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Applications · Time Series

Fangxu Yu, Xingang Guo, Lingzhi Yuan, Haoqiang Kang, Hongyu Zhao, Lianhui Qin, Furong Huang, Bin Hu, Tianyi Zhou

Time series data is ubiquitous in real-world scenarios and crucial for critical applications ranging from energy management to traffic control. Consequently, the ability to reason over time series is a fundamental skill for generalist models to solve complex problems. However, current benchmarks for generalist models largely overlook this dimension. To bridge this gap, we introduce TSRBench, a comprehensive multi-modal benchmark designed to stress-test the full spectrum of time series reasoning capabilities. TSRBench features: i) a diverse set of 4125 problems from 14 domains, and is categorized into 4 major dimensions: Perception, Reasoning, Prediction, and Decision-Making. ii) 15 tasks from the 4 dimensions evaluating essential reasoning capabilities (e.g., numerical reasoning). Through extensive experiments, we evaluated over 30 leading proprietary and open-source LLMs, VLMs, and TSLLMs within TSRBench. Our findings reveal that: i) scaling laws hold for perception and reasoning but break down for prediction; ii) strong reasoning does not guarantee accurate context-aware forecasting, indicating a decoupling between semantic understanding and numerical prediction; and iii) despite the complementary nature of textual and visual forms of time series as inputs, current multimodal models fail to effectively fuse them for reciprocal performance gains. TSRBench provides a standardized evaluation platform that not only highlights existing challenges but also offers valuable insights to advance generalist models.

Applications · Time Series

Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: function-valued causal influence. In such models, each directed relationship corresponds not to a single weight or coefficient, but to a state-dependent function whose effect varies across regimes, magnitudes, and contexts of the system. In this paper, we formalize function-valued causal influence in nonlinear multivariate time series and show that common scalar summaries, such as aggregated contribution magnitudes, constitute severe information bottlenecks. Using Neural Additive Vector Autoregression as a representative architecture, we demonstrate that edges with indistinguishable scalar causal scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. These differences explain persistent discrepancies between causal score magnitude, interpretability, and predictive relevance that cannot be resolved by significance testing alone. We present a general framework for extracting and visualizing causal response functions from neural autoregressive models using learned contribution tensors and local attribution methods. Through controlled synthetic systems and an applied case study of democratic development, we show how function-valued analysis reveals regime-specific and asymmetric causal structure that is systematically missed by coefficient-centric or score-centric approaches. Our results suggest that meaningful interpretation of nonlinear causal time-series models requires moving beyond scalar causal scores toward explicit analysis of causal response functions. This reframing clarifies the representational content of modern causal discovery methods and provides a foundation for more faithful interpretation of complex dynamical systems.

Applications · Time Series

Sijie Xiong, Cheng Tang, Atsushi Shimada

Time series forecasting plays a crucial role in a wide range of real-world applications and has become increasingly complex with the growth of multivariate dimensions and extended historical observations, leading to the prosperity of deep forecasting models. Previous models are hindered by three major challenges: high computational complexity, inefficient token utilization caused by redundancy and scarcity, and temporal distribution shifts resulting from non-stationary dynamics. Inspired by Koopman theory and the success of multilevel encoder–decoder architectures with skip connections, we design an input-dependent Koopman module to decompose time series into Koopman dynamics and residual dynamics. Building upon this formulation, we propose a U-shaped Multilevel Attention module (UMA) that integrates element-wise attention filtering and linear attention, giving rise to KUMA. The input-dependent Koopman operator mitigates the issue of operator mixture and alleviates temporal distribution shifts, while UMA achieves a favorable balance between token redundancy and token scarcity with acceptable computational efficiency. Comprehensive evaluations across 12 benchmark datasets demonstrate that KUMA achieves superior performance compared to existing excellent approaches.

Deep Learning · Sequential Models, Time series

Shohaib Shaffiey, Massimiliano Pierobon

The fields of AI-based disease fingerprinting, drug discovery and repurposing are currently among the emerging frontiers of machine learning applied to medicine. One major challenge is to obtain robust $\textit{in-silico}$ modeling of disease progression while accounting for the vastly different time scales of biochemical interactions, from gene expression to protein abundance and metabolic flux. Discrete sequence models inadequately represent such multi-scale interactions, and standard Neural Ordinary Differential Equations (NODEs) often fail to train stably under stiffness (different time scales). To address this, in this paper a Tri-Scale Stiff NODE is introduced, defined by hierarchically coupled latent differential equations that model the causal flow from genes to proteins and metabolites, and optimized using reconstruction error and information-theoretic mutual information. This enables continuous-time modeling of cellular responses to identify not only disease dynamics, but also drug perturbations that act within narrow time windows, often invisible to discrete-time approaches. Lyapunov analysis provides a theoretical guarantee that the modeled trajectories remain stable and well-behaved even under extreme stiffness. The developed modeling methodology is tested upon a public dataset (STATegra B-cell differentiation) and utilized for a proof-of-concept drug repurposing pipeline.

Applications · Time Series

Qingwen Zeng, Dajun Guo, Zhaoge Bi, lining chen, Jushang Qiu, Yitian Yang, Carl Yang, Huaming Chen, Ling Chen

Time series forecasting is critical in domains such as finance, energy, and healthcare, yet real-world datasets often exhibit non-stationarity, noise, missing values, and distribution shifts, posing severe challenges for generalization. In practice, industry solutions typically rely on customized forecasting frameworks that combine imputation, decomposition, and specialized models. However, such frameworks are costly to engineer and maintain. Moreover, we observe that many frameworks suffer from the impacts of distribution shifts, which degrade their respective performance. It motivates a paradigm that transfers reliably across heterogeneous datasets while accumulating reusable strategy knowledge for large-scale, dynamic environments. Although large language model-based agents have recently shown strong reasoning and tool-use capabilities, existing approaches do not consistently adapt forecasting workflows across diverse time series. We identify two primary factors, including limited strategy-level supervision and the inherent complexity of mapping dataset-specific meta-features to effective forecasting strategies. To address these challenges, we propose BECRA, a novel agent training paradigm that learns forecasting intelligence through contrast-aware exploration and agent-level causal lesson extraction, without human-annotated supervision. BECRA distills symbolic strategy lessons that support in-context planning on unseen datasets, enabling zero-shot training adaptation.

Applications · Time Series

Hanyin Cheng, Jingrong Zhou, Yang Shu, Chenjuan Guo

Probabilistic forecasting with exogenous variables is vital for decision-making but remains underexplored compared to deterministic methods. We propose KITE, a knowledge-guided probabilistic modeling framework designed to bridge this gap by addressing two key bottlenecks: (1) topological disparity in sampling initialization and (2) spurious covariate correlations during the iterative conditional generation process. KITE introduces a *History-Conditional Manifold* to construct an informative source distribution from historical dynamics, effectively anchoring the starting point closer to the target space. Additionally, a *Knowledge-Guided Conditioning* module is developed to regularize variable interactions using statistical priors, suppressing spurious correlations and enhancing the robustness of covariate conditioning. Extensive experiments demonstrate that KITE outperforms state-of-the-art methods in both deterministic and probabilistic forecasting.

Applications · Time Series

Aoyu Liu, Liming Wei, YAYING ZHANG

Most spatio-temporal forecasting models assume in-distribution data and can degrade sharply under non-stationary environments. Existing methods for handling distribution shift largely rely on discrete graph inference, making it difficult to disentangle universal dynamics from environment-specific changes and to respect the continuous physical nature of spatio-temporal fields. To this end, we propose STPDE, a general framework that reformulates spatio-temporal dynamics as the evolution of inhomogeneous partial differential equations. STPDE explicitly decomposes dynamics into an Invariant Diffusion Operator that captures universal mechanisms and an Environment Basis Manifold that parameterizes local heterogeneous media. We show that the Green's function of the Laplacian can be effectively approximated by linear attention, enabling global diffusion at scale. Combined with stochastic environment perturbations, STPDE improves robustness under heterogeneous and shifting environments. Extensive experiments on in-distribution forecasting, out-of-distribution generalization, few-shot cross-city transfer, and continual learning demonstrate consistent improvements over state-of-the-art baselines with competitive computational efficiency.

Applications · Time Series

Heng Zhou, Xin Sun, Chao LI

Real-world time series inherently exhibit complex temporal patterns. Within chaotic systems, significant mixing and entanglement occur between different time-varying modes. Given that time series exhibit distinctly different patterns at various sampling scales, downsampling to extract multiscale features is a common approach. However, conventional downsampling causes high-frequency components in the original signal, those exceeding the new Nyquist frequency, to undergo spectral folding. This erroneously introduces spurious low-frequency patterns, perceived as low-frequency noise, thereby leading to the ***aliasing problem***. To address this problem, we propose a Decomposition-Prevention-Fusion architecture framework called **DMANet**, which introduces the **D**ynamic **M**ultiscale **A**nti-Aliasing **Net**work. Specifically, DMANet comprises two key components: Multiscale Convolutional Downsampling, designed to capture temporal dependencies and inter-channel interactions, and an Anti-Aliasing Operation, which includes Pre-Sampling Anti-Aliasing Filtering and Post-Sampling Interpolation. These designs guarantee the fidelity of multiscale features before and after downsampling. We show that by mitigating the risk of aliasing, our proposed simple convolutional downsampling architecture achieves performance competitive with common baselines. Our codes are available at https://anonymous.4open.science/r/DMANet.

Applications · Time Series

Junkai Lu, Peng Chen, Xingjian Wu, Yang Shu, Chenjuan Guo, Christian S Jensen, Bin Yang

Time series reasoning demands both the perception of complex dynamics and logical depth. However, existing LLM-based approaches exhibit two limitations: they often treat time series merely as text or images, failing to capture the patterns like trends and seasonalities needed to answer specific questions; and when trained on a mix of simple and complex tasks, simpler objectives often dominate the learning process, hindering the development of deep reasoning capabilities. To address these limitations, we propose the Pattern-Aware Alignment and Balanced Reasoning model (PATRA), introducing a pattern-aware mechanism that extracts trend and seasonality patterns from time series to achieve deep alignment. Furthermore, we design a task-aware balanced reward to harmonize learning across tasks of varying difficulty, incentivizing the generation of coherent Chains of Thought. Extensive experiments show that PATRA outperforms strong baselines across diverse Time Series Question Answering (TSQA) tasks, demonstrating superior cross-modal understanding and reasoning capability.

Applications · Time Series

Lekai Qian, Haoyu Gu, Jingwei Zhao, Ziyu Wang

Tokenizing music to fit the general framework of language models is a compelling challenge, especially considering the diverse symbolic structures in which music can be represented (e.g., sequences, grids, and graphs). To date, most approaches tokenize symbolic music as sequences of musical events, such as onsets, pitches, time shifts, or compound note events. This strategy is intuitive and has proven effective in Transformer-based models, but it treats the regularity of musical time implicitly: individual tokens may span different durations, resulting in non-uniform time progression. In this paper, we instead consider whether an alternative tokenization is possible, where an uniform-length musical step (e.g., a beat) serves as the basic unit. Specifically, we encode all events within a single time step at the same pitch as one token, and group tokens explicitly by time step, which resembles a sparse encoding of a piano roll representation. We evaluate the proposed tokenization on music continuation and accompaniment generation tasks, comparing it with mainstream event-based methods. Results show improved musical quality and long-term structural coherence, while additional analyses confirm higher efficiency and more effective capture of long-range patterns with the proposed tokenization.

Deep Learning · Sequential Models, Time series

Yisong Fu, Zezhi Shao, Chengqing Yu, Yujie Li, Yongjun Xu, Xueqi Cheng, Fei Wang

We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.

Applications · Health / Medicine

Yiqi Su, Ray Lee, Jiaming Cui, Naren Ramakrishnan

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across seasonal and non-seasonal settings—including early outbreaks and multi-wave regimes—our approach reduces long-horizon RMSE by 15–35%, improves peak timing error by 1–3 weeks, and lowers peak magnitude bias by up to 30% relative strong time-series, neural ODE, and hybrid baselines, without relying on auxiliary covariates.

Applications · Time Series

Minh Nguyen, Van Dai Do, Huu Nguyen, Dung Nguyen, Kien Do, Hung Le

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal–Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models.

Deep Learning · Foundation Models

Gerardo Pastrana, Sina Pakazad, Henrik Ohlsson, Utsav Dutta

Traditional time series models are often task-specific and rely heavily on manual feature engineering. While Transformer-based architectures have revolutionized sequence modeling in language and vision, their potential for general-purpose time series representation learning remains underexplored, particularly for heterogeneous sensor data. We introduce CHARM (Channel-Aware Representation Model), a model designed to improve representations for multivariate time series by incorporating channel-level textual descriptions into its architecture. This allows the model to leverage contextual information associated with individual sensors while remaining invariant to channel order. CHARM is trained using a Joint Embedding Predictive Architecture (JEPA) with a novel loss that promotes informative and temporally stable embeddings. We find that CHARM’s latent-space prediction encourages robustness to sensor-level noise and supports learning underlying temporal structure. In addition, the description-aware gating mechanism provides a degree of interpretability through learned inter-channel relationships. Across a range of downstream tasks—including univariate and multivariate anomaly detection, classification, and short- and long-term forecasting—the learned embeddings achieve strong performance using only a lightweight linear probe.

Applications · Health / Medicine

Sirui Li, Shuhan Xiao, Mihir Joshi, Ahmed Metwally, Daniel McDuff, Wei Wang, Yuzhe Yang

The rise of large language models (LLMs) has shifted time series analysis from narrow analytics to general-purpose reasoning. Yet, existing benchmarks cover only a small set of health time series modalities and tasks, failing to reflect the diverse domains and extensive temporal dependencies inherent in real-world physiological modeling. To bridge these gaps, we introduce HEARTS (Health Reasoning over Time Series), a unified benchmark for evaluating hierarchical reasoning capabilities of LLMs over general health time series. HEARTS integrates 16 real-world datasets across 12 health domains and 20 signal modalities, and defines a comprehensive taxonomy of 110 tasks grouped into four core capabilities: Perception, Inference, Generation, and Deduction. Evaluating 14 state-of-the-art LLMs on more than 20K test samples reveals intriguing findings. First, LLMs substantially underperform specialized models, and their performance is only weakly related to general reasoning scores. Moreover, LLMs often rely on simple heuristics and struggle with multi-step temporal reasoning. Finally, performance declines with increasing temporal complexity, with similar failure modes within model families, indicating that scaling alone is insufficient. By making these gaps measurable, HEARTS provides a standardized testbed and living benchmark for developing next-generation LLM agents capable of reasoning over diverse health signals.

Addison J. Wu, Ryan Liu, Xuechunzi Bai, Thomas Griffiths

As large language models (LLMs) are adopted into frameworks that grant them the capacity to make real decisions, it is increasingly important to ensure that they are unbiased. In this paper, we argue that the predominant approach of simply removing existing biases from models is not enough. Using a paradigm from the psychology literature, we demonstrate that LLMs can spontaneously develop novel social biases about artificial demographic groups even when no inherent differences exist. These biases result in highly stratified task allocations, which are less fair than assignments by human participants and are exacerbated by newer and larger models. In social science, emergent biases like these have been shown to result from exploration-exploitation trade-offs, where the decision-maker explores too little, allowing early observations to strongly influence impressions about entire demographic groups. To alleviate this effect, we examine a series of interventions targeting model inputs, problem structure, and explicit steering. We find that explicitly incentivizing exploration most robustly reduces stratification, highlighting the need for better multifaceted objectives to mitigate bias. These results reveal that LLMs are not merely passive mirrors of human social biases, but can actively create new ones from experience, raising urgent questions about how these systems will shape societies over time.

General Machine Learning · Sequential, Network, and Time Series Modeling

Lele Cao

Game world modeling (GWM) and reinforcement learning (RL) are often confounded because research papers rarely quantify how difficult the underlying transition prediction problem is at the declared interface (pixels/tokens/latents with finite history). We propose the Transition Complexity Profile (TCP): a small, reproducible set of metrics that characterizes an environment's (or gameplay dataset's) induced transition kernel by (i) intrinsic one-step branching, (ii) interaction-induced uncertainty and opponent influence when observable, and (iii) temporal/spatial dependency span via standardized probe curves. TCP is reported with an explicit reference distribution, protocol stochasticity, and a versioned measurement budget (sampling/resampling and fixed probe compute), enabling comparable numbers across benchmarks. We outline how common game families and modern "neural game engine" domains populate this landscape and call for TCP to become standard benchmark metadata and a required statistic in GWM and RL papers.

Theory · Domain Adaptation and Transfer Learning

Jiaxuan Cheng

Plasticity—a neural network's ability to adapt to new tasks—is critical for continual and transfer learning. Existing measures, such as effective rank, dead neuron fraction, and weight norm, lack theoretical grounding and correlate poorly with performance on new tasks. We introduce *local redundancy*, an information-theoretic measure derived from universal compression theory. We define local redundancy as the worst-case redundancy of a local model family—parameters in an infinitesimal neighborhood along gradient directions—and show this is a principled measure of plasticity. Although local redundancy is intractable to compute exactly, we prove that the expected squared gradient norm on a synthetic memorization task provides an efficiently computable lower bound. Experiments on continual image classification and time series transfer learning demonstrate that local redundancy predicts downstream performance better than existing measures and enables pretraining checkpoint selection where validation loss plateaus.

Deep Learning · Sequential Models, Time series

Ruben Solozabal, Velibor Bojkovic, Hilal AlQuabeh, Klea Ziu, Kentaro Inui, Martin Takac

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce \emph{WaveSSM}, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, \textit{WaveSSM} outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.

Applications · Time Series

Haochen Yuan, Yutong Wang, Yihong Chen, Yunbo Wang, Xiaokang Yang

Few-shot time series forecasting is fundamentally challenged by the scarcity of high-quality training data and the risk of severe overfitting. To address this issue, we propose ReAugment, a reinforcement learning (RL) framework that explicitly learns where and how to augment time series data. ReAugment maintains a zoo of forecasting models and measures prediction diversity across them to identify training samples that are most prone to overfitting. These samples serve as anchor points and are used as inputs to the data augmentation process. We then employ an RL approach to learn transformation policies, using a model zoo-guided reward function to bias the transformed data to overfit-prone regions of the training distribution that are most beneficial for generalization. A key advantage of the RL formulation is that it avoids backpropagating gradients through the forecasting models, thereby mitigating gradient vanishing. Experiments across diverse forecasting architectures demonstrate the effectiveness of ReAugment in both few-shot and standard time series forecasting.