Daily Papers

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General Time Series Forecasting Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 28 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The codebase, datasets, and a leaderboard showing all the results in detail will be available soon.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

Time series analysis is of immense importance in extensive applications, such as weather forecasting, anomaly detection, and action recognition. This paper focuses on temporal variation modeling, which is the common key problem of extensive analysis tasks. Previous methods attempt to accomplish this directly from the 1D time series, which is extremely challenging due to the intricate temporal patterns. Based on the observation of multi-periodicity in time series, we ravel out the complex temporal variations into the multiple intraperiod- and interperiod-variations. To tackle the limitations of 1D time series in representation capability, we extend the analysis of temporal variations into the 2D space by transforming the 1D time series into a set of 2D tensors based on multiple periods. This transformation can embed the intraperiod- and interperiod-variations into the columns and rows of the 2D tensors respectively, making the 2D-variations to be easily modeled by 2D kernels. Technically, we propose the TimesNet with TimesBlock as a task-general backbone for time series analysis. TimesBlock can discover the multi-periodicity adaptively and extract the complex temporal variations from transformed 2D tensors by a parameter-efficient inception block. Our proposed TimesNet achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection. Code is available at this repository: https://github.com/thuml/TimesNet.

Foundation models have emerged as a powerful tool for many AI problems. Despite the tremendous success of foundation models, effective adaptation to new tasks, particularly those with limited labels, remains an open question and lacks theoretical understanding. An emerging solution with recent success in vision and NLP involves finetuning a foundation model on a selection of relevant tasks, before its adaptation to a target task with limited labeled samples. In this paper, we study the theoretical justification of this multitask finetuning approach. Our theoretical analysis reveals that with a diverse set of related tasks, this multitask finetuning leads to reduced error in the target task, in comparison to directly adapting the same pretrained model. We quantify the relationship between finetuning tasks and target tasks by diversity and consistency metrics, and further propose a practical task selection algorithm. We substantiate our theoretical claims with extensive empirical evidence. Further, we present results affirming our task selection algorithm adeptly chooses related finetuning tasks, providing advantages to the model performance on target tasks. We believe our study shed new light on the effective adaptation of foundation models to new tasks that lack abundant labels. Our code is available at https://github.com/OliverXUZY/Foudation-Model_Multitask.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

Foundation models have emerged as a promising approach in time series forecasting (TSF). Existing approaches either fine-tune large language models (LLMs) or build large-scale time-series datasets to develop TSF foundation models. However, these methods face challenges due to the severe cross-domain gap or in-domain heterogeneity. In this paper, we explore a new road to building a TSF foundation model from rich and high-quality natural images, based on the intrinsic similarities between images and time series. To bridge the gap between the two domains, we reformulate the TSF task as an image reconstruction task, which is further processed by a visual masked autoencoder (MAE) self-supervised pre-trained on the ImageNet dataset. Surprisingly, without further adaptation in the time-series domain, the proposed VisionTS could achieve superior zero-shot forecasting performance compared to existing TSF foundation models. With minimal fine-tuning, VisionTS could further improve the forecasting and achieve state-of-the-art performance in most cases. These findings suggest that visual models could be a free lunch for TSF and highlight the potential for future cross-domain research between computer vision and TSF. Our code is publicly available at https://github.com/Keytoyze/VisionTS.

In this work, we leverage pre-trained Large Language Models (LLMs) to enhance time-series forecasting. Mirroring the growing interest in unifying models for Natural Language Processing and Computer Vision, we envision creating an analogous model for long-term time-series forecasting. Due to limited large-scale time-series data for building robust foundation models, our approach LLM4TS focuses on leveraging the strengths of pre-trained LLMs. By combining time-series patching with temporal encoding, we have enhanced the capability of LLMs to handle time-series data effectively. Inspired by the supervised fine-tuning in chatbot domains, we prioritize a two-stage fine-tuning process: first conducting supervised fine-tuning to orient the LLM towards time-series data, followed by task-specific downstream fine-tuning. Furthermore, to unlock the flexibility of pre-trained LLMs without extensive parameter adjustments, we adopt several Parameter-Efficient Fine-Tuning (PEFT) techniques. Drawing on these innovations, LLM4TS has yielded state-of-the-art results in long-term forecasting. Our model has also shown exceptional capabilities as both a robust representation learner and an effective few-shot learner, thanks to the knowledge transferred from the pre-trained LLM.

The rapid development of AI systems has been greatly influenced by the emergence of foundation models. A common approach for targeted problems involves fine-tuning these pre-trained foundation models for specific target tasks, resulting in a rapid spread of models fine-tuned across a diverse array of tasks. This work focuses on the problem of merging multiple fine-tunings of the same foundation model derived from a spectrum of auxiliary tasks. We introduce a new simple method, Model Breadcrumbs, which consists of a sparsely defined set of weights that carve out a trajectory within the weight space of a pre-trained model, enhancing task performance when traversed. These breadcrumbs are constructed by subtracting the weights from a pre-trained model before and after fine-tuning, followed by a sparsification process that eliminates weight outliers and negligible perturbations. Our experiments demonstrate the effectiveness of Model Breadcrumbs to simultaneously improve performance across multiple tasks. This contribution aligns with the evolving paradigm of updatable machine learning, reminiscent of the collaborative principles underlying open-source software development, fostering a community-driven effort to reliably update machine learning models. Our method is shown to be more efficient and unlike previous proposals does not require hyperparameter tuning for each new task added. Through extensive experimentation involving various models, tasks, and modalities we establish that integrating Model Breadcrumbs offers a simple, efficient, and highly effective approach for constructing multi-task models and facilitating updates to foundation models.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

The past decade has witnessed significant advances in time series modeling with deep learning. While achieving state-of-the-art results, the best-performing architectures vary highly across applications and domains. Meanwhile, for natural language processing, the Generative Pre-trained Transformer (GPT) has demonstrated impressive performance via training one general-purpose model across various textual datasets. It is intriguing to explore whether GPT-type architectures can be effective for time series, capturing the intrinsic dynamic attributes and leading to significant accuracy improvements. In this paper, we propose a novel framework, TEMPO, that can effectively learn time series representations. We focus on utilizing two essential inductive biases of the time series task for pre-trained models: (i) decomposition of the complex interaction between trend, seasonal and residual components; and (ii) introducing the selection-based prompts to facilitate distribution adaptation in non-stationary time series. TEMPO expands the capability for dynamically modeling real-world temporal phenomena from data within diverse domains. Our experiments demonstrate the superior performance of TEMPO over state-of-the-art methods on a number of time series benchmark datasets. This performance gain is observed not only in standard supervised learning settings but also in scenarios involving previously unseen datasets as well as in scenarios with multi-modal inputs. This compelling finding highlights TEMPO's potential to constitute a foundational model-building framework.

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world small-sample scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progresses have been achieved as the emergence of large language models, exhibiting unprecedented ability in few-shot generalization, scalability, and task generality, which is however absent in time series models. To change the current practices of training small models on specific datasets from scratch, this paper aims at an early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), that is pre-trained by autoregressive next token prediction on large multi-domain datasets, and is fine-tuned to downstream scenarios with promising abilities as an LTSM.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more. In this paper, we propose a framework for rigorously evaluating the capabilities of LLMs on time series understanding, encompassing both univariate and multivariate forms. We introduce a comprehensive taxonomy of time series features, a critical framework that delineates various characteristics inherent in time series data. Leveraging this taxonomy, we have systematically designed and synthesized a diverse dataset of time series, embodying the different outlined features. This dataset acts as a solid foundation for assessing the proficiency of LLMs in comprehending time series. Our experiments shed light on the strengths and limitations of state-of-the-art LLMs in time series understanding, revealing which features these models readily comprehend effectively and where they falter. In addition, we uncover the sensitivity of LLMs to factors including the formatting of the data, the position of points queried within a series and the overall time series length.

This work summarizes two strategies for completing time-series (TS) tasks using today's language model (LLM): LLM-for-TS, design and train a fundamental large model for TS data; TS-for-LLM, enable the pre-trained LLM to handle TS data. Considering the insufficient data accumulation, limited resources, and semantic context requirements, this work focuses on TS-for-LLM methods, where we aim to activate LLM's ability for TS data by designing a TS embedding method suitable for LLM. The proposed method is named TEST. It first tokenizes TS, builds an encoder to embed them by instance-wise, feature-wise, and text-prototype-aligned contrast, and then creates prompts to make LLM more open to embeddings, and finally implements TS tasks. Experiments are carried out on TS classification and forecasting tasks using 8 LLMs with different structures and sizes. Although its results cannot significantly outperform the current SOTA models customized for TS tasks, by treating LLM as the pattern machine, it can endow LLM's ability to process TS data without compromising the language ability. This paper is intended to serve as a foundational work that will inspire further research.

Foundation Models (FMs) are models trained on large corpora of data that, at very large scale, can generalize to new tasks without any task-specific finetuning. As these models continue to grow in size, innovations continue to push the boundaries of what these models can do on language and image tasks. This paper aims to understand an underexplored area of FMs: classical data tasks like cleaning and integration. As a proof-of-concept, we cast five data cleaning and integration tasks as prompting tasks and evaluate the performance of FMs on these tasks. We find that large FMs generalize and achieve SoTA performance on data cleaning and integration tasks, even though they are not trained for these data tasks. We identify specific research challenges and opportunities that these models present, including challenges with private and domain specific data, and opportunities to make data management systems more accessible to non-experts. We make our code and experiments publicly available at: https://github.com/HazyResearch/fm_data_tasks.

Time series data are ubiquitous across a wide range of real-world domains. While real-world time series analysis (TSA) requires human experts to integrate numerical series data with multimodal domain-specific knowledge, most existing TSA models rely solely on numerical data, overlooking the significance of information beyond numerical series. This oversight is due to the untapped potential of textual series data and the absence of a comprehensive, high-quality multimodal dataset. To overcome this obstacle, we introduce Time-MMD, the first multi-domain, multimodal time series dataset covering 9 primary data domains. Time-MMD ensures fine-grained modality alignment, eliminates data contamination, and provides high usability. Additionally, we develop MM-TSFlib, the first multimodal time-series forecasting (TSF) library, seamlessly pipelining multimodal TSF evaluations based on Time-MMD for in-depth analyses. Extensive experiments conducted on Time-MMD through MM-TSFlib demonstrate significant performance enhancements by extending unimodal TSF to multimodality, evidenced by over 15% mean squared error reduction in general, and up to 40% in domains with rich textual data. More importantly, our datasets and library revolutionize broader applications, impacts, research topics to advance TSA. The dataset and library are available at https://github.com/AdityaLab/Time-MMD and https://github.com/AdityaLab/MM-TSFlib.

The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. Our framework facilitates rigorous comparisons, providing new insights on the distinctive characteristics of each model class. For instance, we compare linear attention and selective SSMs, detailing their differences and conditions under which both are equivalent. We also provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. Additionally, we substantiate these new insights with empirical validations and mathematical arguments. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.

Multi-task learning (MTL) has been successfully used in many real-world applications, which aims to simultaneously solve multiple tasks with a single model. The general idea of multi-task learning is designing kinds of global parameter sharing mechanism and task-specific feature extractor to improve the performance of all tasks. However, challenge still remains in balancing the trade-off of various tasks since model performance is sensitive to the relationships between them. Less correlated or even conflict tasks will deteriorate the performance by introducing unhelpful or negative information. Therefore, it is important to efficiently exploit and learn fine-grained feature representation corresponding to each task. In this paper, we propose an Adaptive Pattern Extraction Multi-task (APEM) framework, which is adaptive and flexible for large-scale industrial application. APEM is able to fully utilize the feature information by learning the interactions between the input feature fields and extracted corresponding tasks-specific information. We first introduce a DeepAuto Group Transformer module to automatically and efficiently enhance the feature expressivity with a modified set attention mechanism and a Squeeze-and-Excitation operation. Second, explicit Pattern Selector is introduced to further enable selectively feature representation learning by adaptive task-indicator vectors. Empirical evaluations show that APEM outperforms the state-of-the-art MTL methods on public and real-world financial services datasets. More importantly, we explore the online performance of APEM in a real industrial-level recommendation scenario.

Missing values, irregularly collected samples, and multi-resolution signals commonly occur in multivariate time series data, making predictive tasks difficult. These challenges are especially prevalent in the healthcare domain, where patients' vital signs and electronic records are collected at different frequencies and have occasionally missing information due to the imperfections in equipment or patient circumstances. Researchers have handled each of these issues differently, often handling missing data through mean value imputation and then using sequence models over the multivariate signals while ignoring the different resolution of signals. We propose a unified model named Multi-resolution Flexible Irregular Time series Network (Multi-FIT). The building block for Multi-FIT is the FIT network. The FIT network creates an informative dense representation at each time step using signal information such as last observed value, time difference since the last observed time stamp and overall mean for the signal. Vertical FIT (FIT-V) is a variant of FIT which also models the relationship between different temporal signals while creating the informative dense representations for the signal. The multi-FIT model uses multiple FIT networks for sets of signals with different resolutions, further facilitating the construction of flexible representations. Our model has three main contributions: a.) it does not impute values but rather creates informative representations to provide flexibility to the model for creating task-specific representations b.) it models the relationship between different signals in the form of support signals c.) it models different resolutions in parallel before merging them for the final prediction task. The FIT, FIT-V and Multi-FIT networks improve upon the state-of-the-art models for three predictive tasks, including the forecasting of patient survival.

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

Inspired by recent advancements in large language models (LLMs) for Natural Language Processing (NLP), there has been a surge in research focused on developing foundational models for time series forecasting. One approach involves training LLM architectures on tokenized time series data using cross-entropy loss. Although this method has demonstrated promising results, cross-entropy loss is primarily designed for classification tasks and does not account for the distance between classes. To address this limitation, we propose using the Wasserstein loss for such architectures. To validate our approach, we fine-tuned a foundational time series model on 22 zero-shot datasets, comparing the performance of cross-entropy loss with that of Wasserstein loss. Our results demonstrate that replacing cross-entropy loss with Wasserstein loss significantly improves point estimation.

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

Foundation models encompass an extensive knowledge base and offer remarkable transferability. However, this knowledge becomes outdated or insufficient over time. The challenge lies in continuously updating foundation models to accommodate novel information while retaining their original capabilities. Leveraging the fact that foundation models have initial knowledge on various tasks and domains, we propose a novel approach that, instead of updating all parameters equally, localizes the updates to a sparse set of parameters relevant to the task being learned. We strike a balance between efficiency and new task performance, while maintaining the transferability and generalizability of foundation models. We extensively evaluate our method on foundational vision-language models with a diverse spectrum of continual learning tasks. Our method achieves improvements on the accuracy of the newly learned tasks up to 7% while preserving the pretraining knowledge with a negligible decrease of 0.9% on a representative control set accuracy.

Traditional multi-task learning (MTL) methods use dense networks that use the same set of shared weights across several different tasks. This often creates interference where two or more tasks compete to pull model parameters in different directions. In this work, we study whether sparsely activated Mixture-of-Experts (MoE) improve multi-task learning by specializing some weights for learning shared representations and using the others for learning task-specific information. To this end, we devise task-aware gating functions to route examples from different tasks to specialized experts which share subsets of network weights conditioned on the task. This results in a sparsely activated multi-task model with a large number of parameters, but with the same computational cost as that of a dense model. We demonstrate such sparse networks to improve multi-task learning along three key dimensions: (i) transfer to low-resource tasks from related tasks in the training mixture; (ii) sample-efficient generalization to tasks not seen during training by making use of task-aware routing from seen related tasks; (iii) robustness to the addition of unrelated tasks by avoiding catastrophic forgetting of existing tasks.

Human experts typically integrate numerical and textual multimodal information to analyze time series. However, most traditional deep learning predictors rely solely on unimodal numerical data, using a fixed-length window for training and prediction on a single dataset, and cannot adapt to different scenarios. The powered pre-trained large language model has introduced new opportunities for time series analysis. Yet, existing methods are either inefficient in training, incapable of handling textual information, or lack zero-shot forecasting capability. In this paper, we innovatively model time series as a foreign language and construct ChatTime, a unified framework for time series and text processing. As an out-of-the-box multimodal time series foundation model, ChatTime provides zero-shot forecasting capability and supports bimodal input/output for both time series and text. We design a series of experiments to verify the superior performance of ChatTime across multiple tasks and scenarios, and create four multimodal datasets to address data gaps. The experimental results demonstrate the potential and utility of ChatTime.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Multi-horizon forecasting problems often contain a complex mix of inputs -- including static (i.e. time-invariant) covariates, known future inputs, and other exogenous time series that are only observed historically -- without any prior information on how they interact with the target. While several deep learning models have been proposed for multi-step prediction, they typically comprise black-box models which do not account for the full range of inputs present in common scenarios. In this paper, we introduce the Temporal Fusion Transformer (TFT) -- a novel attention-based architecture which combines high-performance multi-horizon forecasting with interpretable insights into temporal dynamics. To learn temporal relationships at different scales, the TFT utilizes recurrent layers for local processing and interpretable self-attention layers for learning long-term dependencies. The TFT also uses specialized components for the judicious selection of relevant features and a series of gating layers to suppress unnecessary components, enabling high performance in a wide range of regimes. On a variety of real-world datasets, we demonstrate significant performance improvements over existing benchmarks, and showcase three practical interpretability use-cases of TFT.

In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and classification, forecasting and missing value imputation. By evaluating our models on several benchmark datasets for multivariate time series regression and classification, we show that not only does our modeling approach represent the most successful method employing unsupervised learning of multivariate time series presented to date, but also that it exceeds the current state-of-the-art performance of supervised methods; it does so even when the number of training samples is very limited, while offering computational efficiency. Finally, we demonstrate that unsupervised pre-training of our transformer models offers a substantial performance benefit over fully supervised learning, even without leveraging additional unlabeled data, i.e., by reusing the same data samples through the unsupervised objective.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

The widespread adoption of scalable mobile sensing has led to large amounts of time series data for real-world applications. A fundamental application is multivariate time series forecasting (MTSF), which aims to predict future time series values based on historical observations. Existing MTSF methods suffer from limited parameterization and small-scale training data. Recently, Large language models (LLMs) have been introduced in time series, which achieve promising forecasting performance but incur heavy computational costs. To solve these challenges, we propose TimeCMA, an LLM-empowered framework for time series forecasting with cross-modality alignment. We design a dual-modality encoding module with two branches, where the time series encoding branch extracts relatively low-quality yet pure embeddings of time series through an inverted Transformer. In addition, the LLM-empowered encoding branch wraps the same time series as prompts to obtain high-quality yet entangled prompt embeddings via a Pre-trained LLM. Then, we design a cross-modality alignment module to retrieve high-quality and pure time series embeddings from the prompt embeddings. Moreover, we develop a time series forecasting module to decode the aligned embeddings while capturing dependencies among multiple variables for forecasting. Notably, we tailor the prompt to encode sufficient temporal information into a last token and design the last token embedding storage to reduce computational costs. Extensive experiments on real data offer insight into the accuracy and efficiency of the proposed framework.

We present a self-supervised, time-to-event (TTE) foundation model called MOTOR (Many Outcome Time Oriented Representations) which is pretrained on timestamped sequences of events in electronic health records (EHR) and health insurance claims. TTE models are used for estimating the probability distribution of the time until a specific event occurs, which is an important task in medical settings. TTE models provide many advantages over classification using fixed time horizons, including naturally handling censored observations, but are challenging to train with limited labeled data. MOTOR addresses this challenge by pretraining on up to 55M patient records (9B clinical events). We evaluate MOTOR's transfer learning performance on 19 tasks, across 3 patient databases (a private EHR system, MIMIC-IV, and Merative claims data). Task-specific models adapted from MOTOR improve time-dependent C statistics by 4.6% over state-of-the-art, improve label efficiency by up to 95% ,and are more robust to temporal distributional shifts. We further evaluate cross-site portability by adapting our MOTOR foundation model for six prediction tasks on the MIMIC-IV dataset, where it outperforms all baselines. MOTOR is the first foundation model for medical TTE predictions and we release a 143M parameter pretrained model for research use at [redacted URL].

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

The industry is rich in cases when we are required to make forecasting for large amounts of time series at once. However, we might be in a situation where we can not afford to train a separate model for each of them. Such issue in time series modeling remains without due attention. The remedy for this setting is the establishment of a foundation model. Such a model is expected to work in zero-shot and few-shot regimes. However, what should we take as a training dataset for such kind of model? Witnessing the benefits from the enrichment of NLP datasets with artificially-generated data, we might want to adopt their experience for time series. In contrast to natural language, the process of generation of synthetic time series data is even more favorable because it provides full control of series patterns, time horizons, and number of samples. In this work, we consider the essential question if it is advantageous to train a foundation model on synthetic data or it is better to utilize only a limited number of real-life examples. Our experiments are conducted only for regular time series and speak in favor of leveraging solely the real time series. Moreover, the choice of the proper source dataset strongly influences the performance during inference. When provided access even to a limited quantity of short time series data, employing it within a supervised framework yields more favorable results than training on a larger volume of synthetic data. The code for our experiments is publicly available on Github https://github.com/sb-ai-lab/synthesize_or_not.

Massively multitask neural architectures provide a learning framework for drug discovery that synthesizes information from many distinct biological sources. To train these architectures at scale, we gather large amounts of data from public sources to create a dataset of nearly 40 million measurements across more than 200 biological targets. We investigate several aspects of the multitask framework by performing a series of empirical studies and obtain some interesting results: (1) massively multitask networks obtain predictive accuracies significantly better than single-task methods, (2) the predictive power of multitask networks improves as additional tasks and data are added, (3) the total amount of data and the total number of tasks both contribute significantly to multitask improvement, and (4) multitask networks afford limited transferability to tasks not in the training set. Our results underscore the need for greater data sharing and further algorithmic innovation to accelerate the drug discovery process.

Scientific literature understanding tasks have gained significant attention due to their potential to accelerate scientific discovery. Pre-trained language models (LMs) have shown effectiveness in these tasks, especially when tuned via contrastive learning. However, jointly utilizing pre-training data across multiple heterogeneous tasks (e.g., extreme classification, citation prediction, and literature search) remains largely unexplored. To bridge this gap, we propose a multi-task contrastive learning framework, SciMult, with a focus on facilitating common knowledge sharing across different scientific literature understanding tasks while preventing task-specific skills from interfering with each other. To be specific, we explore two techniques -- task-aware specialization and instruction tuning. The former adopts a Mixture-of-Experts Transformer architecture with task-aware sub-layers; the latter prepends task-specific instructions to the input text so as to produce task-aware outputs. Extensive experiments on a comprehensive collection of benchmark datasets verify the effectiveness of our task-aware specialization strategy in various tasks, where we outperform state-of-the-art scientific LMs.

With large Foundation Models (FMs), language technologies (AI in general) are entering a new paradigm: eliminating the need for developing large-scale task-specific datasets and supporting a variety of tasks through set-ups ranging from zero-shot to few-shot learning. However, understanding FMs capabilities requires a systematic benchmarking effort by comparing FMs performance with the state-of-the-art (SOTA) task-specific models. With that goal, past work focused on the English language and included a few efforts with multiple languages. Our study contributes to ongoing research by evaluating FMs performance for standard Arabic NLP and Speech processing, including a range of tasks from sequence tagging to content classification across diverse domains. We start with zero-shot learning using GPT-3.5-turbo, Whisper, and USM, addressing 33 unique tasks using 59 publicly available datasets resulting in 96 test setups. For a few tasks, FMs performs on par or exceeds the performance of the SOTA models but for the majority it under-performs. Given the importance of prompt for the FMs performance, we discuss our prompt strategies in detail and elaborate on our findings. Our future work on Arabic AI will explore few-shot prompting, expand the range of tasks, and investigate additional open-source models.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

Foundation models are redefining how AI systems are built. Practitioners now follow a standard procedure to build their machine learning solutions: from a pre-trained foundation model, they fine-tune the weights on the target task of interest. So, the Internet is swarmed by a handful of foundation models fine-tuned on many diverse tasks: these individual fine-tunings exist in isolation without benefiting from each other. In our opinion, this is a missed opportunity, as these specialized models contain rich and diverse features. In this paper, we thus propose model ratatouille, a new strategy to recycle the multiple fine-tunings of the same foundation model on diverse auxiliary tasks. Specifically, we repurpose these auxiliary weights as initializations for multiple parallel fine-tunings on the target task; then, we average all fine-tuned weights to obtain the final model. This recycling strategy aims at maximizing the diversity in weights by leveraging the diversity in auxiliary tasks. Empirically, it improves the state of the art on the reference DomainBed benchmark for out-of-distribution generalization. Looking forward, this work contributes to the emerging paradigm of updatable machine learning where, akin to open-source software development, the community collaborates to reliably update machine learning models.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

Keeping track of all relevant recent publications and experimental results for a research area is a challenging task. Prior work has demonstrated the efficacy of information extraction models in various scientific areas. Recently, several datasets have been released for the yet understudied materials science domain. However, these datasets focus on sub-problems such as parsing synthesis procedures or on sub-domains, e.g., solid oxide fuel cells. In this resource paper, we present MuLMS, a new dataset of 50 open-access articles, spanning seven sub-domains of materials science. The corpus has been annotated by domain experts with several layers ranging from named entities over relations to frame structures. We present competitive neural models for all tasks and demonstrate that multi-task training with existing related resources leads to benefits.

Artificial Intelligence (AI) has made incredible progress recently. On the one hand, advanced foundation models like ChatGPT can offer powerful conversation, in-context learning and code generation abilities on a broad range of open-domain tasks. They can also generate high-level solution outlines for domain-specific tasks based on the common sense knowledge they have acquired. However, they still face difficulties with some specialized tasks because they lack enough domain-specific data during pre-training or they often have errors in their neural network computations on those tasks that need accurate executions. On the other hand, there are also many existing models and systems (symbolic-based or neural-based) that can do some domain-specific tasks very well. However, due to the different implementation or working mechanisms, they are not easily accessible or compatible with foundation models. Therefore, there is a clear and pressing need for a mechanism that can leverage foundation models to propose task solution outlines and then automatically match some of the sub-tasks in the outlines to the off-the-shelf models and systems with special functionalities to complete them. Inspired by this, we introduce TaskMatrix.AI as a new AI ecosystem that connects foundation models with millions of APIs for task completion. Unlike most previous work that aimed to improve a single AI model, TaskMatrix.AI focuses more on using existing foundation models (as a brain-like central system) and APIs of other AI models and systems (as sub-task solvers) to achieve diversified tasks in both digital and physical domains. As a position paper, we will present our vision of how to build such an ecosystem, explain each key component, and use study cases to illustrate both the feasibility of this vision and the main challenges we need to address next.

Foundation Models (FMs) serve as a general class for the development of artificial intelligence systems, offering broad potential for generalization across a spectrum of downstream tasks. Despite extensive research into self-supervised learning as the cornerstone of FMs, several outstanding issues persist in Graph Foundation Models that rely on graph self-supervised learning, namely: 1) Homogenization. The extent of generalization capability on downstream tasks remains unclear. 2) Scalability. It is unknown how effectively these models can scale to large datasets. 3) Efficiency. The training time and memory usage of these models require evaluation. 4) Training Stop Criteria. Determining the optimal stopping strategy for pre-training across multiple tasks to maximize performance on downstream tasks. To address these questions, we have constructed a rigorous benchmark that thoroughly analyzes and studies the generalization and scalability of self-supervised Graph Neural Network (GNN) models. Regarding generalization, we have implemented and compared the performance of various self-supervised GNN models, trained to generate node representations, across tasks such as node classification, link prediction, and node clustering. For scalability, we have compared the performance of various models after training using full-batch and mini-batch strategies. Additionally, we have assessed the training efficiency of these models by conducting experiments to test their GPU memory usage and throughput. Through these experiments, we aim to provide insights to motivate future research. The code for this benchmark is publicly available at https://github.com/NYUSHCS/GraphFM.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Recent advancements in the collection and analysis of sequential educational data have brought time series analysis to a pivotal position in educational research, highlighting its essential role in facilitating data-driven decision-making. However, there is a lack of comprehensive summaries that consolidate these advancements. To the best of our knowledge, this paper is the first to provide a comprehensive review of time series analysis techniques specifically within the educational context. We begin by exploring the landscape of educational data analytics, categorizing various data sources and types relevant to education. We then review four prominent time series methods-forecasting, classification, clustering, and anomaly detection-illustrating their specific application points in educational settings. Subsequently, we present a range of educational scenarios and applications, focusing on how these methods are employed to address diverse educational tasks, which highlights the practical integration of multiple time series methods to solve complex educational problems. Finally, we conclude with a discussion on future directions, including personalized learning analytics, multimodal data fusion, and the role of large language models (LLMs) in educational time series. The contributions of this paper include a detailed taxonomy of educational data, a synthesis of time series techniques with specific educational applications, and a forward-looking perspective on emerging trends and future research opportunities in educational analysis. The related papers and resources are available and regularly updated at the project page.

Recent progress in neural forecasting accelerated improvements in the performance of large-scale forecasting systems. Yet, long-horizon forecasting remains a very difficult task. Two common challenges afflicting the task are the volatility of the predictions and their computational complexity. We introduce N-HiTS, a model which addresses both challenges by incorporating novel hierarchical interpolation and multi-rate data sampling techniques. These techniques enable the proposed method to assemble its predictions sequentially, emphasizing components with different frequencies and scales while decomposing the input signal and synthesizing the forecast. We prove that the hierarchical interpolation technique can efficiently approximate arbitrarily long horizons in the presence of smoothness. Additionally, we conduct extensive large-scale dataset experiments from the long-horizon forecasting literature, demonstrating the advantages of our method over the state-of-the-art methods, where N-HiTS provides an average accuracy improvement of almost 20% over the latest Transformer architectures while reducing the computation time by an order of magnitude (50 times). Our code is available at bit.ly/3VA5DoT

We present time vectors, a simple tool to customize language models to new time periods. Time vectors are created by finetuning a language model on data from a single time (e.g., a year or month), and then subtracting the weights of the original pretrained model. This vector specifies a direction in weight space that, as our experiments show, improves performance on text from that time period. Time vectors specialized to adjacent time periods appear to be positioned closer together in a manifold. Using this structure, we interpolate between time vectors to induce new models that perform better on intervening and future time periods, without any additional training. We demonstrate the consistency of our findings across different tasks, domains, model sizes, and time scales. Our results suggest that time is encoded in the weight space of finetuned models.

Multi-modal large language models (MLLMs) have enabled numerous advances in understanding and reasoning in domains like vision, but we have not yet seen this broad success for time-series. Although prior works on time-series MLLMs have shown promising performance in time-series forecasting, very few works show how an LLM could be used for time-series reasoning in natural language. We propose a novel multi-modal time-series LLM approach that learns generalizable information across various domains with powerful zero-shot performance. First, we train a lightweight time-series encoder on top of an LLM to directly extract time-series information. Then, we fine-tune our model with chain-of-thought augmented time-series tasks to encourage the model to generate reasoning paths. We show that our model learns a latent representation that reflects specific time-series features (e.g. slope, frequency), as well as outperforming GPT-4o on a set of zero-shot reasoning tasks on a variety of domains.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

Transformers have gained popularity in time series forecasting for their ability to capture long-sequence interactions. However, their high memory and computing requirements pose a critical bottleneck for long-term forecasting. To address this, we propose TSMixer, a lightweight neural architecture exclusively composed of multi-layer perceptron (MLP) modules for multivariate forecasting and representation learning on patched time series. Inspired by MLP-Mixer's success in computer vision, we adapt it for time series, addressing challenges and introducing validated components for enhanced accuracy. This includes a novel design paradigm of attaching online reconciliation heads to the MLP-Mixer backbone, for explicitly modeling the time-series properties such as hierarchy and channel-correlations. We also propose a novel Hybrid channel modeling and infusion of a simple gating approach to effectively handle noisy channel interactions and generalization across diverse datasets. By incorporating these lightweight components, we significantly enhance the learning capability of simple MLP structures, outperforming complex Transformer models with minimal computing usage. Moreover, TSMixer's modular design enables compatibility with both supervised and masked self-supervised learning methods, making it a promising building block for time-series Foundation Models. TSMixer outperforms state-of-the-art MLP and Transformer models in forecasting by a considerable margin of 8-60%. It also outperforms the latest strong benchmarks of Patch-Transformer models (by 1-2%) with a significant reduction in memory and runtime (2-3X). The source code of our model is officially released as PatchTSMixer in the HuggingFace. Model: https://huggingface.co/docs/transformers/main/en/model_doc/patchtsmixer Examples: https://github.com/ibm/tsfm/#notebooks-links

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Multi-Task Learning (MTL) is a powerful technique that has gained popularity due to its performance improvement over traditional Single-Task Learning (STL). However, MTL is often challenging because there is an exponential number of possible task groupings, which can make it difficult to choose the best one, and some groupings might produce performance degradation due to negative interference between tasks. Furthermore, existing solutions are severely suffering from scalability issues, limiting any practical application. In our paper, we propose a new data-driven method that addresses these challenges and provides a scalable and modular solution for classification task grouping based on hand-crafted features, specifically Data Maps, which capture the training behavior for each classification task during the MTL training. We experiment with the method demonstrating its effectiveness, even on an unprecedented number of tasks (up to 100).

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine learning is witnessing a paradigm transition from shallow methods to more sophisticated deep learning approaches. The capabilities of foundation models to generalize and adapt motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm. This paradigm envisions models that are pre-trained on extensive graph data and can be adapted for various graph tasks. Despite this burgeoning interest, there is a noticeable lack of clear definitions and systematic analyses pertaining to this new domain. To this end, this article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies. We proceed to classify the existing work related to GFMs into three distinct categories, based on their dependence on graph neural networks and large language models. In addition to providing a thorough review of the current state of GFMs, this article also outlooks potential avenues for future research in this rapidly evolving domain.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

In this study, we propose Feature-aligned N-BEATS as a domain generalization model for univariate time series forecasting problems. The proposed model is an extension of the doubly residual stacking architecture of N-BEATS (Oreshkin et al. [34]) into a representation learning framework. The model is a new structure that involves marginal feature probability measures (i.e., pushforward measures of multiple source domains) induced by the intricate composition of residual operators of N-BEATS in each stack and aligns them stack-wise via an entropic regularized Wasserstein distance referred to as the Sinkhorn divergence (Genevay et al. [14]). The loss function consists of a typical forecasting loss for multiple source domains and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS's interpretable design. We conduct a comprehensive experimental evaluation of the proposed approach and the results demonstrate the model's forecasting and generalization capabilities in comparison with methods based on the original N-BEATS.

Can meta-learning discover generic ways of processing time series (TS) from a diverse dataset so as to greatly improve generalization on new TS coming from different datasets? This work provides positive evidence to this using a broad meta-learning framework which we show subsumes many existing meta-learning algorithms. Our theoretical analysis suggests that residual connections act as a meta-learning adaptation mechanism, generating a subset of task-specific parameters based on a given TS input, thus gradually expanding the expressive power of the architecture on-the-fly. The same mechanism is shown via linearization analysis to have the interpretation of a sequential update of the final linear layer. Our empirical results on a wide range of data emphasize the importance of the identified meta-learning mechanisms for successful zero-shot univariate forecasting, suggesting that it is viable to train a neural network on a source TS dataset and deploy it on a different target TS dataset without retraining, resulting in performance that is at least as good as that of state-of-practice univariate forecasting models.

Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared representation that filters out unwanted variability among subjects. Some recent work has implemented probabilistic models to extract a shared representation in task fMRI. In the present work, we improve upon these models by incorporating temporal information in the common latent structures. We introduce a new model, Shared Gaussian Process Factor Analysis (S-GPFA), that discovers shared latent trajectories and subject-specific functional topographies, while modelling temporal correlation in fMRI data. We demonstrate the efficacy of our model in revealing ground truth latent structures using simulated data, and replicate experimental performance of time-segment matching and inter-subject similarity on the publicly available Raider and Sherlock datasets. We further test the utility of our model by analyzing its learned model parameters in the large multi-site SPINS dataset, on a social cognition task from participants with and without schizophrenia.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

In this paper, we empirically study the optimization dynamics of multi-task learning, particularly focusing on those that govern a collection of tasks with significant data imbalance. We present a simple yet effective method of pre-training on high-resource tasks, followed by fine-tuning on a mixture of high/low-resource tasks. We provide a thorough empirical study and analysis of this method's benefits showing that it achieves consistent improvements relative to the performance trade-off profile of standard static weighting. We analyze under what data regimes this method is applicable and show its improvements empirically in neural machine translation (NMT) and multi-lingual language modeling.

Recent years have seen significant advancements in foundation models through generative pre-training, yet algorithmic innovation in this space has largely stagnated around autoregressive models for discrete signals and diffusion models for continuous signals. This stagnation creates a bottleneck that prevents us from fully unlocking the potential of rich multi-modal data, which in turn limits the progress on multimodal intelligence. We argue that an inference-first perspective, which prioritizes scaling efficiency during inference time across sequence length and refinement steps, can inspire novel generative pre-training algorithms. Using Inductive Moment Matching (IMM) as a concrete example, we demonstrate how addressing limitations in diffusion models' inference process through targeted modifications yields a stable, single-stage algorithm that achieves superior sample quality with over an order of magnitude greater inference efficiency.

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

This position paper explores the rapid development of Foundation Models (FMs) in AI and their implications for intelligence and reasoning. It examines the characteristics of FMs, including their training on vast datasets and use of embedding spaces to capture semantic relationships. The paper discusses recent advancements in FMs' reasoning abilities which we argue cannot be attributed to increased model size but to novel training techniques which yield learning phenomena like grokking. It also addresses the challenges in benchmarking FMs and compares their structure to the human brain. We argue that while FMs show promising developments in reasoning and knowledge representation, understanding their inner workings remains a significant challenge, similar to ongoing efforts in neuroscience to comprehend human brain function. Despite having some similarities, fundamental differences between FMs and the structure of human brain warn us against making direct comparisons or expecting neuroscience to provide immediate insights into FM function.

Triggered by the realization that AI emulators can rival the performance of traditional numerical weather prediction models running on HPC systems, there is now an increasing number of large AI models that address use cases such as forecasting, downscaling, or nowcasting. While the parallel developments in the AI literature focus on foundation models -- models that can be effectively tuned to address multiple, different use cases -- the developments on the weather and climate side largely focus on single-use cases with particular emphasis on mid-range forecasting. We close this gap by introducing Prithvi WxC, a 2.3 billion parameter foundation model developed using 160 variables from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Prithvi WxC employs an encoder-decoder-based architecture, incorporating concepts from various recent transformer models to effectively capture both regional and global dependencies in the input data. The model has been designed to accommodate large token counts to model weather phenomena in different topologies at fine resolutions. Furthermore, it is trained with a mixed objective that combines the paradigms of masked reconstruction with forecasting. We test the model on a set of challenging downstream tasks namely: Autoregressive rollout forecasting, Downscaling, Gravity wave flux parameterization, and Extreme events estimation. The pretrained model with 2.3 billion parameters, along with the associated fine-tuning workflows, has been publicly released as an open-source contribution via Hugging Face.

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

Existing benchmarks for evaluating foundation models mainly focus on single-document, text-only tasks. However, they often fail to fully capture the complexity of research workflows, which typically involve interpreting non-textual data and gathering information across multiple documents. To address this gap, we introduce M3SciQA, a multi-modal, multi-document scientific question answering benchmark designed for a more comprehensive evaluation of foundation models. M3SciQA consists of 1,452 expert-annotated questions spanning 70 natural language processing paper clusters, where each cluster represents a primary paper along with all its cited documents, mirroring the workflow of comprehending a single paper by requiring multi-modal and multi-document data. With M3SciQA, we conduct a comprehensive evaluation of 18 foundation models. Our results indicate that current foundation models still significantly underperform compared to human experts in multi-modal information retrieval and in reasoning across multiple scientific documents. Additionally, we explore the implications of these findings for the future advancement of applying foundation models in multi-modal scientific literature analysis.

Recent approaches to multi-task learning (MTL) have focused on modelling connections between tasks at the decoder level. This leads to a tight coupling between tasks, which need retraining if a new task is inserted or removed. We argue that MTL is a stepping stone towards universal feature learning (UFL), which is the ability to learn generic features that can be applied to new tasks without retraining. We propose Medusa to realize this goal, designing task heads with dual attention mechanisms. The shared feature attention masks relevant backbone features for each task, allowing it to learn a generic representation. Meanwhile, a novel Multi-Scale Attention head allows the network to better combine per-task features from different scales when making the final prediction. We show the effectiveness of Medusa in UFL (+13.18% improvement), while maintaining MTL performance and being 25% more efficient than previous approaches.

Transformers have been actively studied for time-series forecasting in recent years. While often showing promising results in various scenarios, traditional Transformers are not designed to fully exploit the characteristics of time-series data and thus suffer some fundamental limitations, e.g., they generally lack of decomposition capability and interpretability, and are neither effective nor efficient for long-term forecasting. In this paper, we propose ETSFormer, a novel time-series Transformer architecture, which exploits the principle of exponential smoothing in improving Transformers for time-series forecasting. In particular, inspired by the classical exponential smoothing methods in time-series forecasting, we propose the novel exponential smoothing attention (ESA) and frequency attention (FA) to replace the self-attention mechanism in vanilla Transformers, thus improving both accuracy and efficiency. Based on these, we redesign the Transformer architecture with modular decomposition blocks such that it can learn to decompose the time-series data into interpretable time-series components such as level, growth and seasonality. Extensive experiments on various time-series benchmarks validate the efficacy and advantages of the proposed method. Code is available at https://github.com/salesforce/ETSformer.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

Training AI models that generalize across tasks and domains has long been among the open problems driving AI research. The emergence of Foundation Models made it easier to obtain expert models for a given task, but the heterogeneity of data that may be encountered at test time often means that any single expert is insufficient. We consider the Fusion of Experts (FoE) problem of fusing outputs of expert models with complementary knowledge of the data distribution and formulate it as an instance of supervised learning. Our method is applicable to both discriminative and generative tasks and leads to significant performance improvements in image and text classification, text summarization, multiple-choice QA, and automatic evaluation of generated text. We also extend our method to the "frugal" setting where it is desired to reduce the number of expert model evaluations at test time.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

Conventional Time Series Classification (TSC) methods are often black boxes that obscure inherent interpretation of their decision-making processes. In this work, we leverage Multiple Instance Learning (MIL) to overcome this issue, and propose a new framework called MILLET: Multiple Instance Learning for Locally Explainable Time series classification. We apply MILLET to existing deep learning TSC models and show how they become inherently interpretable without compromising (and in some cases, even improving) predictive performance. We evaluate MILLET on 85 UCR TSC datasets and also present a novel synthetic dataset that is specially designed to facilitate interpretability evaluation. On these datasets, we show MILLET produces sparse explanations quickly that are of higher quality than other well-known interpretability methods. To the best of our knowledge, our work with MILLET, which is available on GitHub (https://github.com/JAEarly/MILTimeSeriesClassification), is the first to develop general MIL methods for TSC and apply them to an extensive variety of domains

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Foundation Models (FMs) have demonstrated unprecedented capabilities including zero-shot learning, high fidelity data synthesis, and out of domain generalization. However, as we show in this paper, FMs still have poor out-of-the-box performance on expert tasks (e.g. retrieval of car manuals technical illustrations from language queries), data for which is either unseen or belonging to a long-tail part of the data distribution of the huge datasets used for FM pre-training. This underlines the necessity to explicitly evaluate and finetune FMs on such expert tasks, arguably ones that appear the most in practical real-world applications. In this paper, we propose a first of its kind FETA benchmark built around the task of teaching FMs to understand technical documentation, via learning to match their graphical illustrations to corresponding language descriptions. Our FETA benchmark focuses on text-to-image and image-to-text retrieval in public car manuals and sales catalogue brochures. FETA is equipped with a procedure for completely automatic annotation extraction (code would be released upon acceptance), allowing easy extension of FETA to more documentation types and application domains in the future. Our automatic annotation leads to an automated performance metric shown to be consistent with metrics computed on human-curated annotations (also released). We provide multiple baselines and analysis of popular FMs on FETA leading to several interesting findings that we believe would be very valuable to the FM community, paving the way towards real-world application of FMs for practical expert tasks currently 'overlooked' by standard benchmarks focusing on common objects.

Multi-task learning has the potential to improve generalization by maximizing positive transfer between tasks while reducing task interference. Fully achieving this potential is hindered by manually designed architectures that remain static throughout training. On the contrary, learning in the brain occurs through structural changes that are in tandem with changes in synaptic strength. Thus, we propose Multi-Task Structural Learning (MTSL) that simultaneously learns the multi-task architecture and its parameters. MTSL begins with an identical single-task network for each task and alternates between a task-learning phase and a structural-learning phase. In the task learning phase, each network specializes in the corresponding task. In each of the structural learning phases, starting from the earliest layer, locally similar task layers first transfer their knowledge to a newly created group layer before being removed. MTSL then uses the group layer in place of the corresponding removed task layers and moves on to the next layers. Our empirical results show that MTSL achieves competitive generalization with various baselines and improves robustness to out-of-distribution data.

Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art (SOTA) performance on standard benchmarks. However, these LLM-based models have a significant drawback due to the large model size, with the number of trainable parameters in the millions. In this paper, we propose an alternative approach to leveraging the success of language modeling in the time series domain. Instead of fine-tuning LLMs, we utilize a language embedding model to embed time series and then pair the embeddings with a simple classification head composed of convolutional neural networks (CNN) and multilayer perceptron (MLP). We conducted extensive experiments on well-established time series classification benchmark datasets. We demonstrated LETS-C not only outperforms the current SOTA in classification accuracy but also offers a lightweight solution, using only 14.5% of the trainable parameters on average compared to the SOTA model. Our findings suggest that leveraging language encoders to embed time series data, combined with a simple yet effective classification head, offers a promising direction for achieving high-performance time series classification while maintaining a lightweight model architecture.

AI systems are notorious for their fragility; minor input changes can potentially cause major output swings. When such systems are deployed in critical areas like finance, the consequences of their uncertain behavior could be severe. In this paper, we focus on multi-modal time-series forecasting, where imprecision due to noisy or incorrect data can lead to erroneous predictions, impacting stakeholders such as analysts, investors, and traders. Recently, it has been shown that beyond numeric data, graphical transformations can be used with advanced visual models to achieve better performance. In this context, we introduce a rating methodology to assess the robustness of Multi-Modal Time-Series Forecasting Models (MM-TSFM) through causal analysis, which helps us understand and quantify the isolated impact of various attributes on the forecasting accuracy of MM-TSFM. We apply our novel rating method on a variety of numeric and multi-modal forecasting models in a large experimental setup (six input settings of control and perturbations, ten data distributions, time series from six leading stocks in three industries over a year of data, and five time-series forecasters) to draw insights on robust forecasting models and the context of their strengths. Within the scope of our study, our main result is that multi-modal (numeric + visual) forecasting, which was found to be more accurate than numeric forecasting in previous studies, can also be more robust in diverse settings. Our work will help different stakeholders of time-series forecasting understand the models` behaviors along trust (robustness) and accuracy dimensions to select an appropriate model for forecasting using our rating method, leading to improved decision-making.

We build upon time-series classification by leveraging the capabilities of Vision Language Models (VLMs). We find that VLMs produce competitive results after two or less epochs of fine-tuning. We develop a novel approach that incorporates graphical data representations as images in conjunction with numerical data. This approach is rooted in the hypothesis that graphical representations can provide additional contextual information that numerical data alone may not capture. Additionally, providing a graphical representation can circumvent issues such as limited context length faced by LLMs. To further advance this work, we implemented a scalable end-to-end pipeline for training on different scenarios, allowing us to isolate the most effective strategies for transferring learning capabilities from LLMs to Time Series Classification (TSC) tasks. Our approach works with univariate and multivariate time-series data. In addition, we conduct extensive and practical experiments to show how this approach works for time-series classification and generative labels.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series. We present TimeX, a time series consistency model for training explainers. TimeX trains an interpretable surrogate to mimic the behavior of a pretrained time series model. It addresses the issue of model faithfulness by introducing model behavior consistency, a novel formulation that preserves relations in the latent space induced by the pretrained model with relations in the latent space induced by TimeX. TimeX provides discrete attribution maps and, unlike existing interpretability methods, it learns a latent space of explanations that can be used in various ways, such as to provide landmarks to visually aggregate similar explanations and easily recognize temporal patterns. We evaluate TimeX on eight synthetic and real-world datasets and compare its performance against state-of-the-art interpretability methods. We also conduct case studies using physiological time series. Quantitative evaluations demonstrate that TimeX achieves the highest or second-highest performance in every metric compared to baselines across all datasets. Through case studies, we show that the novel components of TimeX show potential for training faithful, interpretable models that capture the behavior of pretrained time series models.

To handle the scarcity and heterogeneity of electroencephalography (EEG) data for Brain-Computer Interface (BCI) tasks, and to harness the power of large publicly available data sets, we propose Neuro-GPT, a foundation model consisting of an EEG encoder and a GPT model. The foundation model is pre-trained on a large-scale data set using a self-supervised task that learns how to reconstruct masked EEG segments. We then fine-tune the model on a Motor Imagery Classification task to validate its performance in a low-data regime (9 subjects). Our experiments demonstrate that applying a foundation model can significantly improve classification performance compared to a model trained from scratch, which provides evidence for the generalizability of the foundation model and its ability to address challenges of data scarcity and heterogeneity in EEG. The code is publicly available at github.com/wenhui0206/NeuroGPT.

Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based "foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.

Recent works suggest that transformer models are capable of multi-tasking on diverse NLP tasks and adapting to new tasks efficiently. However, the potential of these multi-task models may be limited as they use the same set of parameters for all tasks. In contrast, humans tackle tasks in a more flexible way, by making proper presumptions on what skills and knowledge are relevant and executing only the necessary computations. Inspired by this, we propose to use task-level mixture-of-expert models, which has a collection of transformer layers (i.e., experts) and a router component that chooses from these experts dynamically and flexibly. We find that these models help improve the average performance gain (ARG) metric by 2.6% when adapting to unseen tasks in the few-shot setting and by 5.6% in the zero-shot generalization setting. Further, we show that the learned routing decisions partly rediscover human categorization of NLP tasks -- certain experts are strongly associated with extractive tasks, some with classification tasks, and some with tasks requiring world knowledge.

Recent innovations in transformers have shown their superior performance in natural language processing (NLP) and computer vision (CV). The ability to capture long-range dependencies and interactions in sequential data has also triggered a great interest in time series modeling, leading to the widespread use of transformers in many time series applications. However, being the most common and crucial application, the adaptation of transformers to time series forecasting has remained limited, with both promising and inconsistent results. In contrast to the challenges in NLP and CV, time series problems not only add the complexity of order or temporal dependence among input sequences but also consider trend, level, and seasonality information that much of this data is valuable for decision making. The conventional training scheme has shown deficiencies regarding model overfitting, data scarcity, and privacy issues when working with transformers for a forecasting task. In this work, we propose attentive federated transformers for time series stock forecasting with better performance while preserving the privacy of participating enterprises. Empirical results on various stock data from the Yahoo! Finance website indicate the superiority of our proposed scheme in dealing with the above challenges and data heterogeneity in federated learning.

Understanding time series is crucial for its application in real-world scenarios. Recently, large language models (LLMs) have been increasingly applied to time series tasks, leveraging their strong language capabilities to enhance various applications. However, research on multimodal LLMs (MLLMs) for time series understanding and reasoning remains limited, primarily due to the scarcity of high-quality datasets that align time series with textual information. This paper introduces ChatTS, a novel MLLM designed for time series analysis. ChatTS treats time series as a modality, similar to how vision MLLMs process images, enabling it to perform both understanding and reasoning with time series. To address the scarcity of training data, we propose an attribute-based method for generating synthetic time series with detailed attribute descriptions. We further introduce Time Series Evol-Instruct, a novel approach that generates diverse time series Q&As, enhancing the model's reasoning capabilities. To the best of our knowledge, ChatTS is the first MLLM that takes multivariate time series as input, which is fine-tuned exclusively on synthetic datasets. We evaluate its performance using benchmark datasets with real-world data, including six alignment tasks and four reasoning tasks. Our results show that ChatTS significantly outperforms existing vision-based MLLMs (e.g., GPT-4o) and text/agent-based LLMs, achieving a 46.0% improvement in alignment tasks and a 25.8% improvement in reasoning tasks.

Multi-task learning (MTL) aims to enhance the performance and efficiency of machine learning models by simultaneously training them on multiple tasks. However, MTL research faces two challenges: 1) effectively modeling the relationships between tasks to enable knowledge sharing, and 2) jointly learning task-specific and shared knowledge. In this paper, we present a novel model called Adaptive Task-to-Task Fusion Network (AdaTT) to address both challenges. AdaTT is a deep fusion network built with task-specific and optional shared fusion units at multiple levels. By leveraging a residual mechanism and a gating mechanism for task-to-task fusion, these units adaptively learn both shared knowledge and task-specific knowledge. To evaluate AdaTT's performance, we conduct experiments on a public benchmark and an industrial recommendation dataset using various task groups. Results demonstrate AdaTT significantly outperforms existing state-of-the-art baselines. Furthermore, our end-to-end experiments reveal that the model exhibits better performance compared to alternatives.

Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.git

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

Rigorous and reproducible evaluation is critical for assessing the state of the art and for guiding scientific advances in Artificial Intelligence. Evaluation is challenging in practice due to several reasons, including benchmark saturation, lack of transparency in methods used for measurement, development challenges in extracting measurements for generative tasks, and, more generally, the extensive number of capabilities required for a well-rounded comparison across models. We make three contributions to alleviate the above challenges. First, we present Eureka, an open-source framework for standardizing evaluations of large foundation models beyond single-score reporting and rankings. Second, we introduce Eureka-Bench as an extensible collection of benchmarks testing capabilities that (i) are still challenging for state-of-the-art models and (ii) represent fundamental but overlooked language and multimodal capabilities. The inherent space for improvement in non-saturated benchmarks enables us to discover meaningful differences between models at a capability level. Third, using Eureka, we conduct an analysis of 12 state-of-the-art models, providing in-depth insights into failure understanding and model comparison, which can be leveraged to plan targeted improvements. In contrast to recent trends in reports and leaderboards showing absolute rankings and claims for one model or another to be the best, our analysis shows that there is no such best model. Different models have different strengths, but there are models that appear more often than others as best performers for some capabilities. Despite the recent improvements, current models still struggle with several fundamental capabilities including detailed image understanding, benefiting from multimodal input when available rather than fully relying on language, factuality and grounding for information retrieval, and over refusals.

State-of-the-art parameter-efficient fine-tuning methods rely on introducing adapter modules between the layers of a pretrained language model. However, such modules are trained separately for each task and thus do not enable sharing information across tasks. In this paper, we show that we can learn adapter parameters for all layers and tasks by generating them using shared hypernetworks, which condition on task, adapter position, and layer id in a transformer model. This parameter-efficient multi-task learning framework allows us to achieve the best of both worlds by sharing knowledge across tasks via hypernetworks while enabling the model to adapt to each individual task through task-specific adapters. Experiments on the well-known GLUE benchmark show improved performance in multi-task learning while adding only 0.29% parameters per task. We additionally demonstrate substantial performance improvements in few-shot domain generalization across a variety of tasks. Our code is publicly available in https://github.com/rabeehk/hyperformer.

Diffusion models have demonstrated highly-expressive generative capabilities in vision and NLP. Recent studies in reinforcement learning (RL) have shown that diffusion models are also powerful in modeling complex policies or trajectories in offline datasets. However, these works have been limited to single-task settings where a generalist agent capable of addressing multi-task predicaments is absent. In this paper, we aim to investigate the effectiveness of a single diffusion model in modeling large-scale multi-task offline data, which can be challenging due to diverse and multimodal data distribution. Specifically, we propose Multi-Task Diffusion Model (MTDiff), a diffusion-based method that incorporates Transformer backbones and prompt learning for generative planning and data synthesis in multi-task offline settings. MTDiff leverages vast amounts of knowledge available in multi-task data and performs implicit knowledge sharing among tasks. For generative planning, we find MTDiff outperforms state-of-the-art algorithms across 50 tasks on Meta-World and 8 maps on Maze2D. For data synthesis, MTDiff generates high-quality data for testing tasks given a single demonstration as a prompt, which enhances the low-quality datasets for even unseen tasks.

Modern techniques like contrastive learning have been effectively used in many areas, including computer vision, natural language processing, and graph-structured data. Creating positive examples that assist the model in learning robust and discriminative representations is a crucial stage in contrastive learning approaches. Usually, preset human intuition directs the selection of relevant data augmentations. Due to patterns that are easily recognized by humans, this rule of thumb works well in the vision and language domains. However, it is impractical to visually inspect the temporal structures in time series. The diversity of time series augmentations at both the dataset and instance levels makes it difficult to choose meaningful augmentations on the fly. In this study, we address this gap by analyzing time series data augmentation using information theory and summarizing the most commonly adopted augmentations in a unified format. We then propose a contrastive learning framework with parametric augmentation, AutoTCL, which can be adaptively employed to support time series representation learning. The proposed approach is encoder-agnostic, allowing it to be seamlessly integrated with different backbone encoders. Experiments on univariate forecasting tasks demonstrate the highly competitive results of our method, with an average 6.5\% reduction in MSE and 4.7\% in MAE over the leading baselines. In classification tasks, AutoTCL achieves a 1.2% increase in average accuracy.

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.

Humans possess an extraordinary ability to create and utilize tools, allowing them to overcome physical limitations and explore new frontiers. With the advent of foundation models, AI systems have the potential to be equally adept in tool use as humans. This paradigm, i.e., tool learning with foundation models, combines the strengths of specialized tools and foundation models to achieve enhanced accuracy, efficiency, and automation in problem-solving. Despite its immense potential, there is still a lack of a comprehensive understanding of key challenges, opportunities, and future endeavors in this field. To this end, we present a systematic investigation of tool learning in this paper. We first introduce the background of tool learning, including its cognitive origins, the paradigm shift of foundation models, and the complementary roles of tools and models. Then we recapitulate existing tool learning research into tool-augmented and tool-oriented learning. We formulate a general tool learning framework: starting from understanding the user instruction, models should learn to decompose a complex task into several subtasks, dynamically adjust their plan through reasoning, and effectively conquer each sub-task by selecting appropriate tools. We also discuss how to train models for improved tool-use capabilities and facilitate the generalization in tool learning. Considering the lack of a systematic tool learning evaluation in prior works, we experiment with 17 representative tools and show the potential of current foundation models in skillfully utilizing tools. Finally, we discuss several open problems that require further investigation for tool learning. Overall, we hope this paper could inspire future research in integrating tools with foundation models.

We develop task scaling laws and model ladders to predict the individual task performance of pretrained language models (LMs) in the overtrained setting. Standard power laws for language modeling loss cannot accurately model task performance. Therefore, we leverage a two-step prediction approach: first use model and data size to predict a task-specific loss, and then use this task loss to predict task performance. We train a set of small-scale "ladder" models, collect data points to fit the parameterized functions of the two prediction steps, and make predictions for two target models: a 7B model trained to 4T tokens and a 13B model trained to 5T tokens. Training the ladder models only costs 1% of the compute used for the target models. On four multiple-choice tasks written in ranked classification format, we can predict the accuracy of both target models within 2 points of absolute error. We have higher prediction error on four other tasks (average absolute error 6.9) and find that these are often tasks with higher variance in task metrics. We also find that using less compute to train fewer ladder models tends to deteriorate predictions. Finally, we empirically show that our design choices and the two-step approach lead to superior performance in establishing scaling laws.

Transferring learned patterns from pretrained neural language models has been shown to significantly improve effectiveness across a variety of language-based tasks, meanwhile further tuning on intermediate tasks has been demonstrated to provide additional performance benefits, provided the intermediate task is sufficiently related to the target task. However, how to identify related tasks is an open problem, and brute-force searching effective task combinations is prohibitively expensive. Hence, the question arises, are we able to improve the effectiveness and efficiency of tasks with no training examples through selective fine-tuning? In this paper, we explore statistical measures that approximate the divergence between domain representations as a means to estimate whether tuning using one task pair will exhibit performance benefits over tuning another. This estimation can then be used to reduce the number of task pairs that need to be tested by eliminating pairs that are unlikely to provide benefits. Through experimentation over 58 tasks and over 6,600 task pair combinations, we demonstrate that statistical measures can distinguish effective task pairs, and the resulting estimates can reduce end-to-end runtime by up to 40%.

Large Language Models (LLMs) have recently demonstrated a remarkable ability to model time series data. These capabilities can be partly explained if LLMs understand basic time series concepts. However, our knowledge of what these models understand about time series data remains relatively limited. To address this gap, we introduce TimeSeriesExam, a configurable and scalable multiple-choice question exam designed to assess LLMs across five core time series understanding categories: pattern recognition, noise understanding, similarity analysis, anomaly detection, and causality analysis. TimeSeriesExam comprises of over 700 questions, procedurally generated using 104 carefully curated templates and iteratively refined to balance difficulty and their ability to discriminate good from bad models. We test 7 state-of-the-art LLMs on the TimeSeriesExam and provide the first comprehensive evaluation of their time series understanding abilities. Our results suggest that closed-source models such as GPT-4 and Gemini understand simple time series concepts significantly better than their open-source counterparts, while all models struggle with complex concepts such as causality analysis. We believe that the ability to programatically generate questions is fundamental to assessing and improving LLM's ability to understand and reason about time series data.

Health conditions among patients in intensive care units (ICUs) are monitored via electronic health records (EHRs), composed of numerical time series and lengthy clinical note sequences, both taken at irregular time intervals. Dealing with such irregularity in every modality, and integrating irregularity into multimodal representations to improve medical predictions, is a challenging problem. Our method first addresses irregularity in each single modality by (1) modeling irregular time series by dynamically incorporating hand-crafted imputation embeddings into learned interpolation embeddings via a gating mechanism, and (2) casting a series of clinical note representations as multivariate irregular time series and tackling irregularity via a time attention mechanism. We further integrate irregularity in multimodal fusion with an interleaved attention mechanism across temporal steps. To the best of our knowledge, this is the first work to thoroughly model irregularity in multimodalities for improving medical predictions. Our proposed methods for two medical prediction tasks consistently outperforms state-of-the-art (SOTA) baselines in each single modality and multimodal fusion scenarios. Specifically, we observe relative improvements of 6.5\%, 3.6\%, and 4.3\% in F1 for time series, clinical notes, and multimodal fusion, respectively. These results demonstrate the effectiveness of our methods and the importance of considering irregularity in multimodal EHRs.

The pervasive deployment of Large Language Models-LLMs in various sectors often neglects the nuanced requirements of individuals and small organizations, who benefit more from models precisely tailored to their specific business contexts rather than those with broadly superior general capabilities. This work introduces AnyTaskTune, a novel fine-tuning methodology coined as Task-Fine-Tune, specifically developed to elevate model performance on a diverse array of domain-specific tasks. This method involves a meticulous process to identify and define targeted sub-tasks within a domain, followed by the creation of specialized enhancement datasets for fine-tuning, thereby optimizing task-specific model performance. We conducted comprehensive fine-tuning experiments not only in the legal domain for tasks such as keyword extraction and sentence prediction but across over twenty different sub-tasks derived from the domains of finance, healthcare, law, psychology, consumer services, and human resources. To substantiate our approach and facilitate community engagement, we will open-source these bilingual task datasets. Our findings demonstrate that models fine-tuned using the Task-Fine-Tune methodology not only achieve superior performance on these specific tasks but also significantly outperform models with higher general capabilities in their respective domains. Our work is publicly available at https://github.com/PandaVT/DataTager.

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Neural-based multi-task learning (MTL) has gained significant improvement, and it has been successfully applied to recommendation system (RS). Recent deep MTL methods for RS (e.g. MMoE, PLE) focus on designing soft gating-based parameter-sharing networks that implicitly learn a generalized representation for each task. However, MTL methods may suffer from performance degeneration when dealing with conflicting tasks, as negative transfer effects can occur on the task-shared bottom representation. This can result in a reduced capacity for MTL methods to capture task-specific characteristics, ultimately impeding their effectiveness and hindering the ability to generalize well on all tasks. In this paper, we focus on the bottom representation learning of MTL in RS and propose the Deep Task-specific Bottom Representation Network (DTRN) to alleviate the negative transfer problem. DTRN obtains task-specific bottom representation explicitly by making each task have its own representation learning network in the bottom representation modeling stage. Specifically, it extracts the user's interests from multiple types of behavior sequences for each task through the parameter-efficient hypernetwork. To further obtain the dedicated representation for each task, DTRN refines the representation of each feature by employing a SENet-like network for each task. The two proposed modules can achieve the purpose of getting task-specific bottom representation to relieve tasks' mutual interference. Moreover, the proposed DTRN is flexible to combine with existing MTL methods. Experiments on one public dataset and one industrial dataset demonstrate the effectiveness of the proposed DTRN.

Retrieving relevant contexts from a large corpus is a crucial step for tasks such as open-domain question answering and fact checking. Although neural retrieval outperforms traditional methods like tf-idf and BM25, its performance degrades considerably when applied to out-of-domain data. Driven by the question of whether a neural retrieval model can be universal and perform robustly on a wide variety of problems, we propose a multi-task trained model. Our approach not only outperforms previous methods in the few-shot setting, but also rivals specialised neural retrievers, even when in-domain training data is abundant. With the help of our retriever, we improve existing models for downstream tasks and closely match or improve the state of the art on multiple benchmarks.

As the Chinese stock market continues to evolve and its market structure grows increasingly complex, traditional quantitative trading methods are facing escalating challenges. Particularly, due to policy uncertainty and the frequent market fluctuations triggered by sudden economic events, existing models often struggle to accurately predict market dynamics. To address these challenges, this paper introduces Stockformer, a price-volume factor stock selection model that integrates wavelet transformation and a multitask self-attention network, aimed at enhancing responsiveness and predictive accuracy regarding market instabilities. Through discrete wavelet transform, Stockformer decomposes stock returns into high and low frequencies, meticulously capturing long-term market trends and short-term fluctuations, including abrupt events. Moreover, the model incorporates a Dual-Frequency Spatiotemporal Encoder and graph embedding techniques to effectively capture complex temporal and spatial relationships among stocks. Employing a multitask learning strategy, it simultaneously predicts stock returns and directional trends. Experimental results show that Stockformer outperforms existing advanced methods on multiple real stock market datasets. In strategy backtesting, Stockformer consistently demonstrates exceptional stability and reliability across market conditions-whether rising, falling, or fluctuating-particularly maintaining high performance during downturns or volatile periods, indicating a high adaptability to market fluctuations. To foster innovation and collaboration in the financial analysis sector, the Stockformer model's code has been open-sourced and is available on the GitHub repository: https://github.com/Eric991005/Multitask-Stockformer.

Model merging has recently emerged as a cost-efficient paradigm for multi-task learning. Among current approaches, task arithmetic stands out for its simplicity and effectiveness. In this paper, we motivate the effectiveness of task vectors by linking them to multi-task gradients. We show that in a single-epoch scenario, task vectors are mathematically equivalent to the gradients obtained via gradient descent in a multi-task setting, and still approximate these gradients in subsequent epochs. Furthermore, we show that task vectors perform optimally when equality is maintained, and their effectiveness is largely driven by the first epoch's gradient. Building on this insight, we propose viewing model merging as a single step in an iterative process that Alternates between Tuning and Merging (ATM). This method acts as a bridge between model merging and multi-task gradient descent, achieving state-of-the-art results with the same data and computational requirements. We extensively evaluate ATM across diverse settings, achieving up to 20% higher accuracy in computer vision and NLP tasks, compared to the best baselines. Finally, we provide both empirical and theoretical support for its effectiveness, demonstrating increased orthogonality between task vectors and proving that ATM minimizes an upper bound on the loss obtained by jointly finetuning all tasks.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (\eg a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, in this paper, we propose JiuZhang~2.0, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the cross-task knowledge sharing to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts~(MoE) architecture for modeling mathematical text, so as to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design multi-task continual pre-training and multi-task fine-tuning strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. In order to further improve the general capacity of solving different complex tasks, we leverage large language models~(LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

This open access book provides a comprehensive overview of the state of the art in research and applications of Foundation Models and is intended for readers familiar with basic Natural Language Processing (NLP) concepts. Over the recent years, a revolutionary new paradigm has been developed for training models for NLP. These models are first pre-trained on large collections of text documents to acquire general syntactic knowledge and semantic information. Then, they are fine-tuned for specific tasks, which they can often solve with superhuman accuracy. When the models are large enough, they can be instructed by prompts to solve new tasks without any fine-tuning. Moreover, they can be applied to a wide range of different media and problem domains, ranging from image and video processing to robot control learning. Because they provide a blueprint for solving many tasks in artificial intelligence, they have been called Foundation Models. After a brief introduction to basic NLP models the main pre-trained language models BERT, GPT and sequence-to-sequence transformer are described, as well as the concepts of self-attention and context-sensitive embedding. Then, different approaches to improving these models are discussed, such as expanding the pre-training criteria, increasing the length of input texts, or including extra knowledge. An overview of the best-performing models for about twenty application areas is then presented, e.g., question answering, translation, story generation, dialog systems, generating images from text, etc. For each application area, the strengths and weaknesses of current models are discussed, and an outlook on further developments is given. In addition, links are provided to freely available program code. A concluding chapter summarizes the economic opportunities, mitigation of risks, and potential developments of AI.

Single-task models have proven pivotal in solving specific tasks; however, they have limitations in real-world applications where multi-tasking is necessary and domain shifts are exhibited. Recently, instructional prompts have shown significant improvement towards multi-task generalization; however, the effect of instructional prompts and Multi-Task Learning (MTL) has not been systematically studied in the biomedical domain. Motivated by this, this paper explores the impact of instructional prompts for biomedical MTL. We introduce the BoX, a collection of 32 instruction tasks for Biomedical NLP across (X) various categories. Using this meta-dataset, we propose a unified model termed In-BoXBART, that can jointly learn all tasks of the BoX without any task-specific modules. To the best of our knowledge, this is the first attempt to propose a unified model in the biomedical domain and use instructions to achieve generalization across several biomedical tasks. Experimental results indicate that the proposed model: 1) outperforms the single-task baseline by ~3% and multi-task (without instruction) baseline by ~18% on an average, and 2) shows ~23% improvement compared to the single-task baseline in few-shot learning (i.e., 32 instances per task) on an average. Our analysis indicates that there is significant room for improvement across tasks in the BoX, implying the scope for future research direction.

Global channel pruning (GCP) aims to remove a subset of channels (filters) across different layers from a deep model without hurting the performance. Previous works focus on either single task model pruning or simply adapting it to multitask scenario, and still face the following problems when handling multitask pruning: 1) Due to the task mismatch, a well-pruned backbone for classification task focuses on preserving filters that can extract category-sensitive information, causing filters that may be useful for other tasks to be pruned during the backbone pruning stage; 2) For multitask predictions, different filters within or between layers are more closely related and interacted than that for single task prediction, making multitask pruning more difficult. Therefore, aiming at multitask model compression, we propose a Performance-Aware Global Channel Pruning (PAGCP) framework. We first theoretically present the objective for achieving superior GCP, by considering the joint saliency of filters from intra- and inter-layers. Then a sequentially greedy pruning strategy is proposed to optimize the objective, where a performance-aware oracle criterion is developed to evaluate sensitivity of filters to each task and preserve the globally most task-related filters. Experiments on several multitask datasets show that the proposed PAGCP can reduce the FLOPs and parameters by over 60% with minor performance drop, and achieves 1.2xsim3.3x acceleration on both cloud and mobile platforms.

In this study, we introduce FEET, a standardized protocol designed to guide the development and benchmarking of foundation models. While numerous benchmark datasets exist for evaluating these models, we propose a structured evaluation protocol across three distinct scenarios to gain a comprehensive understanding of their practical performance. We define three primary use cases: frozen embeddings, few-shot embeddings, and fully fine-tuned embeddings. Each scenario is detailed and illustrated through two case studies: one in sentiment analysis and another in the medical domain, demonstrating how these evaluations provide a thorough assessment of foundation models' effectiveness in research applications. We recommend this protocol as a standard for future research aimed at advancing representation learning models.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

This paper argues that continual learning methods can benefit by splitting the capacity of the learner across multiple models. We use statistical learning theory and experimental analysis to show how multiple tasks can interact with each other in a non-trivial fashion when a single model is trained on them. The generalization error on a particular task can improve when it is trained with synergistic tasks, but can also deteriorate when trained with competing tasks. This theory motivates our method named Model Zoo which, inspired from the boosting literature, grows an ensemble of small models, each of which is trained during one episode of continual learning. We demonstrate that Model Zoo obtains large gains in accuracy on a variety of continual learning benchmark problems. Code is available at https://github.com/grasp-lyrl/modelzoo_continual.

Reasoning about time is essential for Large Language Models (LLMs) to understand the world. Previous works focus on solving specific tasks, primarily on time-sensitive question answering. While these methods have proven effective, they cannot generalize to a wider spectrum of temporal reasoning tasks. Therefore, we propose a crucial question: Can we build a universal framework to handle a variety of temporal reasoning tasks? To that end, we systematically study 38 temporal reasoning tasks. Based on the observation that 19 tasks are directly related to mathematics, we first leverage the available mathematical dataset to set a solid foundation for temporal reasoning. However, the in-depth study indicates that focusing solely on mathematical enhancement falls short of addressing pure temporal reasoning tasks. To mitigate this limitation, we propose a simple but effective self-critic temporal optimization method to enhance the model's temporal reasoning capabilities without sacrificing general task abilities. Finally, we develop Timo, a model designed to excel in temporal reasoning at the 7B and 13B scales. Notably, Timo outperforms the counterpart LLMs by 10.0 and 7.6 in average accuracy scores and achieves the new state-of-the-art (SOTA) performance of comparable size. Extensive experiments further validate our framework's effectiveness and its generalization across diverse temporal tasks. The code is available at https://github.com/zhaochen0110/Timo.

This work presents AstroPT, an autoregressive pretrained transformer developed with astronomical use-cases in mind. The AstroPT models presented here have been pretrained on 8.6 million 512 times 512 pixel grz-band galaxy postage stamp observations from the DESI Legacy Survey DR8. We train a selection of foundation models of increasing size from 1 million to 2.1 billion parameters, and find that AstroPT follows a similar saturating log-log scaling law to textual models. We also find that the models' performances on downstream tasks as measured by linear probing improves with model size up to the model parameter saturation point. We believe that collaborative community development paves the best route towards realising an open source `Large Observation Model' -- a model trained on data taken from the observational sciences at the scale seen in natural language processing. To this end, we release the source code, weights, and dataset for AstroPT under the MIT license, and invite potential collaborators to join us in collectively building and researching these models.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. Despite recent attempts to design efficient and effective architecture backbone for multi-dimensional data, such as images and multivariate time series, existing models are either data independent, or fail to allow inter- and intra-dimension communication. Recently, State Space Models (SSMs), and more specifically Selective State Space Models, with efficient hardware-aware implementation, have shown promising potential for long sequence modeling. Motivated by the success of SSMs, we present MambaMixer, a new architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels, called Selective Token and Channel Mixer. MambaMixer connects selective mixers using a weighted averaging mechanism, allowing layers to have direct access to early features. As a proof of concept, we design Vision MambaMixer (ViM2) and Time Series MambaMixer (TSM2) architectures based on the MambaMixer block and explore their performance in various vision and time series forecasting tasks. Our results underline the importance of selective mixing across both tokens and channels. In ImageNet classification, object detection, and semantic segmentation tasks, ViM2 achieves competitive performance with well-established vision models and outperforms SSM-based vision models. In time series forecasting, TSM2 achieves outstanding performance compared to state-of-the-art methods while demonstrating significantly improved computational cost. These results show that while Transformers, cross-channel attention, and MLPs are sufficient for good performance in time series forecasting, neither is necessary.

We demonstrate the efficacy of using intermediate representations from a single foundation model to enhance various music downstream tasks. We introduce SoniDo , a music foundation model (MFM) designed to extract hierarchical features from target music samples. By leveraging hierarchical intermediate features, SoniDo constrains the information granularity, leading to improved performance across various downstream tasks including both understanding and generative tasks. We specifically evaluated this approach on representative tasks such as music tagging, music transcription, music source separation, and music mixing. Our results reveal that the features extracted from foundation models provide valuable enhancements in training downstream task models. This highlights the capability of using features extracted from music foundation models as a booster for downstream tasks. Our approach not only benefits existing task-specific models but also supports music downstream tasks constrained by data scarcity. This paves the way for more effective and accessible music processing solutions.

Machine-based prediction of real-world events is garnering attention due to its potential for informed decision-making. Whereas traditional forecasting predominantly hinges on structured data like time-series, recent breakthroughs in language models enable predictions using unstructured text. In particular, (Zou et al., 2022) unveils AutoCast, a new benchmark that employs news articles for answering forecasting queries. Nevertheless, existing methods still trail behind human performance. The cornerstone of accurate forecasting, we argue, lies in identifying a concise, yet rich subset of news snippets from a vast corpus. With this motivation, we introduce AutoCast++, a zero-shot ranking-based context retrieval system, tailored to sift through expansive news document collections for event forecasting. Our approach first re-ranks articles based on zero-shot question-passage relevance, honing in on semantically pertinent news. Following this, the chosen articles are subjected to zero-shot summarization to attain succinct context. Leveraging a pre-trained language model, we conduct both the relevance evaluation and article summarization without needing domain-specific training. Notably, recent articles can sometimes be at odds with preceding ones due to new facts or unanticipated incidents, leading to fluctuating temporal dynamics. To tackle this, our re-ranking mechanism gives preference to more recent articles, and we further regularize the multi-passage representation learning to align with human forecaster responses made on different dates. Empirical results underscore marked improvements across multiple metrics, improving the performance for multiple-choice questions (MCQ) by 48% and true/false (TF) questions by up to 8%.

In a rapidly evolving job market, skill demand forecasting is crucial as it enables policymakers and businesses to anticipate and adapt to changes, ensuring that workforce skills align with market needs, thereby enhancing productivity and competitiveness. Additionally, by identifying emerging skill requirements, it directs individuals towards relevant training and education opportunities, promoting continuous self-learning and development. However, the absence of comprehensive datasets presents a significant challenge, impeding research and the advancement of this field. To bridge this gap, we present Job-SDF, a dataset designed to train and benchmark job-skill demand forecasting models. Based on 10.35 million public job advertisements collected from major online recruitment platforms in China between 2021 and 2023, this dataset encompasses monthly recruitment demand for 2,324 types of skills across 521 companies. Our dataset uniquely enables evaluating skill demand forecasting models at various granularities, including occupation, company, and regional levels. We benchmark a range of models on this dataset, evaluating their performance in standard scenarios, in predictions focused on lower value ranges, and in the presence of structural breaks, providing new insights for further research. Our code and dataset are publicly accessible via the https://github.com/Job-SDF/benchmark.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Transformer-based architectures achieved breakthrough performance in natural language processing and computer vision, yet they remain inferior to simpler linear baselines in multivariate long-term forecasting. To better understand this phenomenon, we start by studying a toy linear forecasting problem for which we show that transformers are incapable of converging to their true solution despite their high expressive power. We further identify the attention of transformers as being responsible for this low generalization capacity. Building upon this insight, we propose a shallow lightweight transformer model that successfully escapes bad local minima when optimized with sharpness-aware optimization. We empirically demonstrate that this result extends to all commonly used real-world multivariate time series datasets. In particular, SAMformer surpasses current state-of-the-art methods and is on par with the biggest foundation model MOIRAI while having significantly fewer parameters. The code is available at https://github.com/romilbert/samformer.