiments demonstrate the superiority of our proposed methods on various benchmarks. Code will be available at https://github.com/HJYao00/Mulberry

Large Language Models (LLMs) are evolving at an unprecedented pace and have exhibited considerable capability in the realm of natural language processing (NLP) with world knowledge. Benefiting from ultra-large-scale training corpora, a single LLM can manage typical NLP tasks competently. However, its performance in executing reasoning tasks is still confined by the limitations of its internal representations. To push this boundary further, we introduce Corex in this paper, a suite of novel general-purpose strategies that transform LLMs into autonomous agents pioneering multi-model collaborations for complex task-solving. Inspired by human behaviors, Corex is constituted by diverse collaboration paradigms including Debate, Review, and Retrieve modes, which collectively work towards enhancing the factuality, faithfulness, and reliability of the reasoning process. These paradigms foster task-agnostic approaches that enable LLMs to ''think outside the box,'' thereby overcoming hallucinations and providing better solutions. Through extensive experiments across four different types of reasoning tasks, we demonstrate that orchestrating multiple LLMs to work in concert yields substantially better performance compared to existing methods. Further results and in-depth analysis demonstrate the cost-effectiveness of our method, facilitating collaboration among different LLMs and promoting annotation efficiency.

Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core perspectives: the robustness of LLMs to structural perturbations in tables, the comparative analysis of textual and symbolic reasoning on tables, and the potential of boosting model performance through the aggregation of multiple reasoning pathways. We discover that structural variance of tables presenting the same content reveals a notable performance decline, particularly in symbolic reasoning tasks. This prompts the proposal of a method for table structure normalization. Moreover, textual reasoning slightly edges out symbolic reasoning, and a detailed error analysis reveals that each exhibits different strengths depending on the specific tasks. Notably, the aggregation of textual and symbolic reasoning pathways, bolstered by a mix self-consistency mechanism, resulted in achieving SOTA performance, with an accuracy of 73.6% on WIKITABLEQUESTIONS, representing a substantial advancement over previous existing table processing paradigms of LLMs.

Zero-shot coordination in cooperative artificial intelligence (AI) remains a significant challenge, which means effectively coordinating with a wide range of unseen partners. Previous algorithms have attempted to address this challenge by optimizing fixed objectives within a population to improve strategy or behaviour diversity. However, these approaches can result in a loss of learning and an inability to cooperate with certain strategies within the population, known as cooperative incompatibility. To address this issue, we propose the Cooperative Open-ended LEarning (COLE) framework, which constructs open-ended objectives in cooperative games with two players from the perspective of graph theory to assess and identify the cooperative ability of each strategy. We further specify the framework and propose a practical algorithm that leverages knowledge from game theory and graph theory. Furthermore, an analysis of the learning process of the algorithm shows that it can efficiently overcome cooperative incompatibility. The experimental results in the Overcooked game environment demonstrate that our method outperforms current state-of-the-art methods when coordinating with different-level partners. Our demo is available at https://sites.google.com/view/cole-2023.

Enhancing the reasoning capabilities of large language models (LLMs) is crucial for enabling them to tackle complex, multi-step problems. Multi-agent frameworks have shown great potential in enhancing LLMs' reasoning capabilities. However, the lack of effective cooperation between LLM agents hinders their performance, especially for multi-step reasoning tasks. This paper proposes a novel cooperative multi-agent reasoning framework (CoPlanner) by separating reasoning steps and assigning distinct duties to different agents. CoPlanner consists of two LLM agents: a planning agent and a reasoning agent. The planning agent provides high-level strategic hints, while the reasoning agent follows these hints and infers answers. By training the planning agent's policy through the interactive reasoning process via Proximal Policy Optimization (PPO), the LLaMA-3-8B-based CoPlanner outperforms the previous best method by 9.94\% on LogiQA and 3.09\% on BBH. Our results demonstrate that the guidance from the planning agent and the effective cooperation between the agents contribute to the superior performance of CoPlanner in tackling multi-step reasoning problems.

We introduce SELF-DISCOVER, a general framework for LLMs to self-discover the task-intrinsic reasoning structures to tackle complex reasoning problems that are challenging for typical prompting methods. Core to the framework is a self-discovery process where LLMs select multiple atomic reasoning modules such as critical thinking and step-by-step thinking, and compose them into an explicit reasoning structure for LLMs to follow during decoding. SELF-DISCOVER substantially improves GPT-4 and PaLM 2's performance on challenging reasoning benchmarks such as BigBench-Hard, grounded agent reasoning, and MATH, by as much as 32% compared to Chain of Thought (CoT). Furthermore, SELF-DISCOVER outperforms inference-intensive methods such as CoT-Self-Consistency by more than 20%, while requiring 10-40x fewer inference compute. Finally, we show that the self-discovered reasoning structures are universally applicable across model families: from PaLM 2-L to GPT-4, and from GPT-4 to Llama2, and share commonalities with human reasoning patterns.

Enabling effective collaboration among LLMs is a crucial step toward developing autonomous systems capable of solving complex problems. While LLMs are typically used as single-model generators, where humans critique and refine their outputs, the potential for jointly-trained collaborative models remains largely unexplored. Despite promising results in multi-agent communication and debate settings, little progress has been made in training models to work together on tasks. In this paper, we present a first step toward "Multi-agent LLM training" (MALT) on reasoning problems. Our approach employs a sequential multi-agent setup with heterogeneous LLMs assigned specialized roles: a generator, verifier, and refinement model iteratively solving problems. We propose a trajectory-expansion-based synthetic data generation process and a credit assignment strategy driven by joint outcome based rewards. This enables our post-training setup to utilize both positive and negative trajectories to autonomously improve each model's specialized capabilities as part of a joint sequential system. We evaluate our approach across MATH, GSM8k, and CQA, where MALT on Llama 3.1 8B models achieves relative improvements of 14.14%, 7.12%, and 9.40% respectively over the same baseline model. This demonstrates an early advance in multi-agent cooperative capabilities for performance on mathematical and common sense reasoning questions. More generally, our work provides a concrete direction for research around multi-agent LLM training approaches.

Large language models (LLMs) have dramatically enhanced the field of language intelligence, as demonstrably evidenced by their formidable empirical performance across a spectrum of complex reasoning tasks. Additionally, theoretical proofs have illuminated their emergent reasoning capabilities, providing a compelling showcase of their advanced cognitive abilities in linguistic contexts. Critical to their remarkable efficacy in handling complex reasoning tasks, LLMs leverage the intriguing chain-of-thought (CoT) reasoning techniques, obliging them to formulate intermediate steps en route to deriving an answer. The CoT reasoning approach has not only exhibited proficiency in amplifying reasoning performance but also in enhancing interpretability, controllability, and flexibility. In light of these merits, recent research endeavors have extended CoT reasoning methodologies to nurture the development of autonomous language agents, which adeptly adhere to language instructions and execute actions within varied environments. This survey paper orchestrates a thorough discourse, penetrating vital research dimensions, encompassing: (i) the foundational mechanics of CoT techniques, with a focus on elucidating the circumstances and justification behind its efficacy; (ii) the paradigm shift in CoT; and (iii) the burgeoning of language agents fortified by CoT approaches. Prospective research avenues envelop explorations into generalization, efficiency, customization, scaling, and safety. This paper caters to a wide audience, including beginners seeking comprehensive knowledge of CoT reasoning and language agents, as well as experienced researchers interested in foundational mechanics and engaging in cutting-edge discussions on these topics. A repository for the related papers is available at https://github.com/Zoeyyao27/CoT-Igniting-Agent.

When humans cooperate, they frequently coordinate their activity through both verbal communication and non-verbal actions, using this information to infer a shared goal and plan. How can we model this inferential ability? In this paper, we introduce a model of a cooperative team where one agent, the principal, may communicate natural language instructions about their shared plan to another agent, the assistant, using GPT-3 as a likelihood function for instruction utterances. We then show how a third person observer can infer the team's goal via multi-modal Bayesian inverse planning from actions and instructions, computing the posterior distribution over goals under the assumption that agents will act and communicate rationally to achieve them. We evaluate this approach by comparing it with human goal inferences in a multi-agent gridworld, finding that our model's inferences closely correlate with human judgments (R = 0.96). When compared to inference from actions alone, we also find that instructions lead to more rapid and less uncertain goal inference, highlighting the importance of verbal communication for cooperative agents.

Prompt engineering and calibration make large language models excel at reasoning tasks, including multiple choice commonsense reasoning. From a practical perspective, we investigate and evaluate these strategies on smaller language models. Through experiments on five commonsense reasoning benchmarks, we find that each strategy favors certain models, but their joint effects are mostly negative.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Building AIs with adaptive behaviors in human-AI cooperation stands as a pivotal focus in AGI research. Current methods for developing cooperative agents predominantly rely on learning-based methods, where policy generalization heavily hinges on past interactions with specific teammates. These approaches constrain the agent's capacity to recalibrate its strategy when confronted with novel teammates. We propose ProAgent, a novel framework that harnesses large language models (LLMs) to fashion a proactive agent empowered with the ability to anticipate teammates' forthcoming decisions and formulate enhanced plans for itself. ProAgent excels at cooperative reasoning with the capacity to dynamically adapt its behavior to enhance collaborative efforts with teammates. Moreover, the ProAgent framework exhibits a high degree of modularity and interpretability, facilitating seamless integration to address a wide array of coordination scenarios. Experimental evaluations conducted within the framework of Overcook-AI unveil the remarkable performance superiority of ProAgent, outperforming five methods based on self-play and population-based training in cooperation with AI agents. Further, when cooperating with human proxy models, its performance exhibits an average improvement exceeding 10\% compared to the current state-of-the-art, COLE. The advancement was consistently observed across diverse scenarios involving interactions with both AI agents of varying characteristics and human counterparts. These findings inspire future research for human-robot collaborations. For a hands-on demonstration, please visit https://pku-proagent.github.io.

Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual process theory in cognitive science, we are the first to unravel the cognitive reasoning abilities of language models. Our framework employs an iterative methodology to construct a Cognitive Tree (CogTree). The root node of this tree represents the initial query, while the leaf nodes consist of straightforward questions that can be answered directly. This construction involves two main components: the implicit extraction module (referred to as the intuitive system) and the explicit reasoning module (referred to as the reflective system). The intuitive system rapidly generates multiple responses by utilizing in-context examples, while the reflective system scores these responses using comparative learning. The scores guide the intuitive system in its subsequent generation step. Our experimental results on two popular and challenging reasoning tasks indicate that it is possible to achieve a performance level comparable to that of GPT-3.5 (with 175B parameters), using a significantly smaller language model that contains fewer parameters (<=7B) than 5% of GPT-3.5.

The emergent reasoning and Theory of Mind (ToM) abilities demonstrated by Large Language Models (LLMs) make them promising candidates for developing coordination agents. In this study, we introduce a new LLM-Coordination Benchmark aimed at a detailed analysis of LLMs within the context of Pure Coordination Games, where participating agents need to cooperate for the most gain. This benchmark evaluates LLMs through two distinct tasks: (1) Agentic Coordination, where LLMs act as proactive participants for cooperation in 4 pure coordination games; (2) Coordination Question Answering (QA), where LLMs are prompted to answer 198 multiple-choice questions from the 4 games for evaluation of three key reasoning abilities: Environment Comprehension, ToM Reasoning, and Joint Planning. Furthermore, to enable LLMs for multi-agent coordination, we introduce a Cognitive Architecture for Coordination (CAC) framework that can easily integrate different LLMs as plug-and-play modules for pure coordination games. Our findings indicate that LLM agents equipped with GPT-4-turbo achieve comparable performance to state-of-the-art reinforcement learning methods in games that require commonsense actions based on the environment. Besides, zero-shot coordination experiments reveal that, unlike RL methods, LLM agents are robust to new unseen partners. However, results on Coordination QA show a large room for improvement in the Theory of Mind reasoning and joint planning abilities of LLMs. The analysis also sheds light on how the ability of LLMs to understand their environment and their partner's beliefs and intentions plays a part in their ability to plan for coordination. Our code is available at https://github.com/eric-ai-lab/llm_coordination.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Extensive work has shown that the performance and interpretability of commonsense reasoning can be improved via knowledge-augmented reasoning methods, where the knowledge that underpins the reasoning process is explicitly verbalized and utilized. However, existing implementations, including "chain-of-thought" and its variants, fall short in capturing the introspective nature of knowledge required in commonsense reasoning, and in accounting for the mutual adaptation between the generation and utilization of knowledge. We propose a novel method to develop an introspective commonsense reasoner, Crystal. To tackle commonsense problems, it first introspects for knowledge statements related to the given question, and subsequently makes an informed prediction that is grounded in the previously introspected knowledge. The knowledge introspection and knowledge-grounded reasoning modes of the model are tuned via reinforcement learning to mutually adapt, where the reward derives from the feedback given by the model itself. Experiments show that Crystal significantly outperforms both the standard supervised finetuning and chain-of-thought distilled methods, and enhances the transparency of the commonsense reasoning process. Our work ultimately validates the feasibility and potential of reinforcing a neural model with self-feedback.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Chain-of-Thought (CoT) Prompting is a dominant paradigm in Large Language Models (LLMs) to enhance complex reasoning. It guides LLMs to present multi-step reasoning, rather than generating the final answer directly. However, CoT encounters difficulties when key information required for reasoning is implicit or missing. This occurs because CoT emphasizes the sequence of reasoning steps while overlooking the early extraction of essential information. We propose a pre-prompting method called Iterative Summarization Pre-Prompting (ISP^2) to refine LLM reasoning when key information is not explicitly provided. First, entities and their corresponding descriptions are extracted to form potential key information pairs. Next, we use a reliability rating to assess these pairs, then merge the two lowest-ranked pairs into a new entity description. This process is repeated until a unique key information pair is obtained. Finally, that pair, along with the original question, is fed into LLMs to produce the answer. Extensive experiments demonstrate a 7.1% improvement compared to existing methods. Unlike traditional prompting, ISP^2 adopts an inductive approach with pre-prompting, offering flexible integration into diverse reasoning frameworks. The code is available at https://github.com/zdhgreat/ISP-2.

Multimodal reasoning is a challenging task that requires models to reason across multiple modalities to answer questions. Existing approaches have made progress by incorporating language and visual modalities into a two-stage reasoning framework, separating rationale generation from answer inference. However, these approaches often fall short due to the inadequate quality of the generated rationales. In this work, we delve into the importance of rationales in model reasoning. We observe that when rationales are completely accurate, the model's accuracy significantly improves, highlighting the need for high-quality rationale generation. Motivated by this, we propose MC-CoT, a self-consistency training strategy that generates multiple rationales and answers, subsequently selecting the most accurate through a voting process. This approach not only enhances the quality of generated rationales but also leads to more accurate and robust answers. Through extensive experiments, we demonstrate that our approach significantly improves model performance across various benchmarks. Remarkably, we show that even smaller base models, when equipped with our proposed approach, can achieve results comparable to those of larger models, illustrating the potential of our approach in harnessing the power of rationales for improved multimodal reasoning. The code is available at https://github.com/chengtan9907/mc-cot.

Step-by-step reasoning approaches like chain of thought (CoT) have proved to be very effective in inducing reasoning capabilities in large language models. However, the success of the CoT approach is fundamentally tied to the model size, and billion parameter-scale models are often needed to get CoT to work. In this paper, we propose a knowledge distillation approach that leverages the step-by-step CoT reasoning capabilities of larger models and distills these abilities into smaller models. In this work, we propose an alternative reasoning scheme, Socratic CoT, that learns a decomposition of the original problem into a sequence of subproblems and uses it to guide the intermediate reasoning steps. We use Socratic CoT to train a combination of two small distilled models: a problem decomposer and a subproblem solver. In practice, given a new problem, the two distilled models work in sync to decompose and solve complex problems. On multiple reasoning datasets (GSM8K, StrategyQA, and SVAMP), our proposed distillation strategies boosts the performance of smaller models over 70% compared to the baselines. Finally, we investigate when Socratic CoT is an effective alternative to CoT, demonstrating cases where a much smaller model (GPT-2 large) can outperform a 10X larger model (GPT-3 6B). Our code is available here: https://github.com/kumar-shridhar/Distiiling-LM

Large language models (LLMs) are restricted to reason in the "language space", where they typically express the reasoning process with a chain-of-thought (CoT) to solve a complex reasoning problem. However, we argue that language space may not always be optimal for reasoning. For example, most word tokens are primarily for textual coherence and not essential for reasoning, while some critical tokens require complex planning and pose huge challenges to LLMs. To explore the potential of LLM reasoning in an unrestricted latent space instead of using natural language, we introduce a new paradigm Coconut (Chain of Continuous Thought). We utilize the last hidden state of the LLM as a representation of the reasoning state (termed "continuous thought"). Rather than decoding this into a word token, we feed it back to the LLM as the subsequent input embedding directly in the continuous space. Experiments show that Coconut can effectively augment the LLM on several reasoning tasks. This novel latent reasoning paradigm leads to emergent advanced reasoning patterns: the continuous thought can encode multiple alternative next reasoning steps, allowing the model to perform a breadth-first search (BFS) to solve the problem, rather than prematurely committing to a single deterministic path like CoT. Coconut outperforms CoT in certain logical reasoning tasks that require substantial backtracking during planning, with fewer thinking tokens during inference. These findings demonstrate the promise of latent reasoning and offer valuable insights for future research.

Large Language Models (LLMs) have shown remarkable capabilities in general natural language processing tasks but often fall short in complex reasoning tasks. Recent studies have explored human-like problem-solving strategies, such as self-correct, to push further the boundary of single-model reasoning ability. In this work, we let a single model "step outside the box" by engaging multiple models to correct each other. We introduce a multi-agent collaboration strategy that emulates the academic peer review process. Each agent independently constructs its own solution, provides reviews on the solutions of others, and assigns confidence levels to its reviews. Upon receiving peer reviews, agents revise their initial solutions. Extensive experiments on three different types of reasoning tasks show that our collaboration approach delivers superior accuracy across all ten datasets compared to existing methods. Further study underscores the effectiveness of integrating confidence in reviews, demonstrates the superiority of feedback exchange over mere solution sharing, and highlights the role of capability and diversity in fostering successful collaboration.

Contextual commonsense inference is the task of generating various types of explanations around the events in a dyadic dialogue, including cause, motivation, emotional reaction, and others. Producing a coherent and non-trivial explanation requires awareness of the dialogue's structure and of how an event is grounded in the context. In this work, we create CICEROv2, a dataset consisting of 8,351 instances from 2,379 dialogues, containing multiple human-written answers for each contextual commonsense inference question, representing a type of explanation on cause, subsequent event, motivation, and emotional reaction. We show that the inferences in CICEROv2 are more semantically diverse than other contextual commonsense inference datasets. To solve the inference task, we propose a collection of pre-training objectives, including concept denoising and utterance sorting to prepare a pre-trained model for the downstream contextual commonsense inference task. Our results show that the proposed pre-training objectives are effective at adapting the pre-trained T5-Large model for the contextual commonsense inference task.

While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves the astonishing accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Code is available at https://github.com/iiis-ai/cumulative-reasoning.

Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which can then be robustly generalized to novel scenarios. Recent work has evaluated large language models (LLMs) on inductive reasoning tasks by directly prompting them yielding "in context learning." This can work well for straightforward inductive tasks, but performs very poorly on more complex tasks such as the Abstraction and Reasoning Corpus (ARC). In this work, we propose to improve the inductive reasoning ability of LLMs by generating explicit hypotheses at multiple levels of abstraction: we prompt the LLM to propose multiple abstract hypotheses about the problem, in natural language, then implement the natural language hypotheses as concrete Python programs. These programs can be directly verified by running on the observed examples and generalized to novel inputs. Because of the prohibitive cost of generation with state-of-the-art LLMs, we consider a middle step to filter the set of hypotheses that will be implemented into programs: we either ask the LLM to summarize into a smaller set of hypotheses, or ask human annotators to select a subset of the hypotheses. We verify our pipeline's effectiveness on the ARC visual inductive reasoning benchmark, its variant 1D-ARC, and string transformation dataset SyGuS. On a random 40-problem subset of ARC, our automated pipeline using LLM summaries achieves 27.5% accuracy, significantly outperforming the direct prompting baseline (accuracy of 12.5%). With the minimal human input of selecting from LLM-generated candidates, the performance is boosted to 37.5%. (And we argue this is a lower bound on the performance of our approach without filtering.) Our ablation studies show that abstract hypothesis generation and concrete program representations are both beneficial for LLMs to perform inductive reasoning tasks.

Large-scale sequence-to-sequence models have shown to be adept at both multiple-choice and open-domain commonsense reasoning tasks. However, the current systems do not provide the ability to control the various attributes of the reasoning chain. To enable better controllability, we propose to study the commonsense reasoning as a template filling task (TemplateCSR) -- where the language models fills reasoning templates with the given constraints as control factors. As an approach to TemplateCSR, we (i) propose a dataset of commonsense reasoning template-expansion pairs and (ii) introduce POTTER, a pretrained sequence-to-sequence model using prompts to perform commonsense reasoning across concepts. Our experiments show that our approach outperforms baselines both in generation metrics and factuality metrics. We also present a detailed error analysis on our approach's ability to reliably perform commonsense reasoning.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

We envision a continuous collaborative learning system where groups of LLM agents work together to solve reasoning problems, drawing on memory they collectively build to improve performance as they gain experience. This work establishes the foundations for such a system by studying the interoperability of chain-of-thought reasoning styles, multi-agent collaboration, and memory banks. Extending beyond the identical agents of self-consistency, we introduce varied-context agents with diverse exemplars and a summarizer agent in place of voting. We generate frozen and continuously learned memory banks of exemplars and pair them with fixed, random, and similarity-based retrieval mechanisms. Our systematic study reveals where various methods contribute to reasoning performance of two LLMs on three grounded reasoning tasks, showing that random exemplar selection can often beat more principled approaches, and in some tasks, inclusion of any exemplars serves only to distract both weak and strong models.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

The Chain-of-Thought (CoT) paradigm has emerged as a critical approach for enhancing the reasoning capabilities of large language models (LLMs). However, despite their widespread adoption and success, CoT methods often exhibit instability due to their inability to consistently ensure the quality of generated reasoning paths, leading to sub-optimal reasoning performance. To address this challenge, we propose the Strategic Chain-of-Thought (SCoT), a novel methodology designed to refine LLM performance by integrating strategic knowledge prior to generating intermediate reasoning steps. SCoT employs a two-stage approach within a single prompt: first eliciting an effective problem-solving strategy, which is then used to guide the generation of high-quality CoT paths and final answers. Our experiments across eight challenging reasoning datasets demonstrate significant improvements, including a 21.05\% increase on the GSM8K dataset and 24.13\% on the Tracking\_Objects dataset, respectively, using the Llama3-8b model. Additionally, we extend the SCoT framework to develop a few-shot method with automatically matched demonstrations, yielding even stronger results. These findings underscore the efficacy of SCoT, highlighting its potential to substantially enhance LLM performance in complex reasoning tasks.

Most existing chain-of-thought (CoT) prompting methods suffer from the issues of generalizability and consistency, as they often rely on instance-specific solutions that may not be applicable to other cases and lack task-level consistency in their reasoning steps. To address these limitations, we propose a comprehensive framework, StrategyLLM, harnessing the capabilities of LLMs to construct generalizable and consistent few-shot prompts for various tasks automatically. To this end, StrategyLLM employs four LLM-based agents: strategy generator, executor, optimizer, and evaluator, working together to generate, evaluate, and select promising strategies for a given task. The experimental results demonstrate that StrategyLLM outperforms the competitive baseline CoT-SC that requires human-annotated solutions on 13 datasets across 4 challenging tasks without human involvement, including math reasoning (34.21% rightarrow 38.79%), commonsense reasoning (70.3% rightarrow 72.5%), algorithmic reasoning (51.7% rightarrow 62.0%), and symbolic reasoning (30.0% rightarrow 79.2%).

Multi-agent interactions, such as communication, teaching, and bluffing, often rely on higher-order social inference, i.e., understanding how others infer oneself. Such intricate reasoning can be effectively modeled through nested multi-agent reasoning. Nonetheless, the computational complexity escalates exponentially with each level of reasoning, posing a significant challenge. However, humans effortlessly perform complex social inferences as part of their daily lives. To bridge the gap between human-like inference capabilities and computational limitations, we propose a novel approach: leveraging neural networks to amortize high-order social inference, thereby expediting nested multi-agent reasoning. We evaluate our method in two challenging multi-agent interaction domains. The experimental results demonstrate that our method is computationally efficient while exhibiting minimal degradation in accuracy.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

Many commonsense reasoning NLP tasks involve choosing between one or more possible answers to a question or prompt based on knowledge that is often implicit. Large pretrained language models (PLMs) can achieve near-human performance on such tasks, while providing little human-interpretable evidence of the underlying reasoning they use. In this work, we show how to use these same models to generate such evidence: inspired by the contrastive nature of human explanations, we use PLMs to complete explanation prompts which contrast alternatives according to the key attribute(s) required to justify the correct answer (for example, peanuts are usually salty while raisins are sweet). Conditioning model decisions on these explanations improves performance on two commonsense reasoning benchmarks, as compared to previous non-contrastive alternatives. These explanations are also judged by humans to be more relevant for solving the task, and facilitate a novel method to evaluate explanation faithfulfness.

While Chain-of-Thought (CoT) prompting boosts Language Models' (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We propose Faithful CoT, a faithful-by-construction framework that decomposes a reasoning task into two stages: Translation (Natural Language query rightarrow symbolic reasoning chain) and Problem Solving (reasoning chain rightarrow answer), using an LM and a deterministic solver respectively. We demonstrate the efficacy of our approach on 10 reasoning datasets from 4 diverse domains. It outperforms traditional CoT prompting on 9 out of the 10 datasets, with an average accuracy gain of 4.4 on Math Word Problems, 1.9 on Planning, 4.0 on Multi-hop Question Answering (QA), and 18.1 on Logical Inference, under greedy decoding. Together with self-consistency decoding, we achieve new state-of-the-art few-shot performance on 7 out of the 10 datasets, showing a strong synergy between faithfulness and accuracy.

Deep learning models perform poorly on tasks that require commonsense reasoning, which often necessitates some form of world-knowledge or reasoning over information not immediately present in the input. We collect human explanations for commonsense reasoning in the form of natural language sequences and highlighted annotations in a new dataset called Common Sense Explanations (CoS-E). We use CoS-E to train language models to automatically generate explanations that can be used during training and inference in a novel Commonsense Auto-Generated Explanation (CAGE) framework. CAGE improves the state-of-the-art by 10% on the challenging CommonsenseQA task. We further study commonsense reasoning in DNNs using both human and auto-generated explanations including transfer to out-of-domain tasks. Empirical results indicate that we can effectively leverage language models for commonsense reasoning.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem is still shadowed by the lack of a well-posed theoretical framework; existing work usually relies on deep language models wholeheartedly, and is potentially susceptible to confounding co-occurrences. Motivated by classical causal principles, we articulate the central question of CCR and draw parallels between human subjects in observational studies and natural languages to adopt CCR to the potential-outcomes framework, which is the first such attempt for commonsense tasks. We propose a novel framework, ROCK, to Reason O(A)bout Commonsense K(C)ausality, which utilizes temporal signals as incidental supervision, and balances confounding effects using temporal propensities that are analogous to propensity scores. The ROCK implementation is modular and zero-shot, and demonstrates good CCR capabilities.

Chain-of-Thought (CoT) prompting can dramatically improve the multi-step reasoning abilities of large language models (LLMs). CoT explicitly encourages the LLM to generate intermediate rationales for solving a problem, by providing a series of reasoning steps in the demonstrations. Despite its success, there is still little understanding of what makes CoT prompting effective and which aspects of the demonstrated reasoning steps contribute to its performance. In this paper, we show that CoT reasoning is possible even with invalid demonstrations - prompting with invalid reasoning steps can achieve over 80-90% of the performance obtained using CoT under various metrics, while still generating coherent lines of reasoning during inference. Further experiments show that other aspects of the rationales, such as being relevant to the query and correctly ordering the reasoning steps, are much more important for effective CoT reasoning. Overall, these findings both deepen our understanding of CoT prompting, and open up new questions regarding LLMs' capability to learn to reason in context.

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose significant challenges to state-of-the-art models. Drawing inspiration from the beam search algorithm, we propose PathFinder, a tree-search-based reasoning path generation approach. It enhances diverse branching and multi-hop reasoning through the integration of dynamic decoding, enabled by varying sampling methods and parameters. Using constrained reasoning, PathFinder integrates novel quality constraints, pruning, and exploration methods to enhance the efficiency and the quality of generation. Moreover, it includes scoring and ranking features to improve candidate selection. Our approach outperforms competitive baselines on three complex arithmetic and commonsense reasoning tasks by 6% on average. Our model generalizes well to longer, unseen reasoning chains, reflecting similar complexities to beam search with large branching factors.

Extensive knowledge graphs (KGs) have been constructed to facilitate knowledge-driven tasks across various scenarios. However, existing work usually develops separate reasoning models for different KGs, lacking the ability to generalize and transfer knowledge across diverse KGs and reasoning settings. In this paper, we propose a prompt-based KG foundation model via in-context learning, namely KG-ICL, to achieve a universal reasoning ability. Specifically, we introduce a prompt graph centered with a query-related example fact as context to understand the query relation. To encode prompt graphs with the generalization ability to unseen entities and relations in queries, we first propose a unified tokenizer that maps entities and relations in prompt graphs to predefined tokens. Then, we propose two message passing neural networks to perform prompt encoding and KG reasoning, respectively. We conduct evaluation on 43 different KGs in both transductive and inductive settings. Results indicate that the proposed KG-ICL outperforms baselines on most datasets, showcasing its outstanding generalization and universal reasoning capabilities. The source code is accessible on GitHub: https://github.com/nju-websoft/KG-ICL.

The recent development of chain-of-thought (CoT) decoding has enabled large language models (LLMs) to generate explicit logical reasoning paths for complex problem-solving. However, research indicates that these paths are not always deliberate and optimal. The tree-of-thought (ToT) method employs tree-searching to extensively explore the reasoning space and find better reasoning paths that CoT decoding might overlook. This deliberation, however, comes at the cost of significantly increased inference complexity. In this work, we demonstrate that fine-tuning LLMs leveraging the search tree constructed by ToT allows CoT to achieve similar or better performance, thereby avoiding the substantial inference burden. This is achieved through Chain of Preference Optimization (CPO), where LLMs are fine-tuned to align each step of the CoT reasoning paths with those of ToT using the inherent preference information in the tree-search process. Extensive experimental results show that CPO significantly improves LLM performance in solving a variety of complex problems, including question answering, fact verification, and arithmetic reasoning, demonstrating its effectiveness. Our code is available at https://github.com/sail-sg/CPO.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

Recent advancements have highlighted that Large Language Models (LLMs) are prone to hallucinations when solving complex reasoning problems, leading to erroneous results. To tackle this issue, researchers incorporate Knowledge Graphs (KGs) to improve the reasoning ability of LLMs. However, existing methods face two limitations: 1) they typically assume that all answers to the questions are contained in KGs, neglecting the incompleteness issue of KGs, and 2) they treat the KG as a static repository and overlook the implicit logical reasoning structures inherent in KGs. In this paper, we introduce SymAgent, an innovative neural-symbolic agent framework that achieves collaborative augmentation between KGs and LLMs. We conceptualize KGs as dynamic environments and transform complex reasoning tasks into a multi-step interactive process, enabling KGs to participate deeply in the reasoning process. SymAgent consists of two modules: Agent-Planner and Agent-Executor. The Agent-Planner leverages LLM's inductive reasoning capability to extract symbolic rules from KGs, guiding efficient question decomposition. The Agent-Executor autonomously invokes predefined action tools to integrate information from KGs and external documents, addressing the issues of KG incompleteness. Furthermore, we design a self-learning framework comprising online exploration and offline iterative policy updating phases, enabling the agent to automatically synthesize reasoning trajectories and improve performance. Experimental results demonstrate that SymAgent with weak LLM backbones (i.e., 7B series) yields better or comparable performance compared to various strong baselines. Further analysis reveals that our agent can identify missing triples, facilitating automatic KG updates.

Pretrained large language models (LLMs) are increasingly utilized across a wide range of natural language processing (NLP) tasks due to their impressive capabilities as few-shot learners. Recent techniques, such as chain-of-thought (CoT) prompting, have significantly advanced multi-step reasoning by introducing step-by-step decomposition, achieving state-of-the-art results on complex reasoning benchmarks. However, these approaches often rely on static prompting templates that do not adapt to task complexity or errors during the reasoning process. In this work, we introduce Adaptive Prompting, a dynamic and iterative framework designed to enhance reasoning by incorporating real-time adjustments to prompt structures and validation mechanisms.Experimental results demonstrate that Adaptive Prompting significantly improves performance on diverse reasoning benchmarks, including arithmetic reasoning (GSM8K, MultiArith), logical reasoning and commonsense tasks, achieving substantial accuracy gains compared to static prompting baselines. By integrating guided prompts, intermediate validation, and self-corrective steps, our approach enables smaller models to achieve competitive performance with larger counterparts, such as GPT-4, while maintaining computational efficiency. The framework achieves this without requiring fine-tuning or task-specific training data, highlighting the untapped potential of iterative reasoning methods.

Modern systems for multi-hop question answering (QA) typically break questions into a sequence of reasoning steps, termed chain-of-thought (CoT), before arriving at a final answer. Often, multiple chains are sampled and aggregated through a voting mechanism over the final answers, but the intermediate steps themselves are discarded. While such approaches improve performance, they do not consider the relations between intermediate steps across chains and do not provide a unified explanation for the predicted answer. We introduce Multi-Chain Reasoning (MCR), an approach which prompts large language models to meta-reason over multiple chains of thought, rather than aggregating their answers. MCR examines different reasoning chains, mixes information between them and selects the most relevant facts in generating an explanation and predicting the answer. MCR outperforms strong baselines on 7 multi-hop QA datasets. Moreover, our analysis reveals that MCR explanations exhibit high quality, enabling humans to verify its answers.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

In-context Learning (ICL) enables large language models (LLMs) to tackle downstream tasks through sophisticated prompting and high-quality demonstrations. However, this traditional ICL paradigm shows limitations when facing complex mathematical reasoning tasks, primarily due to its heavy dependence on example quality and the necessity for human intervention in challenging scenarios. To address these limitations, this paper presents HiAR-ICL, a High-level Automated Reasoning paradigm in ICL that shifts focus from specific examples to abstract thinking patterns, extending the conventional concept of context in ICL. HiAR-ICL introduces five atomic reasoning actions as fundamental components for constructing chain-structured patterns. Using Monte Carlo Tree Search, we explore reasoning paths and construct thought cards to guide subsequent inference. We then develop a cognitive complexity framework that dynamically matches problems with appropriate thought cards. Experimental results demonstrate HiAR-ICL's effectiveness, achieving state-of-the-art accuracy (79.6%) on the MATH benchmark with Qwen2.5-7B-Instruct, surpassing GPT-4o (76.6%) and Claude 3.5 (71.1%).

Self-consistency (SC) has been a widely used decoding strategy for chain-of-thought reasoning. Despite bringing significant performance improvements across a variety of multi-step reasoning tasks, it is a high-cost method that requires multiple sampling with the preset size. In this paper, we propose a simple and scalable sampling process, Early-Stopping Self-Consistency (ESC), to greatly reduce the cost of SC without sacrificing performance. On this basis, one control scheme for ESC is further derivated to dynamically choose the performance-cost balance for different tasks and models. To demonstrate ESC's effectiveness, we conducted extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning over language models with varying scales. The empirical results show that ESC reduces the average number of sampling of chain-of-thought reasoning by a significant margin on six benchmarks, including MATH (-33.8%), GSM8K (-80.1%), StrategyQA (-76.8%), CommonsenseQA (-78.5%), Coin Flip (-84.2%) and Last Letters (-67.4%), while attaining comparable performances.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Chain of Thought (CoT) was introduced in recent research as a method for improving step-by-step reasoning in Large Language Models. However, CoT has limited applications such as its need for hand-crafted few-shot exemplar prompts and no capability to adjust itself to different queries. In this work, we propose a system to automatically generate rationales using CoT. Our method improves multi-step implicit reasoning capabilities by decomposing the implicit query into several explicit questions. This provides interpretability for the model, improving reasoning in weaker LLMs. We test our approach with two Q\&A datasets: StrategyQA and HotpotQA. We show an increase in accuracy with both, especially on StrategyQA. To facilitate further research in this field, the complete source code for this study has been made publicly available on GitHub: https://github.com/miralab-ai/autoreason.

While chain-of-thought (CoT) prompting has revolutionized how LLMs perform reasoning tasks, its current methods and variations (e.g, Self-consistency, ReACT, Reflexion, Tree-of-Thoughts (ToT), Cumulative Reasoning (CR)) suffer from limitations like slowness, limited context grounding, hallucination and inconsistent outputs. To overcome these challenges, we introduce Evidence to Generate (E2G), a novel single-agent, two-step prompting framework. Instead of unverified reasoning claims, this innovative approach leverages the power of "evidence for decision making" by first focusing exclusively on the thought sequences (the series of intermediate steps) explicitly mentioned in the context which then serve as extracted evidence, guiding the LLM's output generation process with greater precision and efficiency. This simple yet powerful approach unlocks the true potential of chain-of-thought like prompting, paving the way for faster, more reliable, and more contextually aware reasoning in LLMs. \tool achieves remarkable results robustly across a wide range of knowledge-intensive reasoning and generation tasks, surpassing baseline approaches with state-of-the-art LLMs. For example, (i) on LogiQA benchmark using GPT-4 as backbone model, \tool achieves a new state-of-the Accuracy of 53.8% exceeding CoT by 18%, ToT by 11%, CR by 9% (ii) a variant of E2G with PaLM2 outperforms the variable-shot performance of Gemini Ultra by 0.9 F1 points, reaching an F1 score of 83.3 on a subset of DROP.

Large language models (LLMs), while promising, face criticisms for biases, hallucinations, and a lack of reasoning capability. This paper introduces SocraSynth, a multi-LLM agent reasoning platform developed to mitigate these issues. SocraSynth utilizes conditional statistics and systematic context enhancement through continuous arguments, alongside adjustable debate contentiousness levels. The platform typically involves a human moderator and two LLM agents representing opposing viewpoints on a given subject. SocraSynth operates in two main phases: knowledge generation and reasoning evaluation. In the knowledge generation phase, the moderator defines the debate topic and contentiousness level, prompting the agents to formulate supporting arguments for their respective stances. The reasoning evaluation phase then employs Socratic reasoning and formal logic principles to appraise the quality of the arguments presented. The dialogue concludes with the moderator adjusting the contentiousness from confrontational to collaborative, gathering final, conciliatory remarks to aid in human reasoning and decision-making. Through case studies in three distinct application domains, this paper showcases SocraSynth's effectiveness in fostering rigorous research, dynamic reasoning, comprehensive assessment, and enhanced collaboration. This underscores the value of multi-agent interactions in leveraging LLMs for advanced knowledge extraction and decision-making support.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

In current NLP research, large-scale language models and their abilities are widely being discussed. Some recent works have also found notable failures of these models. Often these failure examples involve complex reasoning abilities. This work focuses on a simple commonsense ability, reasoning about when an action (or its effect) is feasible. To this end, we introduce FeasibilityQA, a question-answering dataset involving binary classification (BCQ) and multi-choice multi-correct questions (MCQ) that test understanding of feasibility. We show that even state-of-the-art models such as GPT-3, GPT-2, and T5 struggle to answer the feasibility questions correctly. Specifically, on MCQ and BCQ questions, GPT-3 achieves an accuracy of just (19%, 62%) and (25%, 64%) in zero-shot and few-shot settings, respectively. We also evaluate models by providing relevant knowledge statements required to answer the question. We find that the additional knowledge leads to a 7% gain in performance, but the overall performance still remains low. These results make one wonder how much commonsense knowledge about action feasibility is encoded in state-of-the-art models and how well they can reason about it.

This paper addresses the problem of dialogue reasoning with contextualized commonsense inference. We curate CICERO, a dataset of dyadic conversations with five types of utterance-level reasoning-based inferences: cause, subsequent event, prerequisite, motivation, and emotional reaction. The dataset contains 53,105 of such inferences from 5,672 dialogues. We use this dataset to solve relevant generative and discriminative tasks: generation of cause and subsequent event; generation of prerequisite, motivation, and listener's emotional reaction; and selection of plausible alternatives. Our results ascertain the value of such dialogue-centric commonsense knowledge datasets. It is our hope that CICERO will open new research avenues into commonsense-based dialogue reasoning.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Large Language Models (LLMs) have demonstrated remarkable performance in solving complex reasoning tasks through mechanisms like Chain-of-Thought (CoT) prompting, which emphasizes verbose, step-by-step reasoning. However, humans typically employ a more efficient strategy: drafting concise intermediate thoughts that capture only essential information. In this work, we propose Chain of Draft (CoD), a novel paradigm inspired by human cognitive processes, where LLMs generate minimalistic yet informative intermediate reasoning outputs while solving tasks. By reducing verbosity and focusing on critical insights, CoD matches or surpasses CoT in accuracy while using as little as only 7.6% of the tokens, significantly reducing cost and latency across various reasoning tasks.

Emergent chain-of-thought (CoT) reasoning capabilities promise to improve performance and explainability of large language models (LLMs). However, uncertainties remain about how reasoning strategies formulated for previous model generations generalize to new model generations and different datasets. In this small-scale study, we compare different reasoning strategies induced by zero-shot prompting across six recently released LLMs (davinci-002, davinci-003, GPT-3.5-turbo, GPT-4, Flan-T5-xxl and Cohere command-xlarge) on a mixture of six question-answering datasets, including datasets from scientific and medical domains. Our findings demonstrate that while some variations in effectiveness occur, gains from CoT reasoning strategies remain robust across different models and datasets. GPT-4 has the most benefit from current state-of-the-art reasoning strategies and exhibits the best performance by applying a prompt previously discovered through automated discovery.

Equipped with Chain-of-Thought (CoT), Large language models (LLMs) have shown impressive reasoning ability in various downstream tasks. Even so, suffering from hallucinations and the inability to access external knowledge, LLMs often come with incorrect or unfaithful intermediate reasoning steps, especially in the context of answering knowledge-intensive tasks such as KBQA. To alleviate this issue, we propose a framework called Knowledge-Driven Chain-of-Thought (KD-CoT) to verify and modify reasoning traces in CoT via interaction with external knowledge, and thus overcome the hallucinations and error propagation. Concretely, we formulate the CoT rationale process of LLMs into a structured multi-round QA format. In each round, LLMs interact with a QA system that retrieves external knowledge and produce faithful reasoning traces based on retrieved precise answers. The structured CoT reasoning of LLMs is facilitated by our developed KBQA CoT collection, which serves as in-context learning demonstrations and can also be utilized as feedback augmentation to train a robust retriever. Extensive experiments on WebQSP and ComplexWebQuestion datasets demonstrate the effectiveness of proposed KD-CoT in task-solving reasoning generation, which outperforms the vanilla CoT ICL with an absolute success rate of 8.0% and 5.1%. Furthermore, our proposed feedback-augmented retriever outperforms the state-of-the-art baselines for retrieving knowledge, achieving significant improvement in Hit performance.

Commonsense reasoning is a pivotal skill for large language models, yet it presents persistent challenges in specific tasks requiring this competence. Traditional fine-tuning approaches can be resource-intensive and potentially compromise a model's generalization capacity. Furthermore, state-of-the-art language models like GPT-3.5 and Claude are primarily accessible through API calls, which makes fine-tuning models challenging. To address these challenges, we draw inspiration from the outputs of large models for tailored tasks and semi-automatically developed a set of novel prompts from several perspectives, including task-relevance, supportive evidence generation (e.g. chain-of-thought and knowledge), diverse path decoding to aid the model. Experimental results on ProtoQA dataset demonstrate that with better designed prompts we can achieve the new state-of-art(SOTA) on the ProtoQA leaderboard, improving the Max Answer@1 score by 8%, Max Incorrect@1 score by 4% (breakthrough 50% for the first time) compared to the previous SOTA model and achieved an improvement on StrategyQA and CommonsenseQA2.0 (3% and 1%, respectively). Furthermore, with the generated Chain-of-Thought and knowledge, we can improve the interpretability of the model while also surpassing the previous SOTA models. We hope that our work can provide insight for the NLP community to develop better prompts and explore the potential of large language models for more complex reasoning tasks.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

As large language models (LLMs) perform more difficult tasks, it becomes harder to verify the correctness and safety of their behavior. One approach to help with this issue is to prompt LLMs to externalize their reasoning, e.g., by having them generate step-by-step reasoning as they answer a question (Chain-of-Thought; CoT). The reasoning may enable us to check the process that models use to perform tasks. However, this approach relies on the stated reasoning faithfully reflecting the model's actual reasoning, which is not always the case. To improve over the faithfulness of CoT reasoning, we have models generate reasoning by decomposing questions into subquestions. Decomposition-based methods achieve strong performance on question-answering tasks, sometimes approaching that of CoT while improving the faithfulness of the model's stated reasoning on several recently-proposed metrics. By forcing the model to answer simpler subquestions in separate contexts, we greatly increase the faithfulness of model-generated reasoning over CoT, while still achieving some of the performance gains of CoT. Our results show it is possible to improve the faithfulness of model-generated reasoning; continued improvements may lead to reasoning that enables us to verify the correctness and safety of LLM behavior.

While Large Language Models (LLMs) have demonstrated their proficiency in complex reasoning tasks, their performance in dynamic, interactive, and competitive scenarios - such as business strategy and stock market analysis - remains underexplored. To bridge this gap, we formally explore the dynamic reasoning capabilities of LLMs for decision-making in rapidly evolving environments. We introduce two game theory-based pilot challenges that mirror the complexities of real-world dynamic decision-making. These challenges are well-defined, enabling clear, controllable, and precise evaluation of LLMs' dynamic reasoning abilities. Through extensive experiments, we find that existing reasoning methods tend to falter in dynamic settings that require k-level thinking - a key concept not tackled by previous works. To address this, we propose a novel reasoning approach for LLMs, named "K-Level Reasoning". This approach adopts the perspective of rivals to recursively employ k-level thinking based on available historical information, which significantly improves the prediction accuracy of rivals' subsequent moves and informs more strategic decision-making. This research not only sets a robust quantitative benchmark for the assessment of dynamic reasoning but also markedly enhances the proficiency of LLMs in dynamic contexts.

The concept of Artificial Intelligence has gained a lot of attention over the last decade. In particular, AI-based tools have been employed in several scenarios and are, by now, pervading our everyday life. Nonetheless, most of these systems lack many capabilities that we would naturally consider to be included in a notion of "intelligence". In this work, we present an architecture that, inspired by the cognitive theory known as Thinking Fast and Slow by D. Kahneman, is tasked with solving planning problems in different settings, specifically: classical and multi-agent epistemic. The system proposed is an instance of a more general AI paradigm, referred to as SOFAI (for Slow and Fast AI). SOFAI exploits multiple solving approaches, with different capabilities that characterize them as either fast or slow, and a metacognitive module to regulate them. This combination of components, which roughly reflects the human reasoning process according to D. Kahneman, allowed us to enhance the reasoning process that, in this case, is concerned with planning in two different settings. The behavior of this system is then compared to state-of-the-art solvers, showing that the newly introduced system presents better results in terms of generality, solving a wider set of problems with an acceptable trade-off between solving times and solution accuracy.

Chain-of-thought prompting combined with pre-trained large language models has achieved encouraging results on complex reasoning tasks. In this paper, we propose a new decoding strategy, self-consistency, to replace the naive greedy decoding used in chain-of-thought prompting. It first samples a diverse set of reasoning paths instead of only taking the greedy one, and then selects the most consistent answer by marginalizing out the sampled reasoning paths. Self-consistency leverages the intuition that a complex reasoning problem typically admits multiple different ways of thinking leading to its unique correct answer. Our extensive empirical evaluation shows that self-consistency boosts the performance of chain-of-thought prompting with a striking margin on a range of popular arithmetic and commonsense reasoning benchmarks, including GSM8K (+17.9%), SVAMP (+11.0%), AQuA (+12.2%), StrategyQA (+6.4%) and ARC-challenge (+3.9%).

Recently, large-scale pre-trained language models have demonstrated impressive performance on several commonsense-reasoning benchmark datasets. However, building machines with commonsense to compose realistically plausible sentences remains challenging. In this paper, we present a constrained text generation task, CommonGen associated with a benchmark dataset, to explicitly test machines for the ability of generative commonsense reasoning. Given a set of common concepts (e.g., {dog, frisbee, catch, throw}); the task is to generate a coherent sentence describing an everyday scenario using these concepts (e.g., "a man throws a frisbee and his dog catches it"). The CommonGen task is challenging because it inherently requires 1) relational reasoning with background commonsense knowledge, and 2) compositional generalization ability to work on unseen concept combinations. Our dataset, constructed through a combination of crowdsourced and existing caption corpora, consists of 79k commonsense descriptions over 35k unique concept-sets. Experiments show that there is a large gap between state-of-the-art text generation models (e.g., T5) and human performance. Furthermore, we demonstrate that the learned generative commonsense reasoning capability can be transferred to improve downstream tasks such as CommonsenseQA by generating additional context.

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations (or ``chain-of-thought'' (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for symbolic programming. To make progress towards understanding in-context learning, we curate synthetic datasets containing equivalent (natural, symbolic) data pairs, where symbolic examples contain first-order logic rules and predicates from knowledge bases (KBs). Then we revisit neuro-symbolic approaches and use Language Models as Logic Programmer (LMLP) that learns from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs, recovering Prolog's backward chaining algorithm. Comprehensive experiments are included to systematically compare LMLP with CoT in deductive reasoning settings, showing that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks even with fewer parameters.

We propose a novel framework, Meta Chain-of-Thought (Meta-CoT), which extends traditional Chain-of-Thought (CoT) by explicitly modeling the underlying reasoning required to arrive at a particular CoT. We present empirical evidence from state-of-the-art models exhibiting behaviors consistent with in-context search, and explore methods for producing Meta-CoT via process supervision, synthetic data generation, and search algorithms. Finally, we outline a concrete pipeline for training a model to produce Meta-CoTs, incorporating instruction tuning with linearized search traces and reinforcement learning post-training. Finally, we discuss open research questions, including scaling laws, verifier roles, and the potential for discovering novel reasoning algorithms. This work provides a theoretical and practical roadmap to enable Meta-CoT in LLMs, paving the way for more powerful and human-like reasoning in artificial intelligence.

Commonsense reasoning is a critical AI capability, but it is difficult to construct challenging datasets that test common sense. Recent neural question answering systems, based on large pre-trained models of language, have already achieved near-human-level performance on commonsense knowledge benchmarks. These systems do not possess human-level common sense, but are able to exploit limitations of the datasets to achieve human-level scores. We introduce the CODAH dataset, an adversarially-constructed evaluation dataset for testing common sense. CODAH forms a challenging extension to the recently-proposed SWAG dataset, which tests commonsense knowledge using sentence-completion questions that describe situations observed in video. To produce a more difficult dataset, we introduce a novel procedure for question acquisition in which workers author questions designed to target weaknesses of state-of-the-art neural question answering systems. Workers are rewarded for submissions that models fail to answer correctly both before and after fine-tuning (in cross-validation). We create 2.8k questions via this procedure and evaluate the performance of multiple state-of-the-art question answering systems on our dataset. We observe a significant gap between human performance, which is 95.3%, and the performance of the best baseline accuracy of 67.5% by the BERT-Large model.

Scaling up language models to billions of parameters has opened up possibilities for in-context learning, allowing instruction tuning and few-shot learning on tasks that the model was not specifically trained for. This has achieved breakthrough performance on language tasks such as translation, summarization, and question-answering. Furthermore, in addition to these associative "System 1" tasks, recent advances in Chain-of-thought prompt learning have demonstrated strong "System 2" reasoning abilities, answering a question in the field of artificial general intelligence whether LLMs can reason. The field started with the question whether LLMs can solve grade school math word problems. This paper reviews the rapidly expanding field of prompt-based reasoning with LLMs. Our taxonomy identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. Finally, we highlight the relation between reasoning and prompt-based learning, and we discuss the relation between reasoning, sequential decision processes, and reinforcement learning. We find that self-improvement, self-reflection, and some metacognitive abilities of the reasoning processes are possible through the judicious use of prompts. True self-improvement and self-reasoning, to go from reasoning with LLMs to reasoning by LLMs, remains future work.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Existing agents based on large language models (LLMs) demonstrate robust problem-solving capabilities by integrating LLMs' inherent knowledge, strong in-context learning and zero-shot capabilities, and the use of tools combined with intricately designed LLM invocation workflows by humans. However, these agents still exhibit shortcomings in long-term reasoning and under-use the potential of existing tools, leading to noticeable deficiencies in complex real-world reasoning scenarios. To address these limitations, we introduce Sibyl, a simple yet powerful LLM-based agent framework designed to tackle complex reasoning tasks by efficiently leveraging a minimal set of tools. Drawing inspiration from Global Workspace Theory, Sibyl incorporates a global workspace to enhance the management and sharing of knowledge and conversation history throughout the system. Furthermore, guided by Society of Mind Theory, Sibyl implements a multi-agent debate-based jury to self-refine the final answers, ensuring a comprehensive and balanced approach. This approach aims to reduce system complexity while expanding the scope of problems solvable-from matters typically resolved by humans in minutes to those requiring hours or even days, thus facilitating a shift from System-1 to System-2 thinking. Sibyl has been designed with a focus on scalability and ease of debugging by incorporating the concept of reentrancy from functional programming from its inception, with the aim of seamless and low effort integration in other LLM applications to improve capabilities. Our experimental results on the GAIA benchmark test set reveal that the Sibyl agent instantiated with GPT-4 achieves state-of-the-art performance with an average score of 34.55%, compared to other agents based on GPT-4. We hope that Sibyl can inspire more reliable and reusable LLM-based agent solutions to address complex real-world reasoning tasks.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Recent advancements in the field of large language models, particularly through the Chain of Thought (CoT) approach, have demonstrated significant improvements in solving complex problems. However, existing models either tend to sacrifice detailed reasoning for brevity due to user preferences, or require extensive and expensive training data to learn complicated reasoning ability, limiting their potential in solving complex tasks. To bridge this gap, following the concept of scaling test-time, we propose a simple method by encouraging models to adopt a more patient reasoning style without the need of introducing new knowledge or skills. To employ a preference optimization approach, we generate detailed reasoning processes as positive examples and simple answers as negative examples, thereby training the model to favor thoroughness in its responses. Our results demonstrate a performance increase of up to 6.7% on GSM8k with training just on a lightweight dataset.

Most benchmark datasets targeting commonsense reasoning focus on everyday scenarios: physical knowledge like knowing that you could fill a cup under a waterfall [Talmor et al., 2019], social knowledge like bumping into someone is awkward [Sap et al., 2019], and other generic situations. However, there is a rich space of commonsense inferences anchored to knowledge about specific entities: for example, deciding the truthfulness of a claim "Harry Potter can teach classes on how to fly on a broomstick." Can models learn to combine entity knowledge with commonsense reasoning in this fashion? We introduce CREAK, a testbed for commonsense reasoning about entity knowledge, bridging fact-checking about entities (Harry Potter is a wizard and is skilled at riding a broomstick) with commonsense inferences (if you're good at a skill you can teach others how to do it). Our dataset consists of 13k human-authored English claims about entities that are either true or false, in addition to a small contrast set. Crowdworkers can easily come up with these statements and human performance on the dataset is high (high 90s); we argue that models should be able to blend entity knowledge and commonsense reasoning to do well here. In our experiments, we focus on the closed-book setting and observe that a baseline model finetuned on existing fact verification benchmark struggles on CREAK. Training a model on CREAK improves accuracy by a substantial margin, but still falls short of human performance. Our benchmark provides a unique probe into natural language understanding models, testing both its ability to retrieve facts (e.g., who teaches at the University of Chicago?) and unstated commonsense knowledge (e.g., butlers do not yell at guests).

Chain-of-Thought (CoT) prompting has marked a significant advancement in enhancing the reasoning capabilities of large language models (LLMs). Previous studies have developed various extensions of CoT, which focus primarily on enhancing end-task performance. In addition, there has been research on assessing the quality of reasoning chains in CoT. This raises an intriguing question: Is it possible to predict the accuracy of LLM outputs by scrutinizing the reasoning chains they generate? To answer this research question, we introduce a benchmark, R2PE, designed specifically to explore the relationship between reasoning chains and performance in various reasoning tasks spanning five different domains. This benchmark aims to measure the falsehood of the final output of LLMs based on the reasoning steps. To make full use of information in multiple reasoning chains, we propose the process discernibility score (PDS) framework that beats the answer-checking baseline by a large margin. Concretely, this resulted in an average of 5.1% increase in the F1 score across all 45 subsets within R2PE. We further demonstrate our PDS's efficacy in advancing open-domain QA accuracy. Data and code are available at https://github.com/XinXU-USTC/R2PE.

Relational reasoning is a central component of generally intelligent behavior, but has proven difficult for neural networks to learn. In this paper we describe how to use Relation Networks (RNs) as a simple plug-and-play module to solve problems that fundamentally hinge on relational reasoning. We tested RN-augmented networks on three tasks: visual question answering using a challenging dataset called CLEVR, on which we achieve state-of-the-art, super-human performance; text-based question answering using the bAbI suite of tasks; and complex reasoning about dynamic physical systems. Then, using a curated dataset called Sort-of-CLEVR we show that powerful convolutional networks do not have a general capacity to solve relational questions, but can gain this capacity when augmented with RNs. Our work shows how a deep learning architecture equipped with an RN module can implicitly discover and learn to reason about entities and their relations.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Mastering commonsense understanding and reasoning is a pivotal skill essential for conducting engaging conversations. While there have been several attempts to create datasets that facilitate commonsense inferences in dialogue contexts, existing datasets tend to lack in-depth details, restate information already present in the conversation, and often fail to capture the multifaceted nature of commonsense reasoning. In response to these limitations, we compile a new synthetic dataset for commonsense reasoning in dialogue contexts using GPT, ConvoSense, that boasts greater contextual novelty, offers a higher volume of inferences per example, and substantially enriches the detail conveyed by the inferences. Our dataset contains over 500,000 inferences across 12,000 dialogues with 10 popular inference types, which empowers the training of generative commonsense models for dialogue that are superior in producing plausible inferences with high novelty when compared to models trained on the previous datasets. To the best of our knowledge, ConvoSense is the first of its kind to provide such a multitude of novel inferences at such a large scale.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in large language models (LLMs). We observe that CoT shares significant similarities with self-training in terms of their learning processes. Motivated by these parallels, this paper explores the underlying relationship between CoT and self-training, demonstrating how insights from self-training can enhance CoT performance. Specifically, our study first reveals that CoT, like self-training, follows the principle of semantic entropy minimization. Leveraging this insight, we propose a novel CoT framework that incorporates two key components: (i) a task-specific prompt module designed to guide LLMs in generating high-quality initial reasoning processes, and (ii) an adaptive reasoning iteration module for progressively refining the reasoning process.

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments through game-theoretic tasks, e.g., board and card games that require pure logic and strategic reasoning to compete with opponents. We first propose GTBench, a language-driven environment composing 10 widely-recognized tasks, across a comprehensive game taxonomy: complete versus incomplete information, dynamic versus static, and probabilistic versus deterministic scenarios. Then, we investigate two key problems: (1) Characterizing game-theoretic reasoning of LLMs; (2) LLM-vs-LLM competitions as reasoning evaluation. We observe that (1) LLMs have distinct behaviors regarding various gaming scenarios; for example, LLMs fail in complete and deterministic games yet they are competitive in probabilistic gaming scenarios; (2) Open-source LLMs, e.g., CodeLlama-34b-Instruct, are less competitive than commercial LLMs, e.g., GPT-4, in complex games. In addition, code-pretraining greatly benefits strategic reasoning, while advanced reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) do not always help. Detailed error profiles are also provided for a better understanding of LLMs' behavior.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

A computational ethics framework is essential for AI and autonomous systems operating in complex, real-world environments. Existing approaches often lack the adaptability needed to integrate ethical principles into dynamic and ambiguous contexts, limiting their effectiveness across diverse scenarios. To address these challenges, we outline the necessary ingredients for building a holistic, meta-level framework that combines intermediate representations, probabilistic reasoning, and knowledge representation. The specifications therein emphasize scalability, supporting ethical reasoning at both individual decision-making levels and within the collective dynamics of multi-agent systems. By integrating theoretical principles with contextual factors, it facilitates structured and context-aware decision-making, ensuring alignment with overarching ethical standards. We further explore proposed theorems outlining how ethical reasoners should operate, offering a foundation for practical implementation. These constructs aim to support the development of robust and ethically reliable AI systems capable of navigating the complexities of real-world moral decision-making scenarios.

Large Language Models, such as Generative Pre-trained Transformer 3 (aka. GPT-3), have been developed to understand language through the analysis of extensive text data, allowing them to identify patterns and connections between words. While LLMs have demonstrated impressive performance across various text-related tasks, they encounter challenges in tasks associated with reasoning. To address this challenge, Chain of Thought(CoT) prompting method has been proposed as a means to enhance LLMs' proficiency in complex reasoning tasks like solving math word problems and answering questions based on logical argumentative reasoning. The primary aim of this research is to assess how well four language models can grade reflective essays of third-year medical students. The assessment will specifically target the evaluation of critical thinking skills using CoT prompting. The research will provide the following contributions; to introduce and educate on the process of instructing models to evaluate reflective essays from a dataset they have not been previously trained on; to illustrate the use of CoT prompting as an instructional approach for training large models to carry out particular tasks. Our results suggest that among all the models, Llama-7b performs the least effectively, displaying the highest mean squared error. Conversely, ChatGPT emerges as the superior model, boasting a higher Cohen kappa score value of 0.53. Lastly, it's important to note that the selected models do prioritise user privacy by allowing users to delete their own conducted conversations.

Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as self-consistency, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose self-agreement, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model's decoder to generate a diverse set of reasoning paths, and subsequently prompts the language model one more time to determine the optimal answer by selecting the most agreed answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.

We introduce Agentic Reasoning, a framework that enhances large language model (LLM) reasoning by integrating external tool-using agents. Unlike conventional LLM-based reasoning approaches, which rely solely on internal inference, Agentic Reasoning dynamically engages web search, code execution, and structured reasoning-context memory to solve complex problems requiring deep research and multi-step logical deduction. Our framework introduces the Mind Map agent, which constructs a structured knowledge graph to track logical relationships, improving deductive reasoning. Additionally, the integration of web-search and coding agents enables real-time retrieval and computational analysis, enhancing reasoning accuracy and decision-making. Evaluations on PhD-level scientific reasoning (GPQA) and domain-specific deep research tasks demonstrate that our approach significantly outperforms existing models, including leading retrieval-augmented generation (RAG) systems and closed-source LLMs. Moreover, our results indicate that agentic reasoning improves expert-level knowledge synthesis, test-time scalability, and structured problem-solving. The code is at: https://github.com/theworldofagents/Agentic-Reasoning.

Chain-of-Thought (CoT) prompting has proven to be effective in enhancing the reasoning capabilities of Large Language Models (LLMs) with at least 100 billion parameters. However, it is ineffective or even detrimental when applied to reasoning tasks in Smaller Language Models (SLMs) with less than 10 billion parameters. To address this limitation, we introduce Dialogue-guided Chain-of-Thought (DialCoT) which employs a dialogue format to generate intermediate reasoning steps, guiding the model toward the final answer. Additionally, we optimize the model's reasoning path selection using the Proximal Policy Optimization (PPO) algorithm, further enhancing its reasoning capabilities. Our method offers several advantages compared to previous approaches. Firstly, we transform the process of solving complex reasoning questions by breaking them down into a series of simpler sub-questions, significantly reducing the task difficulty and making it more suitable for SLMs. Secondly, we optimize the model's reasoning path selection through the PPO algorithm. We conduct comprehensive experiments on four arithmetic reasoning datasets, demonstrating that our method achieves significant performance improvements compared to state-of-the-art competitors.

How does language inform our downstream thinking? In particular, how do humans make meaning from language -- and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose rational meaning construction, a computational framework for language-informed thinking that combines neural models of language with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a probabilistic language of thought (PLoT) -- a general-purpose symbolic substrate for probabilistic, generative world modeling. Our architecture integrates two powerful computational tools that have not previously come together: we model thinking with probabilistic programs, an expressive representation for flexible commonsense reasoning; and we model meaning construction with large language models (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework in action through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning about agents and their plans. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves.

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to embed entities in vector space for logical query operations, but they suffer from subpar performance on complex queries and dataset-specific representations. In this paper, we propose a novel decoupled approach, Language-guided Abstract Reasoning over Knowledge graphs (LARK), that formulates complex KG reasoning as a combination of contextual KG search and logical query reasoning, to leverage the strengths of graph extraction algorithms and large language models (LLM), respectively. Our experiments demonstrate that the proposed approach outperforms state-of-the-art KG reasoning methods on standard benchmark datasets across several logical query constructs, with significant performance gain for queries of higher complexity. Furthermore, we show that the performance of our approach improves proportionally to the increase in size of the underlying LLM, enabling the integration of the latest advancements in LLMs for logical reasoning over KGs. Our work presents a new direction for addressing the challenges of complex KG reasoning and paves the way for future research in this area.

Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Large Language Models (LLMs) have recently made significant strides in complex reasoning tasks through the Chain-of-Thought technique. Despite this progress, their reasoning is often constrained by their intrinsic understanding, lacking external insights. To address this, we propose Exchange-of-Thought (EoT), a novel framework that enables cross-model communication during problem-solving. Drawing inspiration from network topology, EoT integrates four unique communication paradigms: Memory, Report, Relay, and Debate. This paper delves into the communication dynamics and volume associated with each paradigm. To counterbalance the risks of incorrect reasoning chains, we implement a robust confidence evaluation mechanism within these communications. Our experiments across diverse complex reasoning tasks demonstrate that EoT significantly surpasses established baselines, underscoring the value of external insights in enhancing LLM performance. Furthermore, we show that EoT achieves these superior results in a cost-effective manner, marking a promising advancement for efficient and collaborative AI problem-solving.

In this paper, we propose the use of the popular word-based board game Codenames as a suitable benchmark for evaluating the reasoning capabilities of Large Language Models (LLMs). Codenames presents a highly interesting challenge for achieving successful AI performance, requiring both a sophisticated understanding of language, theory of mind, and epistemic reasoning capabilities. Prior attempts to develop agents for Codenames have largely relied on word embedding techniques, which have a limited vocabulary range and perform poorly when paired with differing approaches. LLMs have demonstrated enhanced reasoning and comprehension capabilities for language-based tasks, but can still suffer in lateral thinking challenges. We evaluate the capabilities of several state-of-the-art LLMs, including GPT-4o, Gemini 1.5, Claude 3.5 Sonnet, and Llama 3.1, across a variety of board setups. Our results indicate that while certain LLMs perform better than others overall, different models exhibit varying emergent behaviours during gameplay and excel at specific roles. We also evaluate the performance of different combinations of LLMs when playing cooperatively together, demonstrating that LLM agents are more generalisable to a wider range of teammates than prior techniques.

To optimally coordinate with others in cooperative games, it is often crucial to have information about one's collaborators: successful driving requires understanding which side of the road to drive on. However, not every feature of collaborators is strategically relevant: the fine-grained acceleration of drivers may be ignored while maintaining optimal coordination. We show that there is a well-defined dichotomy between strategically relevant and irrelevant information. Moreover, we show that, in dynamic games, this dichotomy has a compact representation that can be efficiently computed via a Bellman backup operator. We apply this algorithm to analyze the strategically relevant information for tasks in both a standard and a partially observable version of the Overcooked environment. Theoretical and empirical results show that our algorithms are significantly more efficient than baselines. Videos are available at https://minknowledge.github.io.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a quantitative meta-analysis covering over 100 papers using CoT and ran our own evaluations of 20 datasets across 14 models. Our results show that CoT gives strong performance benefits primarily on tasks involving math or logic, with much smaller gains on other types of tasks. On MMLU, directly generating the answer without CoT leads to almost identical accuracy as CoT unless the question or model's response contains an equals sign, indicating symbolic operations and reasoning. Following this finding, we analyze the behavior of CoT on these problems by separating planning and execution and comparing against tool-augmented LLMs. Much of CoT's gain comes from improving symbolic execution, but it underperforms relative to using a symbolic solver. Our results indicate that CoT can be applied selectively, maintaining performance while saving inference costs. Furthermore, they suggest a need to move beyond prompt-based CoT to new paradigms that better leverage intermediate computation across the whole range of LLM applications.

Chain-of-thought prompting (CoT) advances the reasoning abilities of large language models (LLMs) and achieves superior performance in arithmetic, commonsense, and symbolic reasoning tasks. However, most CoT studies rely on carefully designed human-annotated rational chains to prompt the language model, which poses challenges for real-world applications where labeled training data is available without human-annotated rational chains. This creates barriers to applications of CoT prompting to these general tasks. This paper proposes a new strategy, Automate-CoT (Automatic Prompt Augmentation and Selection with Chain-of-Thought), that can bypass human engineering of CoTs by automatically augmenting rational chains from a small labeled dataset, and then pruning low-quality chains to construct a candidate pool of machine-generated rationale chains based on the labels. Finally, it selects the optimal combination of several rationale chains from the pool for CoT prompting by employing a variance-reduced policy gradient strategy to estimate the significance of each example in a black-box language model. Automate-CoT enables a quick adaptation of the CoT technique to different tasks. Experimental results demonstrate the effectiveness of our method, where state-of-the-art results are achieved on arithmetic reasoning (+2.7\%), commonsense reasoning (+3.4\%), symbolic reasoning (+3.2\%), and non-reasoning tasks (+2.5\%). Our code will be available at https://github.com/shizhediao/automate-cot.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

It is a common practice for recent works in vision language cross-modal reasoning to adopt a binary or multi-choice classification formulation taking as input a set of source image(s) and textual query. In this work, we take a sober look at such an unconditional formulation in the sense that no prior knowledge is specified with respect to the source image(s). Inspired by the designs of both visual commonsense reasoning and natural language inference tasks, we propose a new task termed Premise-based Multi-modal Reasoning(PMR) where a textual premise is the background presumption on each source image. The PMR dataset contains 15,360 manually annotated samples which are created by a multi-phase crowd-sourcing process. With selected high-quality movie screenshots and human-curated premise templates from 6 pre-defined categories, we ask crowd-source workers to write one true hypothesis and three distractors (4 choices) given the premise and image through a cross-check procedure. Besides, we generate adversarial samples to alleviate the annotation artifacts and double the size of PMR. We benchmark various state-of-the-art (pretrained) multi-modal inference models on PMR and conduct comprehensive experimental analyses to showcase the utility of our dataset.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Large Language Models (LLMs) have shown outstanding performance across wide range of downstream tasks. This competency is attributed to their substantial parameter size and pre-training on extensive corpus. Moreover, LLMs have exhibited enhanced reasoning capabilities in tackling complex reasoning tasks, owing to the utilization of a method named ``Chain-of-Thought (CoT) prompting''. This method is designed to generate intermediate reasoning steps that guide the inference of the final answer. However, it is essential to highlight that these advanced reasoning abilities appear to emerge in models with a minimum of 10 billion parameters, thereby limiting its efficacy in situations where computational resources are constrained. In this paper, we investigate the possibility of transferring the reasoning capabilities of LLMs to smaller models via knowledge distillation. Specifically, we propose Sci-CoT, a two-stage framework that separates the processes of generating rationales and inferring answers. This method enables a more efficient use of rationales during the answer inference stage, leading to improved performance on scientific question-answering tasks. Utilizing Sci-CoT, our 80-million parameter model is able to exceed the performance of BLOOM-176B in the ARC-Easy dataset under the few shot setting.

As AI systems pervade human life, ensuring that large language models (LLMs) make safe decisions remains a significant challenge. We introduce the Governance of the Commons Simulation (GovSim), a generative simulation platform designed to study strategic interactions and cooperative decision-making in LLMs. In GovSim, a society of AI agents must collectively balance exploiting a common resource with sustaining it for future use. This environment enables the study of how ethical considerations, strategic planning, and negotiation skills impact cooperative outcomes. We develop an LLM-based agent architecture and test it with the leading open and closed LLMs. We find that all but the most powerful LLM agents fail to achieve a sustainable equilibrium in GovSim, with the highest survival rate below 54%. Ablations reveal that successful multi-agent communication between agents is critical for achieving cooperation in these cases. Furthermore, our analyses show that the failure to achieve sustainable cooperation in most LLMs stems from their inability to formulate and analyze hypotheses about the long-term effects of their actions on the equilibrium of the group. Finally, we show that agents that leverage "Universalization"-based reasoning, a theory of moral thinking, are able to achieve significantly better sustainability. Taken together, GovSim enables us to study the mechanisms that underlie sustainable self-government with specificity and scale. We open source the full suite of our research results, including the simulation environment, agent prompts, and a comprehensive web interface.

The reasoning segmentation task, which demands a nuanced comprehension of intricate queries to accurately pinpoint object regions, is attracting increasing attention. However, Multi-modal Large Language Models (MLLM) often find it difficult to accurately localize the objects described in complex reasoning contexts. We believe that the act of reasoning segmentation should mirror the cognitive stages of human visual search, where each step is a progressive refinement of thought toward the final object. Thus we introduce the Chains of Reasoning and Segmenting (CoReS) and find this top-down visual hierarchy indeed enhances the visual search process. Specifically, we propose a dual-chain structure that generates multi-modal, chain-like outputs to aid the segmentation process. Furthermore, to steer the MLLM's outputs into this intended hierarchy, we incorporate in-context inputs as guidance. Extensive experiments demonstrate the superior performance of our CoReS, which surpasses the state-of-the-art method by 6.5\% on the ReasonSeg dataset. Project: https://chain-of-reasoning-and-segmentation.github.io/.

Large Language Models (LLMs) have demonstrated significant potential in handling complex reasoning tasks through step-by-step rationale generation. However, recent studies have raised concerns regarding the hallucination and flaws in their reasoning process. Substantial efforts are being made to improve the reliability and faithfulness of the generated rationales. Some approaches model reasoning as planning, while others focus on annotating for process supervision. Nevertheless, the planning-based search process often results in high latency due to the frequent assessment of intermediate reasoning states and the extensive exploration space. Additionally, supervising the reasoning process with human annotation is costly and challenging to scale for LLM training. To address these issues, in this paper, we propose a framework to learn planning-based reasoning through direct preference optimization (DPO) on collected trajectories, which are ranked according to synthesized process rewards. Our results on challenging logical reasoning benchmarks demonstrate the effectiveness of our learning framework, showing that our 7B model can surpass the strong counterparts like GPT-3.5-Turbo.

Recent advances in large language models have demonstrated remarkable reasoning capabilities through Chain of Thought (CoT) prompting, but often at the cost of excessive verbosity in their intermediate outputs, which increases computational overhead. We introduce Sketch-of-Thought (SoT), a novel prompting framework that combines cognitive-inspired reasoning paradigms with linguistic constraints to minimize token usage while preserving reasoning accuracy. SoT is designed as a flexible framework that can incorporate any custom reasoning paradigms based on cognitive science, and we instantiate it with three such paradigms - Conceptual Chaining, Chunked Symbolism, and Expert Lexicons - each tailored to different reasoning tasks and selected dynamically via a lightweight routing model. Through comprehensive evaluation across 15 reasoning datasets with multiple languages and multimodal scenarios, we demonstrate that SoT achieves token reductions of 76% with negligible accuracy impact. In certain domains like mathematical and multi-hop reasoning, it even improves accuracy while using significantly fewer tokens. Our code is publicly available: https://www.github.com/SimonAytes/SoT.

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields diminishing performance improvements and heavy computational costs. Recently, OpenAI's o1 model has shown that inference strategies (i.e., Test-time Compute methods) can also significantly enhance the reasoning capabilities of LLMs. However, the mechanisms behind these methods are still unexplored. In our work, to investigate the reasoning patterns of o1, we compare o1 with existing Test-time Compute methods (BoN, Step-wise BoN, Agent Workflow, and Self-Refine) by using OpenAI's GPT-4o as a backbone on general reasoning benchmarks in three domains (i.e., math, coding, commonsense reasoning). Specifically, first, our experiments show that the o1 model has achieved the best performance on most datasets. Second, as for the methods of searching diverse responses (e.g., BoN), we find the reward models' capability and the search space both limit the upper boundary of these methods. Third, as for the methods that break the problem into many sub-problems, the Agent Workflow has achieved better performance than Step-wise BoN due to the domain-specific system prompt for planning better reasoning processes. Fourth, it is worth mentioning that we have summarized six reasoning patterns of o1, and provided a detailed analysis on several reasoning benchmarks.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Generative commonsense reasoning (GCR) in natural language is to reason about the commonsense while generating coherent text. Recent years have seen a surge of interest in improving the generation quality of commonsense reasoning tasks. Nevertheless, these approaches have seldom investigated diversity in the GCR tasks, which aims to generate alternative explanations for a real-world situation or predict all possible outcomes. Diversifying GCR is challenging as it expects to generate multiple outputs that are not only semantically different but also grounded in commonsense knowledge. In this paper, we propose MoKGE, a novel method that diversifies the generative reasoning by a mixture of expert (MoE) strategy on commonsense knowledge graphs (KG). A set of knowledge experts seek diverse reasoning on KG to encourage various generation outputs. Empirical experiments demonstrated that MoKGE can significantly improve the diversity while achieving on par performance on accuracy on two GCR benchmarks, based on both automatic and human evaluations.

Large language models (LLMs) have exhibited complex reasoning abilities by generating question rationales and demonstrated exceptional performance in natural language processing (NLP) tasks. However, these reasoning capabilities generally emerge in models with tens of billions of parameters, creating significant computational challenges for real-world deployment. Recent research has concentrated on improving open-source smaller models through knowledge distillation (KD) from commercial LLMs. Nevertheless, most of these studies rely solely on the responses from one single LLM as the gold rationale for training. In this paper, we introduce a novel Mistake-Aware Peer-Review Distillation (MAPD) approach: 1) Instead of merely obtaining gold rationales from teachers, our method asks teachers to identify and explain the student's mistakes, providing customized instruction learning data. 2) We design a simulated peer-review process between teacher LLMs, which selects only the generated rationales above the acceptance threshold. This reduces the chance of teachers guessing correctly with flawed rationale, improving instructional data quality. Comprehensive experiments and analysis on mathematical, commonsense, and logical reasoning tasks demonstrate the effectiveness of our method.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified mathematical reasoning benchmark consisting of 23 diverse tasks along four dimensions: (i) mathematical abilities e.g., arithmetic, calculus (ii) language format e.g., question-answering, fill-in-the-blanks (iii) language diversity e.g., no language, simple language (iv) external knowledge e.g., commonsense, physics. We construct our benchmark by extending 20 datasets benchmark by collecting task instructions and solutions in the form of Python programs, thereby obtaining explainable solutions in addition to the correct answer. We additionally introduce two evaluation datasets to measure out-of-distribution performance and robustness to language perturbation. Finally, we introduce BHASKARA, a general-purpose mathematical reasoning model trained on LILA. Importantly, we find that multi-tasking leads to significant improvements (average relative improvement of 21.83% F1 score vs. single-task models), while the best performing model only obtains 60.40%, indicating the room for improvement in general mathematical reasoning and understanding.

The emergent few-shot reasoning capabilities of Large Language Models (LLMs) have excited the natural language and machine learning community over recent years. Despite of numerous successful applications, the underlying mechanism of such in-context capabilities still remains unclear. In this work, we hypothesize that the learned semantics of language tokens do the most heavy lifting during the reasoning process. Different from human's symbolic reasoning process, the semantic representations of LLMs could create strong connections among tokens, thus composing a superficial logical chain. To test our hypothesis, we decouple semantics from the language reasoning process and evaluate three kinds of reasoning abilities, i.e., deduction, induction and abduction. Our findings reveal that semantics play a vital role in LLMs' in-context reasoning -- LLMs perform significantly better when semantics are consistent with commonsense but struggle to solve symbolic or counter-commonsense reasoning tasks by leveraging in-context new knowledge. The surprising observations question whether modern LLMs have mastered the inductive, deductive and abductive reasoning abilities as in human intelligence, and motivate research on unveiling the magic existing within the black-box LLMs. On the whole, our analysis provides a novel perspective on the role of semantics in developing and evaluating language models' reasoning abilities. Code is available at {https://github.com/XiaojuanTang/ICSR}.

We present a Conversational Chain-of-Action (Conv-CoA) framework for Open-domain Conversational Question Answering (OCQA). Compared with literature, Conv-CoA addresses three major challenges: (i) unfaithful hallucination that is inconsistent with real-time or domain facts, (ii) weak reasoning performance in conversational scenarios, and (iii) unsatisfying performance in conversational information retrieval. Our key contribution is a dynamic reasoning-retrieval mechanism that extracts the intent of the question and decomposes it into a reasoning chain to be solved via systematic prompting, pre-designed actions, updating the Contextual Knowledge Set (CKS), and a novel Hopfield-based retriever. Methodologically, we propose a resource-efficiency Hopfield retriever to enhance the efficiency and accuracy of conversational information retrieval within our actions. Additionally, we propose a conversational-multi-reference faith score (Conv-MRFS) to verify and resolve conflicts between retrieved knowledge and answers in conversations. Empirically, we conduct comparisons between our framework and 23 state-of-the-art methods across five different research directions and two public benchmarks. These comparisons demonstrate that our Conv-CoA outperforms other methods in both the accuracy and efficiency dimensions.

Existing LLMs exhibit remarkable performance on various NLP tasks, but still struggle with complex real-world tasks, even equipped with advanced strategies like CoT and ReAct. In this work, we propose the CoAct framework, which transfers the hierarchical planning and collaboration patterns in human society to LLM systems. Specifically, our CoAct framework involves two agents: (1) A global planning agent, to comprehend the problem scope, formulate macro-level plans and provide detailed sub-task descriptions to local execution agents, which serves as the initial rendition of a global plan. (2) A local execution agent, to operate within the multi-tier task execution structure, focusing on detailed execution and implementation of specific tasks within the global plan. Experimental results on the WebArena benchmark show that CoAct can re-arrange the process trajectory when facing failures, and achieves superior performance over baseline methods on long-horizon web tasks. Code is available at https://github.com/xmhou2002/CoAct.

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Large Language Models (LLMs) have recently demonstrated exceptional performance in various Natural Language Processing (NLP) tasks. They have also shown the ability to perform chain-of-thought (CoT) reasoning to solve complex problems. Recent studies have explored CoT reasoning in complex multimodal scenarios, such as the science question answering task, by fine-tuning multimodal models with high-quality human-annotated CoT rationales. However, collecting high-quality COT rationales is usually time-consuming and costly. Besides, the annotated rationales are hardly accurate due to the external essential information missed. To address these issues, we propose a novel method termed T-SciQ that aims at teaching science question answering with LLM signals. The T-SciQ approach generates high-quality CoT rationales as teaching signals and is advanced to train much smaller models to perform CoT reasoning in complex modalities. Additionally, we introduce a novel data mixing strategy to produce more effective teaching data samples by policy for simple and complex science question answer problems. Extensive experimental results show that our T-SciQ method achieves a new state-of-the-art performance on the ScienceQA benchmark, with an accuracy of 96.18\%. Moreover, our approach outperforms the most powerful fine-tuned baseline by 4.5\%.

Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning within the discrete vocabulary space and may not always be optimal. While recent efforts explore continuous-space reasoning, they often suffer from catastrophic forgetting, limiting their applicability to state-of-the-art LLMs that already perform well in zero-shot settings with a proper instruction. To address this challenge, we propose a novel approach for continuous-space reasoning that does not require modifying the underlying LLM. Specifically, we employ a lightweight assistant model to generate instance-specific soft thought tokens speculatively as the initial chain of thoughts, which are then mapped into the LLM's representation space via a projection module. Experimental results on five reasoning benchmarks demonstrate that our method enhances LLM reasoning performance through supervised, parameter-efficient fine-tuning.

Leveraging the autonomous decision-making capabilities of large language models (LLMs) demonstrates superior performance in reasoning tasks. Despite the successes of iterative or recursive retrieval-augmented generation (RAG), they often are trapped in a single solution space when confronted with complex tasks. In this paper, we propose a novel thinking pattern in RAG which integrates system analysis with efficient reasoning actions, significantly activating intrinsic reasoning capabilities and expanding the solution space of specific tasks via Monte Carlo Tree Search (MCTS), dubbed AirRAG. Specifically, our approach designs five fundamental reasoning actions that are expanded to a wide tree-based reasoning spaces using MCTS. The extension also uses self-consistency verification to explore potential reasoning paths and implement inference scaling. In addition, computationally optimal strategies are used to apply more inference computation to key actions to achieve further performance improvements. Experimental results demonstrate the effectiveness of AirRAG through considerable performance gains over complex QA datasets. Furthermore, AirRAG is flexible and lightweight, making it easy to integrate with other advanced technologies.

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

The rapid advancement of large language models (LLMs) has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate LLMs' strategic reasoning capabilities, game theory, with its concise structure, has become a preferred approach. However, current research focuses on a limited selection of games, resulting in low coverage. Classic game scenarios risk data leakage, and existing benchmarks often lack extensibility, making them inadequate for evaluating state-of-the-art models. To address these challenges, we propose TMGBench, a benchmark with comprehensive game type coverage, novel scenarios, and flexible organization. Specifically, we incorporate all 144 game types summarized by the Robinson-Goforth topology of 2x2 games, constructed as classic games. We also employ synthetic data generation to create diverse, higher-quality scenarios through topic guidance and human inspection, referred to as story-based games. Lastly, we provide a sustainable framework for increasingly powerful LLMs by treating these games as atomic units and organizing them into more complex forms via sequential, parallel, and nested structures. Our comprehensive evaluation of mainstream LLMs covers tests on rational reasoning, robustness, Theory-of-Mind (ToM), and reasoning in complex forms. Results reveal flaws in accuracy, consistency, and varying mastery of ToM. Additionally, o1-mini, OpenAI's latest reasoning model, achieved accuracy rates of 66.6%, 60.0%, and 70.0% on sequential, parallel, and nested games, highlighting TMGBench's challenges.

Given questions regarding some prototypical situation such as Name something that people usually do before they leave the house for work? a human can easily answer them via acquired experiences. There can be multiple right answers for such questions, with some more common for a situation than others. This paper introduces a new question answering dataset for training and evaluating common sense reasoning capabilities of artificial intelligence systems in such prototypical situations. The training set is gathered from an existing set of questions played in a long-running international game show FAMILY- FEUD. The hidden evaluation set is created by gathering answers for each question from 100 crowd-workers. We also propose a generative evaluation task where a model has to output a ranked list of answers, ideally covering all prototypical answers for a question. After presenting multiple competitive baseline models, we find that human performance still exceeds model scores on all evaluation metrics with a meaningful gap, supporting the challenging nature of the task.

Developing intelligent agents for long-term cooperation in dynamic open-world scenarios is a major challenge in multi-agent systems. Traditional Multi-agent Reinforcement Learning (MARL) frameworks like centralized training decentralized execution (CTDE) struggle with scalability and flexibility. They require centralized long-term planning, which is difficult without custom reward functions, and face challenges in processing multi-modal data. CTDE approaches also assume fixed cooperation strategies, making them impractical in dynamic environments where agents need to adapt and plan independently. To address decentralized multi-agent cooperation, we propose Decentralized Adaptive Knowledge Graph Memory and Structured Communication System (DAMCS) in a novel Multi-agent Crafter environment. Our generative agents, powered by Large Language Models (LLMs), are more scalable than traditional MARL agents by leveraging external knowledge and language for long-term planning and reasoning. Instead of fully sharing information from all past experiences, DAMCS introduces a multi-modal memory system organized as a hierarchical knowledge graph and a structured communication protocol to optimize agent cooperation. This allows agents to reason from past interactions and share relevant information efficiently. Experiments on novel multi-agent open-world tasks show that DAMCS outperforms both MARL and LLM baselines in task efficiency and collaboration. Compared to single-agent scenarios, the two-agent scenario achieves the same goal with 63% fewer steps, and the six-agent scenario with 74% fewer steps, highlighting the importance of adaptive memory and structured communication in achieving long-term goals. We publicly release our project at: https://happyeureka.github.io/damcs.

We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning tasks demand extensive training data (>100,000 examples), we demonstrate that complex mathematical reasoning abilities can be effectively elicited with surprisingly few examples. Through comprehensive experiments, our proposed model LIMO demonstrates unprecedented performance in mathematical reasoning. With merely 817 curated training samples, LIMO achieves 57.1% accuracy on AIME and 94.8% on MATH, improving from previous SFT-based models' 6.5% and 59.2% respectively, while only using 1% of the training data required by previous approaches. LIMO demonstrates exceptional out-of-distribution generalization, achieving 40.5% absolute improvement across 10 diverse benchmarks, outperforming models trained on 100x more data, challenging the notion that SFT leads to memorization rather than generalization. Based on these results, we propose the Less-Is-More Reasoning Hypothesis (LIMO Hypothesis): In foundation models where domain knowledge has been comprehensively encoded during pre-training, sophisticated reasoning capabilities can emerge through minimal but precisely orchestrated demonstrations of cognitive processes. This hypothesis posits that the elicitation threshold for complex reasoning is determined by two key factors: (1) the completeness of the model's encoded knowledge foundation during pre-training, and (2) the effectiveness of post-training examples as "cognitive templates" that show the model how to utilize its knowledge base to solve complex reasoning tasks. To facilitate reproducibility and future research in data-efficient reasoning, we release LIMO as a comprehensive open-source suite at https://github.com/GAIR-NLP/LIMO.

Thinking aloud is an effective meta-cognitive strategy human reasoners apply to solve difficult problems. We suggest to improve the reasoning ability of pre-trained neural language models in a similar way, namely by expanding a task's context with problem elaborations that are dynamically generated by the language model itself. Our main result is that dynamic problem elaboration significantly improves the zero-shot performance of GPT-2 in a deductive reasoning and natural language inference task: While the model uses a syntactic heuristic for predicting an answer, it is capable (to some degree) of generating reasoned additional context which facilitates the successful application of its heuristic. We explore different ways of generating elaborations, including fewshot learning, and find that their relative performance varies with the specific problem characteristics (such as problem difficulty). Moreover, the effectiveness of an elaboration can be explained in terms of the degree to which the elaboration semantically coheres with the corresponding problem. In particular, elaborations that are most faithful to the original problem description may boost accuracy by up to 24%.

Reasoning in a complex and ambiguous environment is a key goal for Reinforcement Learning (RL) agents. While some sophisticated RL agents can successfully solve difficult tasks, they require a large amount of training data and often struggle to generalize to new unseen environments and new tasks. On the other hand, Large Scale Language Models (LSLMs) have exhibited strong reasoning ability and the ability to to adapt to new tasks through in-context learning. However, LSLMs do not inherently have the ability to interrogate or intervene on the environment. In this work, we investigate how to combine these complementary abilities in a single system consisting of three parts: a Planner, an Actor, and a Reporter. The Planner is a pre-trained language model that can issue commands to a simple embodied agent (the Actor), while the Reporter communicates with the Planner to inform its next command. We present a set of tasks that require reasoning, test this system's ability to generalize zero-shot and investigate failure cases, and demonstrate how components of this system can be trained with reinforcement-learning to improve performance.

Non-task oriented dialogue systems have achieved great success in recent years due to largely accessible conversation data and the development of deep learning techniques. Given a context, current systems are able to yield a relevant and fluent response, but sometimes make logical mistakes because of weak reasoning capabilities. To facilitate the conversation reasoning research, we introduce MuTual, a novel dataset for Multi-Turn dialogue Reasoning, consisting of 8,860 manually annotated dialogues based on Chinese student English listening comprehension exams. Compared to previous benchmarks for non-task oriented dialogue systems, MuTual is much more challenging since it requires a model that can handle various reasoning problems. Empirical results show that state-of-the-art methods only reach 71%, which is far behind the human performance of 94%, indicating that there is ample room for improving reasoning ability. MuTual is available at https://github.com/Nealcly/MuTual.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Inductive Reasoning (IR), the ability to summarize rules from examples and apply on new ones, has long been viewed as a primal ability for general intelligence and widely studied by cognitive science and AI researchers. Many benchmarks have been proposed to measure such ability for Large Language Models (LLMs); however, they focus on few-shot (usually <10) setting and lack evaluation for aggregating many pieces of information from long contexts. On the other hand, the ever-growing context length of LLMs have brought forth the novel paradigm of many-shot In-Context Learning (ICL), which addresses new tasks with hundreds to thousands of examples without expensive and inefficient fine-tuning. However, many-shot evaluations are mostly focused on classification (a very limited aspect of IR), and popular long-context LLM tasks such as Needle-In-A-Haystack (NIAH) seldom require complicated intelligence for integrating many pieces of information. To fix the issues from both worlds, we propose MIR-Bench, the first many-shot in-context inductive reasoning benchmark that asks LLM to induce output via input-output examples from underlying functions with diverse data format. Based on MIR-Bench, we study many novel problems for inductive reasoning and many-shot ICL, including robustness against erroneous shots and the effect of Chain-of-Thought (CoT), and acquired insightful findings.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Chain-of-Thought(CoT) prompting and its variants explore equipping large language models (LLMs) with high-level reasoning abilities by emulating human-like linear cognition and logic. However, the human mind is complicated and mixed with both linear and nonlinear thinking. In this work, we propose Inferential Exclusion Prompting (IEP), a novel prompting that combines the principles of elimination and inference in order to guide LLMs to think non-linearly. IEP guides LLMs to plan and then utilize Natural Language Inference (NLI) to deduce each possible solution's entailment relation with context, commonsense, or facts, therefore yielding a broader perspective by thinking back for inferring. This forward planning and backward eliminating process allows IEP to better simulate the complex human thinking processes compared to other CoT-based methods, which only reflect linear cognitive processes. We conducted a series of empirical studies and have corroborated that IEP consistently outperforms CoT across various tasks. Additionally, we observe that integrating IEP and CoT further improves the LLMs' performance on certain tasks, highlighting the necessity of equipping LLMs with mixed logic processes. Moreover, to better evaluate comprehensive features inherent in human logic, we introduce Mental-Ability Reasoning Benchmark (MARB). The benchmark comprises six novel subtasks with a total of 9,115 questions, among which 1,685 are developed with hand-crafted rationale references. We believe both IEP and MARB can serve as a promising direction for unveiling LLMs' logic and verbal reasoning abilities and drive further advancements. MARB will be available at ~anonymity link soon.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

We argue that enabling human-AI dialogue, purposed to support joint reasoning (i.e., 'inquiry'), is important for ensuring that AI decision making is aligned with human values and preferences. In particular, we point to logic-based models of argumentation and dialogue, and suggest that the traditional focus on persuasion dialogues be replaced by a focus on inquiry dialogues, and the distinct challenges that joint inquiry raises. Given recent dramatic advances in the performance of large language models (LLMs), and the anticipated increase in their use for decision making, we provide a roadmap for research into inquiry dialogues for supporting joint human-LLM reasoning tasks that are ethically salient, and that thereby require that decisions are value aligned.

Program-of-Thought (PoT) replaces natural language-based Chain-of-Thought (CoT) as the most popular method in Large Language Models (LLMs) mathematical reasoning tasks by utilizing external tool calls to circumvent computational errors. However, our evaluation of the GPT-4 and Llama series reveals that using PoT introduces more reasoning errors, such as incorrect formulas or flawed logic, compared to CoT. To address this issue, we propose Human-Think Language (HTL), which leverages a suite of strategies that help integrate PoT and CoT, encompassing: (1) a new generation paradigm that uses full CoT reasoning to control code generation. (2) Focus Attention, that directs model attention to the CoT reasoning during PoT to generate more logical code. (3) reinforcement learning that utilizes the accuracy of both CoT and PoT responses as rewards to prevent repetitive reasoning steps in LLMs when solving difficult math problems. Our method achieves an average improvement of 6.5% on the Llama-Base model and 4.3% on the Mistral-Base model across 8 mathematical calculation datasets. It also shows significant effectiveness on five out-of-domain datasets by controlling the model's information flow, exhibiting strong transferability. Additionally, HTL shows the most significant improvement in non-mathematical natural language inference task, contributing to a unified reasoning task framework

A prominent challenge for modern language understanding systems is the ability to answer implicit reasoning questions, where the required reasoning steps for answering the question are not mentioned in the text explicitly. In this work, we investigate why current models struggle with implicit reasoning question answering (QA) tasks, by decoupling inference of reasoning steps from their execution. We define a new task of implicit relation inference and construct a benchmark, IMPLICITRELATIONS, where given a question, a model should output a list of concept-relation pairs, where the relations describe the implicit reasoning steps required for answering the question. Using IMPLICITRELATIONS, we evaluate models from the GPT-3 family and find that, while these models struggle on the implicit reasoning QA task, they often succeed at inferring implicit relations. This suggests that the challenge in implicit reasoning questions does not stem from the need to plan a reasoning strategy alone, but to do it while also retrieving and reasoning over relevant information.

Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive results, especially when combined with self-consistency. Nonetheless, some tasks remain particularly difficult for LLMs to solve. Tree of Thoughts (ToT) and Graph of Thoughts (GoT) emerged as alternatives, dividing the complex problem into paths of subproblems. In this paper, we propose Tree of Problems (ToP), a simpler version of ToT, which we hypothesise can work better for complex tasks that can be divided into identical subtasks. Our empirical results show that our approach outperforms ToT and GoT, and in addition performs better than CoT on complex reasoning tasks. All code for this paper is publicly available here: https://github.com/ArmelRandy/tree-of-problems.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Large language models (LLMs) exhibit impressive emergent abilities in natural language processing, but their democratization is hindered due to huge computation requirements and closed-source nature. Recent research on advancing open-source smaller LMs by distilling knowledge from black-box LLMs has obtained promising results in the instruction-following ability. However, the reasoning ability which is more challenging to foster, is relatively rarely explored. In this paper, we propose a tailored learning approach to distill such reasoning ability to smaller LMs to facilitate the democratization of the exclusive reasoning ability. In contrast to merely employing LLM as a data annotator, we exploit the potential of LLM as a reasoning teacher by building an interactive multi-round learning paradigm. This paradigm enables the student to expose its deficiencies to the black-box teacher who then can provide customized training data in return. Further, to exploit the reasoning potential of the smaller LM, we propose self-reflection learning to motivate the student to learn from self-made mistakes. The learning from self-reflection and LLM are all tailored to the student's learning status, thanks to the seamless integration with the multi-round learning paradigm. Comprehensive experiments and analysis on mathematical and commonsense reasoning tasks demonstrate the effectiveness of our method. The code will be available at https://github.com/Raibows/Learn-to-Reason.

Chain of Thought prompting strategy has enhanced the performance of Large Language Models (LLMs) across various NLP tasks. However, it still has shortcomings when dealing with complex reasoning tasks, following~cot_wei, including understanding errors, calculation errors and process errors (e.g. missing-step and hallucinations). Subsequently, Our in-depth analysis of various error types has found that deeply understanding the whole problem is critical in addressing complicated reasoning tasks. In this paper, we proposed a novel prompt strategy called Deeply Understanding the Problems (DUP) prompting, inspired by how humans solve complex reasoning problems, designed to enhance the comprehensive understanding of problems by LLMs. It consists of three stages: 1) extract the core question; 2) find out problem-solving information based on the core question; 3) generate and extract answers by LLMs. We evaluate the performance of DUP prompting on ten diverse reasoning datasets. Experimental results suggest that DUP prompting significantly outperforms Zero-Shot CoT ~kojima2022large across all datasets. Notably, DUP achieves state-of-the-art on SVAMP (90.4\% to 94.2\%) and GSM8K (94.6\% to 97.1\%).

In numerous artificial intelligence applications, the collaborative efforts of multiple intelligent agents are imperative for the successful attainment of target objectives. To enhance coordination among these agents, a distributed communication framework is often employed. However, indiscriminate information sharing among all agents can be resource-intensive, and the adoption of manually pre-defined communication architectures imposes constraints on inter-agent communication, thus limiting the potential for effective collaboration. Moreover, the communication framework often remains static during inference, which may result in sustained high resource consumption, as in most cases, only key decisions necessitate information sharing among agents. In this study, we introduce a novel approach wherein we conceptualize the communication architecture among agents as a learnable graph. We formulate this problem as the task of determining the communication graph while enabling the architecture parameters to update normally, thus necessitating a bi-level optimization process. Utilizing continuous relaxation of the graph representation and incorporating attention units, our proposed approach, CommFormer, efficiently optimizes the communication graph and concurrently refines architectural parameters through gradient descent in an end-to-end manner. Additionally, we introduce a temporal gating mechanism for each agent, enabling dynamic decisions on whether to receive shared information at a given time, based on current observations, thus improving decision-making efficiency. Extensive experiments on a variety of cooperative tasks substantiate the robustness of our model across diverse cooperative scenarios, where agents are able to develop more coordinated and sophisticated strategies regardless of changes in the number of agents.

Prior approaches to realizing mixed-initiative human--computer referential communication have adopted information-state or collaborative problem-solving approaches. In this paper, we argue for a new approach, inspired by coherence-based models of discourse such as SDRT asher-lascarides:2003a, in which utterances attach to an evolving discourse structure and the associated knowledge graph of speaker commitments serves as an interface to real-world reasoning and conversational strategy. As first steps towards implementing the approach, we describe a simple dialogue system in a referential communication domain that accumulates constraints across discourse, interprets them using a learned probabilistic model, and plans clarification using reinforcement learning.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Commonsense question answering (QA) research requires machines to answer questions based on commonsense knowledge. However, this research requires expensive labor costs to annotate data as the basis of research, and models that rely on fine-tuning paradigms only apply to specific tasks, rather than learn a general commonsense reasoning ability. As a more robust method, zero-shot commonsense question answering shows a good prospect. The current zero-shot framework tries to convert triples in commonsense knowledge graphs (KGs) into QA-form samples as the pre-trained data source to incorporate commonsense knowledge into the model. However, this method ignores the multi-hop relationship in the KG, which is also an important central problem in commonsense reasoning. In this paper, we propose a novel multi-hop commonsense knowledge injection framework. Specifically, it explores multi-hop reasoning paradigm in KGs that conform to linguistic logic, and we further propose two multi-hop QA generation methods based on KGs. Then, we utilize contrastive learning to pre-train the model with the synthetic QA dataset to inject multi-hop commonsense knowledge. Extensive experiments on five commonsense question answering benchmarks demonstrate that our framework achieves state-of-art performance.

In this paper, we introduce Concise Chain-of-Thought (CCoT) prompting. We compared standard CoT and CCoT prompts to see how conciseness impacts response length and correct-answer accuracy. We evaluated this using GPT-3.5 and GPT-4 with a multiple-choice question-and-answer (MCQA) benchmark. CCoT reduced average response length by 48.70% for both GPT-3.5 and GPT-4 while having a negligible impact on problem-solving performance. However, on math problems, GPT-3.5 with CCoT incurs a performance penalty of 27.69%. Overall, CCoT leads to an average per-token cost reduction of 22.67%. These results have practical implications for AI systems engineers using LLMs to solve real-world problems with CoT prompt-engineering techniques. In addition, these results provide more general insight for AI researchers studying the emergent behavior of step-by-step reasoning in LLMs.

The rapid advancement of large language models (LLMs) has significantly enhanced their reasoning abilities, enabling increasingly complex tasks. However, these capabilities often diminish in smaller, more computationally efficient models like GPT-2. Recent research shows that reasoning distillation can help small models acquire reasoning capabilities, but most existing methods focus primarily on improving teacher-generated reasoning paths. Our observations reveal that small models can generate high-quality reasoning paths during sampling, even without chain-of-thought prompting, though these paths are often latent due to their low probability under standard decoding strategies. To address this, we propose Self-Enhanced Reasoning Training (SERT), which activates and leverages latent reasoning capabilities in small models through self-training on filtered, self-generated reasoning paths under zero-shot conditions. Experiments using OpenAI's GPT-3.5 as the teacher model and GPT-2 models as the student models demonstrate that SERT enhances the reasoning abilities of small models, improving their performance in reasoning distillation.

Reasoning is critical for large language models (LLMs) to excel in a wide range of tasks. While methods like Chain-of-Thought (CoT) reasoning enhance LLM performance by decomposing problems into intermediate steps, they also incur significant overhead in token usage, leading to increased costs. We find that the reasoning process of current LLMs is unnecessarily lengthy and it can be compressed by including a reasonable token budget in the prompt, but the choice of token budget plays a crucial role in the actual compression effectiveness. We then propose a token-budget-aware LLM reasoning framework, which dynamically estimates token budgets for different problems based on reasoning complexity and uses the estimated token budgets to guide the reasoning process. Experiments show that our method effectively reduces token costs in CoT reasoning with only a slight performance reduction, offering a practical solution to balance efficiency and accuracy in LLM reasoning. Code: https://github.com/GeniusHTX/TALE.