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Mar 17

MalAlgoQA: Pedagogical Evaluation of Counterfactual Reasoning in Large Language Models and Implications for AI in Education

This paper introduces MalAlgoQA, a novel dataset designed to evaluate the counterfactual reasoning capabilities of Large Language Models (LLMs) through a pedagogical approach. The dataset comprises mathematics and reading comprehension questions, each accompanied by four answer choices and their corresponding rationales. At the heart of MalAlgoQA are ``malgorithms'' - rationales behind incorrect answer choices that represent flawed yet logically coherent reasoning paths. These malgorithms serve as counterfactual scenarios, allowing us to assess an LLM's ability to identify and analyze flawed reasoning patterns. We propose the Malgorithm Identification task, where LLMs are assessed based on their ability to identify corresponding malgorithm given an incorrect answer choice. To evaluate the model performance, we introduce two metrics: Algorithm Identification Accuracy (AIA) for correct answer rationale identification, and Malgorithm Identification Accuracy (MIA) for incorrect answer rationale identification. Our experiments reveal that state-of-the-art LLMs exhibit significant performance drops in MIA compared to AIA, highlighting the challenges in counterfactual reasoning. Surprisingly, we find that the chain-of-thought prompting technique not only fails to consistently enhance MIA but can sometimes lead to underperformance compared to simple prompting. These findings have important implications for developing LLMs with improved counterfactual reasoning, particularly relevant for AI-powered tutoring systems, where identifying and addressing student misconceptions is essential. MalAlgoQA dataset is available https://github.com/luffycodes/MalAlgoQA-Dataset{here}.

Thought-Path Contrastive Learning via Premise-Oriented Data Augmentation for Logical Reading Comprehension

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.

Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Models

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

Cause and Effect: Can Large Language Models Truly Understand Causality?

With the rise of Large Language Models(LLMs), it has become crucial to understand their capabilities and limitations in deciphering and explaining the complex web of causal relationships that language entails. Current methods use either explicit or implicit causal reasoning, yet there is a strong need for a unified approach combining both to tackle a wide array of causal relationships more effectively. This research proposes a novel architecture called Context Aware Reasoning Enhancement with Counterfactual Analysis(CARE CA) framework to enhance causal reasoning and explainability. The proposed framework incorporates an explicit causal detection module with ConceptNet and counterfactual statements, as well as implicit causal detection through LLMs. Our framework goes one step further with a layer of counterfactual explanations to accentuate LLMs understanding of causality. The knowledge from ConceptNet enhances the performance of multiple causal reasoning tasks such as causal discovery, causal identification and counterfactual reasoning. The counterfactual sentences add explicit knowledge of the not caused by scenarios. By combining these powerful modules, our model aims to provide a deeper understanding of causal relationships, enabling enhanced interpretability. Evaluation of benchmark datasets shows improved performance across all metrics, such as accuracy, precision, recall, and F1 scores. We also introduce CausalNet, a new dataset accompanied by our code, to facilitate further research in this domain.

CounterBench: A Benchmark for Counterfactuals Reasoning in Large Language Models

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, CoIn, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs.Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

Counterfactuals for Design: A Model-Agnostic Method For Design Recommendations

We introduce Multi-Objective Counterfactuals for Design (MCD), a novel method for counterfactual optimization in design problems. Counterfactuals are hypothetical situations that can lead to a different decision or choice. In this paper, the authors frame the counterfactual search problem as a design recommendation tool that can help identify modifications to a design, leading to better functional performance. MCD improves upon existing counterfactual search methods by supporting multi-objective queries, which are crucial in design problems, and by decoupling the counterfactual search and sampling processes, thus enhancing efficiency and facilitating objective tradeoff visualization. The paper demonstrates MCD's core functionality using a two-dimensional test case, followed by three case studies of bicycle design that showcase MCD's effectiveness in real-world design problems. In the first case study, MCD excels at recommending modifications to query designs that can significantly enhance functional performance, such as weight savings and improvements to the structural safety factor. The second case study demonstrates that MCD can work with a pre-trained language model to suggest design changes based on a subjective text prompt effectively. Lastly, the authors task MCD with increasing a query design's similarity to a target image and text prompt while simultaneously reducing weight and improving structural performance, demonstrating MCD's performance on a complex multimodal query. Overall, MCD has the potential to provide valuable recommendations for practitioners and design automation researchers looking for answers to their ``What if'' questions by exploring hypothetical design modifications and their impact on multiple design objectives. The code, test problems, and datasets used in the paper are available to the public at decode.mit.edu/projects/counterfactuals/.

ACQUIRED: A Dataset for Answering Counterfactual Questions In Real-Life Videos

Multimodal counterfactual reasoning is a vital yet challenging ability for AI systems. It involves predicting the outcomes of hypothetical circumstances based on vision and language inputs, which enables AI models to learn from failures and explore hypothetical scenarios. Despite its importance, there are only a few datasets targeting the counterfactual reasoning abilities of multimodal models. Among them, they only cover reasoning over synthetic environments or specific types of events (e.g. traffic collisions), making them hard to reliably benchmark the model generalization ability in diverse real-world scenarios and reasoning dimensions. To overcome these limitations, we develop a video question answering dataset, ACQUIRED: it consists of 3.9K annotated videos, encompassing a wide range of event types and incorporating both first and third-person viewpoints, which ensures a focus on real-world diversity. In addition, each video is annotated with questions that span three distinct dimensions of reasoning, including physical, social, and temporal, which can comprehensively evaluate the model counterfactual abilities along multiple aspects. We benchmark our dataset against several state-of-the-art language-only and multimodal models and experimental results demonstrate a significant performance gap (>13%) between models and humans. The findings suggest that multimodal counterfactual reasoning remains an open challenge and ACQUIRED is a comprehensive and reliable benchmark for inspiring future research in this direction.

Generating Pragmatic Examples to Train Neural Program Synthesizers

Programming-by-example is the task of synthesizing a program that is consistent with a set of user-provided input-output examples. As examples are often an under-specification of one's intent, a good synthesizer must choose the intended program from the many that are consistent with the given set of examples. Prior work frames program synthesis as a cooperative game between a listener (that synthesizes programs) and a speaker (a user choosing examples), and shows that models of computational pragmatic inference are effective in choosing the user intended programs. However, these models require counterfactual reasoning over a large set of programs and examples, which is infeasible in realistic program spaces. In this paper, we propose a novel way to amortize this search with neural networks. We sample pairs of programs and examples via self-play between listener and speaker models, and use pragmatic inference to choose informative training examples from this sample.We then use the informative dataset to train models to improve the synthesizer's ability to disambiguate user-provided examples without human supervision. We validate our method on the challenging task of synthesizing regular expressions from example strings, and find that our method (1) outperforms models trained without choosing pragmatic examples by 23% (a 51% relative increase) (2) matches the performance of supervised learning on a dataset of pragmatic examples provided by humans, despite using no human data in training.

Faithful Explanations of Black-box NLP Models Using LLM-generated Counterfactuals

Causal explanations of the predictions of NLP systems are essential to ensure safety and establish trust. Yet, existing methods often fall short of explaining model predictions effectively or efficiently and are often model-specific. In this paper, we address model-agnostic explanations, proposing two approaches for counterfactual (CF) approximation. The first approach is CF generation, where a large language model (LLM) is prompted to change a specific text concept while keeping confounding concepts unchanged. While this approach is demonstrated to be very effective, applying LLM at inference-time is costly. We hence present a second approach based on matching, and propose a method that is guided by an LLM at training-time and learns a dedicated embedding space. This space is faithful to a given causal graph and effectively serves to identify matches that approximate CFs. After showing theoretically that approximating CFs is required in order to construct faithful explanations, we benchmark our approaches and explain several models, including LLMs with billions of parameters. Our empirical results demonstrate the excellent performance of CF generation models as model-agnostic explainers. Moreover, our matching approach, which requires far less test-time resources, also provides effective explanations, surpassing many baselines. We also find that Top-K techniques universally improve every tested method. Finally, we showcase the potential of LLMs in constructing new benchmarks for model explanation and subsequently validate our conclusions. Our work illuminates new pathways for efficient and accurate approaches to interpreting NLP systems.

CausaLM: Causal Model Explanation Through Counterfactual Language Models

Understanding predictions made by deep neural networks is notoriously difficult, but also crucial to their dissemination. As all machine learning based methods, they are as good as their training data, and can also capture unwanted biases. While there are tools that can help understand whether such biases exist, they do not distinguish between correlation and causation, and might be ill-suited for text-based models and for reasoning about high level language concepts. A key problem of estimating the causal effect of a concept of interest on a given model is that this estimation requires the generation of counterfactual examples, which is challenging with existing generation technology. To bridge that gap, we propose CausaLM, a framework for producing causal model explanations using counterfactual language representation models. Our approach is based on fine-tuning of deep contextualized embedding models with auxiliary adversarial tasks derived from the causal graph of the problem. Concretely, we show that by carefully choosing auxiliary adversarial pre-training tasks, language representation models such as BERT can effectively learn a counterfactual representation for a given concept of interest, and be used to estimate its true causal effect on model performance. A byproduct of our method is a language representation model that is unaffected by the tested concept, which can be useful in mitigating unwanted bias ingrained in the data.

DISCO: Distilling Counterfactuals with Large Language Models

Models trained with counterfactually augmented data learn representations of the causal structure of tasks, enabling robust generalization. However, high-quality counterfactual data is scarce for most tasks and not easily generated at scale. When crowdsourced, such data is typically limited in scale and diversity; when generated using supervised methods, it is computationally expensive to extend to new counterfactual dimensions. In this work, we introduce DISCO (DIStilled COunterfactual Data), a new method for automatically generating high quality counterfactual data at scale. DISCO engineers prompts to generate phrasal perturbations with a large general language model. Then, a task-specific teacher model filters these generations to distill high-quality counterfactual data. While task-agnostic, we apply our pipeline to the task of natural language inference (NLI) and find that on challenging evaluations such as the NLI stress test, comparatively smaller student models trained with DISCO generated counterfactuals are more robust (6% absolute) and generalize better across distributions (2%) compared to models trained without data augmentation. Furthermore, DISCO augmented models are 10% more consistent between counterfactual pairs on three evaluation sets, demonstrating that DISCO augmentation enables models to more reliably learn causal representations. Our repository is available at: https://github.com/eric11eca/disco

Prompt Engineering a Prompt Engineer

Prompt engineering is a challenging yet crucial task for optimizing the performance of large language models (LLMs). It requires complex reasoning to examine the model's errors, hypothesize what is missing or misleading in the current prompt, and communicate the task with clarity. While recent works indicate that LLMs can be meta-prompted to perform automatic prompt engineering, their potentials may not be fully untapped due to the lack of sufficient guidance to elicit complex reasoning capabilities in LLMs in the meta-prompt. In this work, we investigate the problem of "prompt engineering a prompt engineer" -- constructing a meta-prompt that more effectively guides LLMs to perform automatic prompt engineering. We introduce and analyze key components, such as a step-by-step reasoning template and context specification, which lead to improved performance. In addition, inspired by common optimization concepts such as batch size, step size and momentum, we introduce their verbalized counterparts to the meta-prompt and investigate their effects. Our final method, named PE2, finds a prompt that outperforms "let's think step by step" by 6.3% on the MultiArith dataset and 3.1% on the GSM8K dataset. To demonstrate its versatility, we apply PE2 to the Instruction Induction benchmark, a suite of counterfactual tasks, and a lengthy, real-world industrial prompt. In these settings, PE2 achieves strong performance and outperforms prior automatic prompt engineering baselines. Further, we show that PE2 makes meaningful and targeted prompt edits, amends erroneous or incomplete prompts, and presents non-trivial counterfactual reasoning abilities.

OCTET: Object-aware Counterfactual Explanations

Nowadays, deep vision models are being widely deployed in safety-critical applications, e.g., autonomous driving, and explainability of such models is becoming a pressing concern. Among explanation methods, counterfactual explanations aim to find minimal and interpretable changes to the input image that would also change the output of the model to be explained. Such explanations point end-users at the main factors that impact the decision of the model. However, previous methods struggle to explain decision models trained on images with many objects, e.g., urban scenes, which are more difficult to work with but also arguably more critical to explain. In this work, we propose to tackle this issue with an object-centric framework for counterfactual explanation generation. Our method, inspired by recent generative modeling works, encodes the query image into a latent space that is structured in a way to ease object-level manipulations. Doing so, it provides the end-user with control over which search directions (e.g., spatial displacement of objects, style modification, etc.) are to be explored during the counterfactual generation. We conduct a set of experiments on counterfactual explanation benchmarks for driving scenes, and we show that our method can be adapted beyond classification, e.g., to explain semantic segmentation models. To complete our analysis, we design and run a user study that measures the usefulness of counterfactual explanations in understanding a decision model. Code is available at https://github.com/valeoai/OCTET.

Large Language Models as Counterfactual Generator: Strengths and Weaknesses

Large language models (LLMs) have demonstrated remarkable performance in a range of natural language understanding and generation tasks. Yet, their ability to generate counterfactuals, which can be used for areas like data augmentation, remains under-explored. This study aims to investigate the counterfactual generation capabilities of LLMs and analysis factors that influence this ability. First, we evaluate how effective are LLMs in counterfactual generation through data augmentation experiments for small language models (SLMs) across four tasks: sentiment analysis, natural language inference, named entity recognition, and relation extraction. While LLMs show promising enhancements in various settings, they struggle in complex tasks due to their self-limitations and the lack of logical guidance to produce counterfactuals that align with commonsense. Second, our analysis reveals the pivotal role of providing accurate task definitions and detailed step-by-step instructions to LLMs in generating counterfactuals. Interestingly, we also find that LLMs can generate reasonable counterfactuals even with unreasonable demonstrations, which illustrates that demonstrations are primarily to regulate the output format.This study provides the first comprehensive insight into counterfactual generation abilities of LLMs, and offers a novel perspective on utilizing LLMs for data augmentation to enhance SLMs.

Towards LLM-guided Causal Explainability for Black-box Text Classifiers

With the advent of larger and more complex deep learning models, such as in Natural Language Processing (NLP), model qualities like explainability and interpretability, albeit highly desirable, are becoming harder challenges to tackle and solve. For example, state-of-the-art models in text classification are black-box by design. Although standard explanation methods provide some degree of explainability, these are mostly correlation-based methods and do not provide much insight into the model. The alternative of causal explainability is more desirable to achieve but extremely challenging in NLP due to a variety of reasons. Inspired by recent endeavors to utilize Large Language Models (LLMs) as experts, in this work, we aim to leverage the instruction-following and textual understanding capabilities of recent state-of-the-art LLMs to facilitate causal explainability via counterfactual explanation generation for black-box text classifiers. To do this, we propose a three-step pipeline via which, we use an off-the-shelf LLM to: (1) identify the latent or unobserved features in the input text, (2) identify the input features associated with the latent features, and finally (3) use the identified input features to generate a counterfactual explanation. We experiment with our pipeline on multiple NLP text classification datasets, with several recent LLMs, and present interesting and promising findings.

Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse

Chain-of-thought (CoT) prompting has become a widely used strategy for working with large language and multimodal models. While CoT has been shown to improve performance across many tasks, determining the settings in which it is effective remains an ongoing effort. In particular, it is still an open question in what settings CoT systematically reduces model performance. In this paper, we seek to identify the characteristics of tasks where CoT reduces performance by drawing inspiration from cognitive psychology, looking at cases where (i) verbal thinking or deliberation hurts performance in humans, and (ii) the constraints governing human performance generalize to language models. Three such cases are implicit statistical learning, visual recognition, and classifying with patterns containing exceptions. In extensive experiments across all three settings, we find that a diverse collection of state-of-the-art models exhibit significant drop-offs in performance (e.g., up to 36.3% absolute accuracy for OpenAI o1-preview compared to GPT-4o) when using inference-time reasoning compared to zero-shot counterparts. We also identify three tasks that satisfy condition (i) but not (ii), and find that while verbal thinking reduces human performance in these tasks, CoT retains or increases model performance. Overall, our results show that while there is not an exact parallel between the cognitive processes of models and those of humans, considering cases where thinking has negative consequences for human performance can help us identify settings where it negatively impacts models. By connecting the literature on human deliberation with evaluations of CoT, we offer a new tool that can be used in understanding the impact of prompt choices and inference-time reasoning.

SACSoN: Scalable Autonomous Control for Social Navigation

Machine learning provides a powerful tool for building socially compliant robotic systems that go beyond simple predictive models of human behavior. By observing and understanding human interactions from past experiences, learning can enable effective social navigation behaviors directly from data. In this paper, our goal is to develop methods for training policies for socially unobtrusive navigation, such that robots can navigate among humans in ways that don't disturb human behavior. We introduce a definition for such behavior based on the counterfactual perturbation of the human: if the robot had not intruded into the space, would the human have acted in the same way? By minimizing this counterfactual perturbation, we can induce robots to behave in ways that do not alter the natural behavior of humans in the shared space. Instantiating this principle requires training policies to minimize their effect on human behavior, and this in turn requires data that allows us to model the behavior of humans in the presence of robots. Therefore, our approach is based on two key contributions. First, we collect a large dataset where an indoor mobile robot interacts with human bystanders. Second, we utilize this dataset to train policies that minimize counterfactual perturbation. We provide supplementary videos and make publicly available the largest-of-its-kind visual navigation dataset on our project page.

Guiding Large Language Models via Directional Stimulus Prompting

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

How FaR Are Large Language Models From Agents with Theory-of-Mind?

"Thinking is for Doing." Humans can infer other people's mental states from observations--an ability called Theory-of-Mind (ToM)--and subsequently act pragmatically on those inferences. Existing question answering benchmarks such as ToMi ask models questions to make inferences about beliefs of characters in a story, but do not test whether models can then use these inferences to guide their actions. We propose a new evaluation paradigm for large language models (LLMs): Thinking for Doing (T4D), which requires models to connect inferences about others' mental states to actions in social scenarios. Experiments on T4D demonstrate that LLMs such as GPT-4 and PaLM 2 seemingly excel at tracking characters' beliefs in stories, but they struggle to translate this capability into strategic action. Our analysis reveals the core challenge for LLMs lies in identifying the implicit inferences about mental states without being explicitly asked about as in ToMi, that lead to choosing the correct action in T4D. To bridge this gap, we introduce a zero-shot prompting framework, Foresee and Reflect (FaR), which provides a reasoning structure that encourages LLMs to anticipate future challenges and reason about potential actions. FaR boosts GPT-4's performance from 50% to 71% on T4D, outperforming other prompting methods such as Chain-of-Thought and Self-Ask. Moreover, FaR generalizes to diverse out-of-distribution story structures and scenarios that also require ToM inferences to choose an action, consistently outperforming other methods including few-shot in-context learning.

Complexity-Based Prompting for Multi-Step Reasoning

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Leveraging Training Data in Few-Shot Prompting for Numerical Reasoning

Chain-of-thought (CoT) prompting with large language models has proven effective in numerous natural language processing tasks, but designing prompts that generalize well to diverse problem types can be challenging, especially in the context of math word problem (MWP) solving. Additionally, it is common to have a large amount of training data that have a better diversity coverage but CoT annotations are not available, which limits the use of supervised learning techniques. To address these issues, we investigate two approaches to leverage the training data in a few-shot prompting scenario: dynamic program prompting and program distillation. Our approach is largely inspired by Gao et al., (2022), where they proposed to replace the CoT with the programs as the intermediate reasoning step. Such a prompting strategy allows us to accurately verify the answer correctness through program execution in MWP solving. Our dynamic program prompting involves annotating the training data by sampling correct programs from a large language model, while program distillation involves adapting a smaller model to the program-annotated training data. Our experiments on three standard MWP datasets demonstrate the effectiveness of these approaches, yielding significant improvements over previous baselines for prompting and fine-tuning. Our results suggest that leveraging a large amount of training data can improve the generalization ability of prompts and boost the performance of fine-tuned small models in MWP solving.

R^3 Prompting: Review, Rephrase and Resolve for Chain-of-Thought Reasoning in Large Language Models under Noisy Context

With the help of Chain-of-Thought (CoT) prompting, Large Language Models (LLMs) have achieved remarkable performance on various reasoning tasks. However, most of them have been evaluated under noise-free context and the dilemma for LLMs to produce inaccurate results under the noisy context has not been fully investigated. Existing studies utilize trigger sentences to encourage LLMs to concentrate on the relevant information but the trigger has limited effect on final answer prediction. Inspired by interactive CoT method, where intermediate reasoning steps are promoted by multiple rounds of interaction between users and LLMs, we propose a novel prompting method, namely R^3 prompting, for CoT reasoning under noisy context. Specifically, R^3 prompting interacts with LLMs to perform key sentence extraction, variable declaration and answer prediction, which corresponds to a thought process of reviewing, rephrasing and resolving. The responses generated at the last interaction will perform as hints to guide toward the responses of the next interaction. Our experiments show that R^3 prompting significantly outperforms existing CoT prompting methods on five reasoning tasks under noisy context. With GPT-3.5-turbo, we observe 3.7% accuracy improvement on average on the reasoning tasks under noisy context compared to the most competitive prompting baseline. More analyses and ablation studies show the robustness and generalization of R^3 prompting method in solving reasoning tasks in LLMs under noisy context.

Can Language Models Falsify? Evaluating Algorithmic Reasoning with Counterexample Creation

There is growing excitement about the potential of Language Models (LMs) to accelerate scientific discovery. Falsifying hypotheses is key to scientific progress, as it allows claims to be iteratively refined over time. This process requires significant researcher effort, reasoning, and ingenuity. Yet current benchmarks for LMs predominantly assess their ability to generate solutions rather than challenge them. We advocate for developing benchmarks that evaluate this inverse capability - creating counterexamples for subtly incorrect solutions. To demonstrate this approach, we start with the domain of algorithmic problem solving, where counterexamples can be evaluated automatically using code execution. Specifically, we introduce REFUTE, a dynamically updating benchmark that includes recent problems and incorrect submissions from programming competitions, where human experts successfully identified counterexamples. Our analysis finds that the best reasoning agents, even OpenAI o3-mini (high) with code execution feedback, can create counterexamples for only <9% of incorrect solutions in REFUTE, even though ratings indicate its ability to solve up to 48% of these problems from scratch. We hope our work spurs progress in evaluating and enhancing LMs' ability to falsify incorrect solutions - a capability that is crucial for both accelerating research and making models self-improve through reliable reflective reasoning.

CX-ToM: Counterfactual Explanations with Theory-of-Mind for Enhancing Human Trust in Image Recognition Models

We propose CX-ToM, short for counterfactual explanations with theory-of mind, a new explainable AI (XAI) framework for explaining decisions made by a deep convolutional neural network (CNN). In contrast to the current methods in XAI that generate explanations as a single shot response, we pose explanation as an iterative communication process, i.e. dialog, between the machine and human user. More concretely, our CX-ToM framework generates sequence of explanations in a dialog by mediating the differences between the minds of machine and human user. To do this, we use Theory of Mind (ToM) which helps us in explicitly modeling human's intention, machine's mind as inferred by the human as well as human's mind as inferred by the machine. Moreover, most state-of-the-art XAI frameworks provide attention (or heat map) based explanations. In our work, we show that these attention based explanations are not sufficient for increasing human trust in the underlying CNN model. In CX-ToM, we instead use counterfactual explanations called fault-lines which we define as follows: given an input image I for which a CNN classification model M predicts class c_pred, a fault-line identifies the minimal semantic-level features (e.g., stripes on zebra, pointed ears of dog), referred to as explainable concepts, that need to be added to or deleted from I in order to alter the classification category of I by M to another specified class c_alt. We argue that, due to the iterative, conceptual and counterfactual nature of CX-ToM explanations, our framework is practical and more natural for both expert and non-expert users to understand the internal workings of complex deep learning models. Extensive quantitative and qualitative experiments verify our hypotheses, demonstrating that our CX-ToM significantly outperforms the state-of-the-art explainable AI models.

Self-regulating Prompts: Foundational Model Adaptation without Forgetting

Prompt learning has emerged as an efficient alternative for fine-tuning foundational models, such as CLIP, for various downstream tasks. Conventionally trained using the task-specific objective, i.e., cross-entropy loss, prompts tend to overfit downstream data distributions and find it challenging to capture task-agnostic general features from the frozen CLIP. This leads to the loss of the model's original generalization capability. To address this issue, our work introduces a self-regularization framework for prompting called PromptSRC (Prompting with Self-regulating Constraints). PromptSRC guides the prompts to optimize for both task-specific and task-agnostic general representations using a three-pronged approach by: (a) regulating prompted representations via mutual agreement maximization with the frozen model, (b) regulating with self-ensemble of prompts over the training trajectory to encode their complementary strengths, and (c) regulating with textual diversity to mitigate sample diversity imbalance with the visual branch. To the best of our knowledge, this is the first regularization framework for prompt learning that avoids overfitting by jointly attending to pre-trained model features, the training trajectory during prompting, and the textual diversity. PromptSRC explicitly steers the prompts to learn a representation space that maximizes performance on downstream tasks without compromising CLIP generalization. We perform extensive experiments on 4 benchmarks where PromptSRC overall performs favorably well compared to the existing methods. Our code and pre-trained models are publicly available at: https://github.com/muzairkhattak/PromptSRC.

Characterizing Mechanisms for Factual Recall in Language Models

Language Models (LMs) often must integrate facts they memorized in pretraining with new information that appears in a given context. These two sources can disagree, causing competition within the model, and it is unclear how an LM will resolve the conflict. On a dataset that queries for knowledge of world capitals, we investigate both distributional and mechanistic determinants of LM behavior in such situations. Specifically, we measure the proportion of the time an LM will use a counterfactual prefix (e.g., "The capital of Poland is London") to overwrite what it learned in pretraining ("Warsaw"). On Pythia and GPT2, the training frequency of both the query country ("Poland") and the in-context city ("London") highly affect the models' likelihood of using the counterfactual. We then use head attribution to identify individual attention heads that either promote the memorized answer or the in-context answer in the logits. By scaling up or down the value vector of these heads, we can control the likelihood of using the in-context answer on new data. This method can increase the rate of generating the in-context answer to 88\% of the time simply by scaling a single head at runtime. Our work contributes to a body of evidence showing that we can often localize model behaviors to specific components and provides a proof of concept for how future methods might control model behavior dynamically at runtime.

Think Beyond Size: Adaptive Prompting for More Effective Reasoning

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.

Learning How To Ask: Cycle-Consistency Refines Prompts in Multimodal Foundation Models

When LLMs perform zero-shot inference, they typically use a prompt with a task specification, and generate a completion. However, there is no work to explore the possibility of the reverse - going from completion to task specification. In this paper, we employ both directions to perform cycle-supervised learning entirely in-context. Our goal is to create a forward map f : X -> Y (e.g. image -> generated caption), coupled with a backward map g : Y -> X (e.g. caption -> generated image) to construct a cycle-consistency "loss" (formulated as an update to the prompt) to enforce g(f(X)) ~= X. The technique, called CyclePrompt, uses cycle-consistency as a free supervisory signal to iteratively craft the prompt. Importantly, CyclePrompt reinforces model performance without expensive fine-tuning, without training data, and without the complexity of external environments (e.g. compilers, APIs). We demonstrate CyclePrompt in two domains: code generation and image captioning. Our results on the HumanEval coding benchmark put us in first place on the leaderboard among models that do not rely on extra training data or usage of external environments, and third overall. Compared to the GPT4 baseline, we improve accuracy from 80.5% to 87.2%. In the vision-language space, we generate detailed image captions which outperform baseline zero-shot GPT4V captions, when tested against natural (VQAv2) and diagrammatic (FigureQA) visual question-answering benchmarks. To the best of our knowledge, this is the first use of self-supervised learning for prompting.

Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

"Sorry, Come Again?" Prompting -- Enhancing Comprehension and Diminishing Hallucination with [PAUSE]-injected Optimal Paraphrasing

Hallucination has emerged as the most vulnerable aspect of contemporary Large Language Models (LLMs). In this paper, we introduce the Sorry, Come Again (SCA) prompting, aimed to avoid LLM hallucinations by enhancing comprehension through: (i) optimal paraphrasing and (ii) injecting [PAUSE] tokens to delay LLM generation. First, we provide an in-depth analysis of linguistic nuances: formality, readability, and concreteness of prompts for 21 LLMs, and elucidate how these nuances contribute to hallucinated generation. Prompts with lower readability, formality, or concreteness pose comprehension challenges for LLMs, similar to those faced by humans. In such scenarios, an LLM tends to speculate and generate content based on its imagination (associative memory) to fill these information gaps. Although these speculations may occasionally align with factual information, their accuracy is not assured, often resulting in hallucination. Recent studies reveal that an LLM often neglects the middle sections of extended prompts, a phenomenon termed as lost in the middle. While a specific paraphrase may suit one LLM, the same paraphrased version may elicit a different response from another LLM. Therefore, we propose an optimal paraphrasing technique to identify the most comprehensible paraphrase of a given prompt, evaluated using Integrated Gradient (and its variations) to guarantee that the LLM accurately processes all words. While reading lengthy sentences, humans often pause at various points to better comprehend the meaning read thus far. We have fine-tuned an LLM with injected [PAUSE] tokens, allowing the LLM to pause while reading lengthier prompts. This has brought several key contributions: (i) determining the optimal position to inject [PAUSE], (ii) determining the number of [PAUSE] tokens to be inserted, and (iii) introducing reverse proxy tuning to fine-tune the LLM for [PAUSE] insertion.

One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Distinguishing Ignorance from Error in LLM Hallucinations

Large language models (LLMs) are susceptible to hallucinations-outputs that are ungrounded, factually incorrect, or inconsistent with prior generations. We focus on close-book Question Answering (CBQA), where previous work has not fully addressed the distinction between two possible kinds of hallucinations, namely, whether the model (1) does not hold the correct answer in its parameters or (2) answers incorrectly despite having the required knowledge. We argue that distinguishing these cases is crucial for detecting and mitigating hallucinations. Specifically, case (2) may be mitigated by intervening in the model's internal computation, as the knowledge resides within the model's parameters. In contrast, in case (1) there is no parametric knowledge to leverage for mitigation, so it should be addressed by resorting to an external knowledge source or abstaining. To help distinguish between the two cases, we introduce Wrong Answer despite having Correct Knowledge (WACK), an approach for constructing model-specific datasets for the second hallucination type. Our probing experiments indicate that the two kinds of hallucinations are represented differently in the model's inner states. Next, we show that datasets constructed using WACK exhibit variations across models, demonstrating that even when models share knowledge of certain facts, they still vary in the specific examples that lead to hallucinations. Finally, we show that training a probe on our WACK datasets leads to better hallucination detection of case (2) hallucinations than using the common generic one-size-fits-all datasets. The code is available at https://github.com/technion-cs-nlp/hallucination-mitigation .

Automatic Chain of Thought Prompting in Large Language Models

Large language models (LLMs) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One leverages a simple prompt like "Let's think step by step" to facilitate step-by-step thinking before answering a question. The other uses a few manual demonstrations one by one, each composed of a question and a reasoning chain that leads to an answer. The superior performance of the second paradigm hinges on the hand-crafting of task-specific demonstrations one by one. We show that such manual efforts may be eliminated by leveraging LLMs with the "Let's think step by step" prompt to generate reasoning chains for demonstrations one by one, i.e., let's think not just step by step, but also one by one. However, these generated chains often come with mistakes. To mitigate the effect of such mistakes, we find that diversity matters for automatically constructing demonstrations. We propose an automatic CoT prompting method: Auto-CoT. It samples questions with diversity and generates reasoning chains to construct demonstrations. On ten public benchmark reasoning tasks with GPT-3, Auto-CoT consistently matches or exceeds the performance of the CoT paradigm that requires manual designs of demonstrations. Code is available at https://github.com/amazon-research/auto-cot

VLUCI: Variational Learning of Unobserved Confounders for Counterfactual Inference

Causal inference plays a vital role in diverse domains like epidemiology, healthcare, and economics. De-confounding and counterfactual prediction in observational data has emerged as a prominent concern in causal inference research. While existing models tackle observed confounders, the presence of unobserved confounders remains a significant challenge, distorting causal inference and impacting counterfactual outcome accuracy. To address this, we propose a novel variational learning model of unobserved confounders for counterfactual inference (VLUCI), which generates the posterior distribution of unobserved confounders. VLUCI relaxes the unconfoundedness assumption often overlooked by most causal inference methods. By disentangling observed and unobserved confounders, VLUCI constructs a doubly variational inference model to approximate the distribution of unobserved confounders, which are used for inferring more accurate counterfactual outcomes. Extensive experiments on synthetic and semi-synthetic datasets demonstrate VLUCI's superior performance in inferring unobserved confounders. It is compatible with state-of-the-art counterfactual inference models, significantly improving inference accuracy at both group and individual levels. Additionally, VLUCI provides confidence intervals for counterfactual outcomes, aiding decision-making in risk-sensitive domains. We further clarify the considerations when applying VLUCI to cases where unobserved confounders don't strictly conform to our model assumptions using the public IHDP dataset as an example, highlighting the practical advantages of VLUCI.

Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization

Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the likelihood of preferred responses often decreases during training. The current work sheds light on the causes and implications of this counter-intuitive phenomenon, which we term likelihood displacement. We demonstrate that likelihood displacement can be catastrophic, shifting probability mass from preferred responses to responses with an opposite meaning. As a simple example, training a model to prefer No over Never can sharply increase the probability of Yes. Moreover, when aligning the model to refuse unsafe prompts, we show that such displacement can unintentionally lead to unalignment, by shifting probability mass from preferred refusal responses to harmful responses (e.g., reducing the refusal rate of Llama-3-8B-Instruct from 74.4% to 33.4%). We theoretically characterize that likelihood displacement is driven by preferences that induce similar embeddings, as measured by a centered hidden embedding similarity (CHES) score. Empirically, the CHES score enables identifying which training samples contribute most to likelihood displacement in a given dataset. Filtering out these samples effectively mitigated unintentional unalignment in our experiments. More broadly, our results highlight the importance of curating data with sufficiently distinct preferences, for which we believe the CHES score may prove valuable.

Debiasing Multimodal Models via Causal Information Minimization

Most existing debiasing methods for multimodal models, including causal intervention and inference methods, utilize approximate heuristics to represent the biases, such as shallow features from early stages of training or unimodal features for multimodal tasks like VQA, etc., which may not be accurate. In this paper, we study bias arising from confounders in a causal graph for multimodal data and examine a novel approach that leverages causally-motivated information minimization to learn the confounder representations. Robust predictive features contain diverse information that helps a model generalize to out-of-distribution data. Hence, minimizing the information content of features obtained from a pretrained biased model helps learn the simplest predictive features that capture the underlying data distribution. We treat these features as confounder representations and use them via methods motivated by causal theory to remove bias from models. We find that the learned confounder representations indeed capture dataset biases, and the proposed debiasing methods improve out-of-distribution (OOD) performance on multiple multimodal datasets without sacrificing in-distribution performance. Additionally, we introduce a novel metric to quantify the sufficiency of spurious features in models' predictions that further demonstrates the effectiveness of our proposed methods. Our code is available at: https://github.com/Vaidehi99/CausalInfoMin

Re-Reading Improves Reasoning in Language Models

Reasoning presents a significant and challenging issue for Large Language Models (LLMs). The predominant focus of research has revolved around developing diverse prompting strategies to guide and structure the reasoning processes of LLMs. However, these approaches based on decoder-only causal language models often operate the input question in a single forward pass, potentially missing the rich, back-and-forth interactions inherent in human reasoning. Scant attention has been paid to a critical dimension, i.e., the input question itself embedded within the prompts. In response, we introduce a deceptively simple yet highly effective prompting strategy, termed question "re-reading". Drawing inspiration from human learning and problem-solving, re-reading entails revisiting the question information embedded within input prompts. This approach aligns seamlessly with the cognitive principle of reinforcement, enabling LLMs to extract deeper insights, identify intricate patterns, establish more nuanced connections, and ultimately enhance their reasoning capabilities across various tasks. Experiments conducted on a series of reasoning benchmarks serve to underscore the effectiveness and generality of our method. Moreover, our findings demonstrate that our approach seamlessly integrates with various language models, though-eliciting prompting methods, and ensemble techniques, further underscoring its versatility and compatibility in the realm of LLMs.

Self-contradictory Hallucinations of Large Language Models: Evaluation, Detection and Mitigation

Large language models (large LMs) are susceptible to producing text with hallucinated content. Self-contradiction, where the LM generates two contradictory sentences within the same context, is an important form of hallucination. In this work, we present a comprehensive analysis on self-contradiction for state-of-the-art, instruction-tuned LMs, including evaluation, detection, and mitigation. To effectively trigger self-contradictions, we design a framework that constrains LMs to generate appropriate sentence pairs. Our evaluation on these sentence pairs reveals that self-contradictions occur frequently across different LMs for both famous and lesser-known topics. Next, we prompt the LMs to detect self-contradictions. Our results indicate that ChatGPT and GPT-4 are able to accurately identify self-contradictions, while Vicuna-13B struggles to do so. For example, with our best prompting method, ChatGPT achieves 91.0% precision and 80.5% recall on the sentence pairs generated by itself. To automatically mitigate self-contradictions, we develop an iterative algorithm that prompts the LMs to remove the detected self-contradictions from the generated text. Our algorithm successfully revises the text such that self-contradictions are significantly reduced, while maintaining its fluency and informativeness. Importantly, our entire pipeline of triggering, detecting, and mitigating self-contradictions is applicable to black-box LMs and does not require any external grounded knowledge.

Understanding prompt engineering may not require rethinking generalization

Zero-shot learning in prompted vision-language models, the practice of crafting prompts to build classifiers without an explicit training process, has achieved impressive performance in many settings. This success presents a seemingly surprising observation: these methods suffer relatively little from overfitting, i.e., when a prompt is manually engineered to achieve low error on a given training set (thus rendering the method no longer actually zero-shot), the approach still performs well on held-out test data. In this paper, we show that we can explain such performance well via recourse to classical PAC-Bayes bounds. Specifically, we show that the discrete nature of prompts, combined with a PAC-Bayes prior given by a language model, results in generalization bounds that are remarkably tight by the standards of the literature: for instance, the generalization bound of an ImageNet classifier is often within a few percentage points of the true test error. We demonstrate empirically that this holds for existing handcrafted prompts and prompts generated through simple greedy search. Furthermore, the resulting bound is well-suited for model selection: the models with the best bound typically also have the best test performance. This work thus provides a possible justification for the widespread practice of prompt engineering, even if it seems that such methods could potentially overfit the training data.

The Unreasonable Effectiveness of Eccentric Automatic Prompts

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Deduction under Perturbed Evidence: Probing Student Simulation Capabilities of Large Language Models

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Reinforcement Learning-based Counter-Misinformation Response Generation: A Case Study of COVID-19 Vaccine Misinformation

The spread of online misinformation threatens public health, democracy, and the broader society. While professional fact-checkers form the first line of defense by fact-checking popular false claims, they do not engage directly in conversations with misinformation spreaders. On the other hand, non-expert ordinary users act as eyes-on-the-ground who proactively counter misinformation -- recent research has shown that 96% counter-misinformation responses are made by ordinary users. However, research also found that 2/3 times, these responses are rude and lack evidence. This work seeks to create a counter-misinformation response generation model to empower users to effectively correct misinformation. This objective is challenging due to the absence of datasets containing ground-truth of ideal counter-misinformation responses, and the lack of models that can generate responses backed by communication theories. In this work, we create two novel datasets of misinformation and counter-misinformation response pairs from in-the-wild social media and crowdsourcing from college-educated students. We annotate the collected data to distinguish poor from ideal responses that are factual, polite, and refute misinformation. We propose MisinfoCorrect, a reinforcement learning-based framework that learns to generate counter-misinformation responses for an input misinformation post. The model rewards the generator to increase the politeness, factuality, and refutation attitude while retaining text fluency and relevancy. Quantitative and qualitative evaluation shows that our model outperforms several baselines by generating high-quality counter-responses. This work illustrates the promise of generative text models for social good -- here, to help create a safe and reliable information ecosystem. The code and data is accessible on https://github.com/claws-lab/MisinfoCorrect.

Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

Thought Propagation: An Analogical Approach to Complex Reasoning with Large Language Models

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Pursuing Counterfactual Fairness via Sequential Autoencoder Across Domains

Recognizing the prevalence of domain shift as a common challenge in machine learning, various domain generalization (DG) techniques have been developed to enhance the performance of machine learning systems when dealing with out-of-distribution (OOD) data. Furthermore, in real-world scenarios, data distributions can gradually change across a sequence of sequential domains. While current methodologies primarily focus on improving model effectiveness within these new domains, they often overlook fairness issues throughout the learning process. In response, we introduce an innovative framework called Counterfactual Fairness-Aware Domain Generalization with Sequential Autoencoder (CDSAE). This approach effectively separates environmental information and sensitive attributes from the embedded representation of classification features. This concurrent separation not only greatly improves model generalization across diverse and unfamiliar domains but also effectively addresses challenges related to unfair classification. Our strategy is rooted in the principles of causal inference to tackle these dual issues. To examine the intricate relationship between semantic information, sensitive attributes, and environmental cues, we systematically categorize exogenous uncertainty factors into four latent variables: 1) semantic information influenced by sensitive attributes, 2) semantic information unaffected by sensitive attributes, 3) environmental cues influenced by sensitive attributes, and 4) environmental cues unaffected by sensitive attributes. By incorporating fairness regularization, we exclusively employ semantic information for classification purposes. Empirical validation on synthetic and real-world datasets substantiates the effectiveness of our approach, demonstrating improved accuracy levels while ensuring the preservation of fairness in the evolving landscape of continuous domains.

Adaptive Chameleon or Stubborn Sloth: Unraveling the Behavior of Large Language Models in Knowledge Clashes

By providing external information to large language models (LLMs), tool augmentation (including retrieval augmentation) has emerged as a promising solution for addressing the limitations of LLMs' static parametric memory. However, how receptive are LLMs to such external evidence, especially when the evidence conflicts with their parametric memory? We present the first comprehensive and controlled investigation into the behavior of LLMs when encountering knowledge conflicts. We propose a systematic framework to elicit high-quality parametric memory from LLMs and construct the corresponding counter-memory, which enables us to conduct a series of controlled experiments. Our investigation reveals seemingly contradicting behaviors of LLMs. On the one hand, different from prior wisdom, we find that LLMs can be highly receptive to external evidence even when that conflicts with their parametric memory, given that the external evidence is coherent and convincing. On the other hand, LLMs also demonstrate a strong confirmation bias when the external evidence contains some information that is consistent with their parametric memory, despite being presented with conflicting evidence at the same time. These results pose important implications that are worth careful consideration for the further development and deployment of tool- and retrieval-augmented LLMs.