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Applications · Time Series

Zexin Yuan, Qinliang Su, Junxi Xiao

Irregular time series arise ubiquitously in real-world systems, where observations are sparse, asynchronous, and governed by underlying continuous-time dynamics. Existing continuous–discrete state-space models typically rely on path-based variational inference, which is computationally expensive or constrained by restrictive posterior assumptions. We propose SDEVI, a novel framework that performs variational inference directly on the joint distribution over discrete-time observations, while guaranteeing consistency with an underlying continuous process governed by a Stochastic Differential Equation(SDE). SDEVI employs a variational posterior induced by linear time-varying SDEs as a scalable inference backbone. To enable intricate dynamics modeling for real-world data, we introduce non-linear-SDE-induced variational inference and generalize our framework to the complex domain. Extensive experiments across healthcare, physics, climate, and IoT benchmarks demonstrate state-of-the-art performance on interpolation, extrapolation, regression, and classification tasks.

General Machine Learning · Causality

Roel Hulsman, Carles Balsells-Rodas, Sara Magliacane

Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.

Applications · Time Series

Fengming Zhang, Wenjie Du, Huan Zhang, Ke Yu, Shen Qu

Time series imputation benefits from leveraging cross-feature correlations, yet existing attention based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, ranking first among 17 methods across 21 experimental settings. Furthermore, our mechanistic analysis reveals that feature attention progressively aligns with underlying physical structure across layers, demonstrating more effectively exploits cross-feature dependencies for imputation.

Theory · Probabilistic Methods

Junxi Xiao, Qinliang Su

Mean-field variational inference (VI) is scalable, but its independence assumption can severely limit inference when the posterior is inherently coupled across instances especially for correlated data. Existing structured VI approaches either impose simple dependence patterns or incur substantial cost as dependence becomes richer, leaving efficient higher-order instance-level dependence modeling largely unresolved. We propose Copula-SVI, which augments amortized marginals with an explicit vine-copula posterior and refines joint samples with Stein updates toward the true posterior. The vine construction makes dependence learning and sampling practical by decomposing it into bivariate copula factors, enabling edge-minibatched training with variance-aware level-wise sampling and efficient dependence-aware initialization via a sparse vine built from the same sampled edges. Experiments on constrained clustering and time series modeling show consistent improvements over strong structured VI baselines and demonstrate efficient higher-order instance-level dependence modeling.

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

Enver Menadjiev, Jihyeon Seong, Jisu Yeo, Jaesik Choi

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose [DistMatch](https://anonymous.4open.science/r/distmatch/), a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov–Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

General Machine Learning · Causality

Minghao Fu, Biwei Huang, Zijian Li, Yujia Zheng, Ignavier Ng, Guangyi Chen, Yingyao Hu, Kun Zhang

Understanding climate dynamics requires going beyond correlations in observational data to uncover their underlying causal process. Latent drivers, such as atmospheric processes, play a critical role in temporal dynamics, while direct causal influences also exist among geographically proximate observed variables. Traditional Causal Representation Learning (CRL) typically focuses on latent factors but overlooks such observable-to-observable causal relations, limiting its applicability to climate analysis. In this paper, we introduce a unified framework that jointly uncovers (i) causal relations among observed variables and (ii) latent driving forces together with their interactions. We establish conditions under which both the hidden dynamic processes and the causal structure among observed variables are simultaneously identifiable from time-series data. Remarkably, our guarantees hold even in the nonparametric setting, leveraging contextual information to recover latent variables and observable relations. Building on these insights, we propose CaDRe (Causal Discovery and Representation learning), a time-series generative model with structural constraints that integrates CRL and causal discovery. Experiments on synthetic datasets validate our theoretical results. On real-world climate datasets, CaDRe not only delivers competitive forecasting accuracy but also recovers visualized causal graphs aligned with domain expertise, thereby offering interpretable insights into climate systems.

Deep Learning · Sequential Models, Time series

Matteo Pinna, Giacomo Lagomarsini, Andrea Ceni, Claudio Gallicchio

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive memory footprint of high-dimensional reservoirs. In this work, we revisit RC through the lens of structured operators and state space modeling to address these limitations, introducing Parallel Echo State Network (ParalESN). ParalESN enables the construction of high-dimensional and efficient reservoirs based on diagonal linear recurrence in the complex space, enabling parallel processing of temporal data. We provide a theoretical analysis demonstrating that ParalESN preserves the Echo State Property and the universality guarantees of traditional Echo State Networks while admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN matches the predictive accuracy of traditional RC on time series benchmarks, while delivering substantial computational savings. On 1-D pixel-level classification tasks, ParalESN achieves competitive accuracy with fully trainable neural networks while reducing computational costs and energy consumption by orders of magnitude. Overall, ParalESN offers a promising, scalable, and principled pathway for integrating RC within the deep learning landscape.

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

Xiaokai Luo, Haotian Xu, Carlos Misael Madrid Padilla, OSCAR HERNAN MADRID PADILLA

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains underexplored in the machine learning and statistics literature. We propose a method that uses low-rank matrices to represent the multivariate Poisson intensity functions, resulting in an adaptive nonparametric detection procedure. Our algorithm is single-pass and requires only constant computational cost per new observation, independent of the elapsed length of the time series. We provide theoretical guarantees to control the overall false alarm probability and characterize the detection delay under temporal dependence. We also develop a new Matrix Bernstein inequality for temporally dependent Poisson point process time series, which may be of independent interest. Numerical experiments demonstrate that our method is both statistically robust and computationally efficient.

Probabilistic Methods · Gaussian Processes

Jihao Andreas Lin, Sebastian Ament, Louis Tiao, David Eriksson, Maximilian Balandat, Eytan Bakshy

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of standard functions, a process that requires expert knowledge, results in limited adaptivity to data, and imposes strong assumptions on the hypothesis space. We study Empirical GPs, a principled framework for constructing flexible, data-driven GP priors that overcome these limitations. Rather than relying on standard parametric kernels, we estimate the mean and covariance functions empirically from a corpus of historical observations, enabling the prior to reflect rich, non-trivial covariance structures present in the data. Theoretically, we show that the resulting model converges to the GP that is closest (in KL-divergence sense) to the real data generating process. Practically, we formulate the problem of learning the GP prior from independent datasets as likelihood estimation and derive an Expectation-Maximization algorithm with closed-form updates, allowing the model handle heterogeneous observation locations across datasets. We demonstrate that Empirical GPs achieve competitive performance on learning curve extrapolation and time series forecasting benchmarks.

Deep Learning · Sequential Models, Time series

Tomoyoshi Kimura, Denizhan Kara, Jinyang Li, Hongjue Zhao, Yigong Hu, Yizhuo Chen, Xiaomin OUYANG, Shengzhong Liu, Tarek Abdelzaher

Internet of Things (IoT) systems continuously collect heterogeneous sensing signals from ubiquitous sensors to support intelligent applications such as human activity analysis, emotion monitoring, and environmental perception. These signals are inherently non-stationary and multi-scale, posing unique challenges for standard tokenization techniques. This paper proposes Dywave, a dynamic tokenization framework for IoT sensing signals that constructs compact input representations aligned with intrinsic temporal structures and underlying physical events. Dywave leverages wavelet-based hierarchical decomposition, identifies meaningful temporal boundaries corresponding to underlying semantic events, and adaptively compresses redundant intervals while preserving temporal coherence. Extensive evaluations on five real-world IoT sensing datasets across activity recognition, stress assessment, and nearby object detection demonstrate that Dywave outperforms state-of-the-art methods by up to 12\% in accuracy, while improving computational efficiency by reducing input token lengths by up to 75\% across mainstream sequence models. Moreover, Dywave exhibits improved robustness to domain shifts and varying sequence lengths.

Optimization · Stochastic

Tianjin Huang, Zhangyang “Atlas” Wang, Haotian Hu, Zhenyu Zhang, Gaojie Jin, Xiang Li, Li Shen, Jiaxing Shang, Tianlong Chen, Ke Li 等

Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence. Widely used safeguards such as gradient clipping mitigate these failures but require threshold tuning and indiscriminately truncate large updates. We propose **GradientStabilizer**, a lightweight, drop-in gradient transform that *preserves the instantaneous gradient direction* while replacing the update magnitude with a statistically stabilized estimate derived from running gradient-norm statistics. We prove that the resulting stabilized magnitude is uniformly bounded on spike steps, independent of the spike size, and show how this boundedness controls optimizer state evolution in adaptive methods. Across LLM pre-training (FP16), quantization-aware pre-training (FP4), ImageNet classification, reinforcement learning, and time-series forecasting, **GradientStabilizer** consistently improves training stability, widens stable learning-rate regions, and reduces divergence relative to clipping-based baselines, even substantially reducing Adam’s sensitivity to weight-decay strength.

Deep Learning · Sequential Models, Time series

Lehui Li, Yuyao Wang, Jisheng Yan, Wei Zhang, Jinliang Deng, Haoliang Sun, Zhongyi Han, Yongshun Gong

Incorporating textual information into time-series forecasting holds promise for addressing event-driven non-stationarity; however, a fundamental modality gap hinders effective fusion: textual descriptions express temporal impacts implicitly and qualitatively, whereas forecasting models rely on explicit and quantitative signals. Through controlled semi-synthetic experiments, we show that existing methods over-attend to redundant tokens and struggle to reliably translate textual semantics into usable numerical cues. To bridge this gap, we propose \method{}, which introduces a Temporal Evolution Semantic Space as an intermediate bottleneck between modalities. This space consists of interpretable, numerically grounded temporal primitives—mean shift, volatility, shape, and lag—extracted from text by an LLM via structured prompting and filtered through confidence-aware gating. Experiments on four real-world datasets demonstrate up to a 29\% reduction in forecasting error compared to state-of-the-art uni-modal and multimodal baselines. The code is available at https://anonymous.4open.science/r/MMTSF.

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

Wanfeng Lu, He Ma, Wei Lin, Qunxi Zhu

Precise prediction of spatiotemporal dynamics over predictive horizons is constrained by the computational cost of high-fidelity solvers and the sparsity, noise, and irregularity of data. We introduce MERLIN, a Koopman-based framework that lifts dynamics to the evolution of learned *observation functionals* with near-linear progression, enabling full-field reconstruction at arbitrary resolutions. Theoretically, we develop a functional Koopman theory for PDEs and compensate for the loss of finite-dimensional linear invariance via the Mori–Zwanzig formalism, which augments the linear backbone with non-Markovian memory terms to improve predictive accuracy. Practically, MERLIN employs discretization-invariant *function encoders* that map partial, irregular observations to observables, and resolution-free *function decoders* that reconstruct states at arbitrary query points. Training under linear constraints yields an interpretable, low-dimensional model that captures principal modes, supports reduced-order modeling, and—augmented with memory correction—delivers stable long-horizon rollouts even in ultra-low-dimensional latent spaces.

General Machine Learning · Evaluation

Medhasweta Sen, Zachary Gottesman, Jiaxing Qiu, C. Bayan Bruss, Nam Nguyen, Thomas Hartvigsen

Recent works propose complex multi-modal models that handle both time series and language, ultimately claiming high performance on complex tasks like time series reasoning and cross-modal question answering. However, they skip foundational evaluations that such complex models should have mastered. So we ask a simple question: $\textit{How well can recent models describe structural properties of time series?}$ To answer this, we propose that successful models should be able to $\textit{recognize}$, $\textit{differentiate}$, and $\textit{generate}$ descriptions of time series. We then create $\textbf{BEDTime}$, a benchmark to assess these novel tasks, that comprises $\textbf{five datasets}$ reformatted across $\textbf{three modalities}$. In evaluating $\textbf{13 state-of-the-art models}$, we find that (1) surprisingly, dedicated time series-language models fall short, despite being designed for similar tasks, (2) vision language models are quite capable, (3) language only methods perform worst, despite many lauding their potential, and (4) all approaches are clearly fragile to a range of real world robustness tests, indicating directions for future work. Together, our findings critique prior works' claims and provide avenues for advancing multi-modal time series modeling.

Deep Learning · Large Language Models

Felix Parker, Nimeesha Chan, Chi Zhang, Kimia Ghobadi

Time series data is fundamental to decision-making across many domains including healthcare, finance, power systems, and logistics. However, analyzing this data correctly often requires incorporating unstructured contextual information, answering domain-specific questions, and generating natural language explanations – capabilities that traditional time series models lack. While Large Language Models (LLMs) excel at contextual reasoning and knowledge integration, they struggle with numerical time series due to inefficient text-based representations and limited exposure to numerical data during pretraining. We address this gap by augmenting an LLM with specialized time series perception through a patch-based encoder-decoder architecture. We train this Time Series-augmented LLM (TsLLM) on a large corpus of over 20 billion tokens of interleaved time series and text spanning diverse tasks: forecasting with contextual information, question-answering, anomaly detection, classification, report generation, and more, all unified as next token prediction. This training enables TsLLM to leverage both its language understanding and newly acquired temporal reasoning capabilities. While not designed to surpass specialized models on traditional benchmarks, TsLLM demonstrates strong performance on tasks requiring the integration of time series analysis with natural language – capabilities that existing approaches cannot provide. It also exhibits strong zero-shot and few-shot performance, showing it can adapt to new data without additional training.

Deep Learning · Large Language Models

Jiakai Li, KE QIN, Rongzheng Wang, Yizhuo Ma, Qizhi Chen, Muquan Li, Shuang Liang

By incorporating test-time compute scaling, large reasoning models (LRMs) are able to solve complex problems by generating explicit chain-of-thought (CoT) reasoning processes. However, they often suffer from overthinking during generation, resulting in redundant token outputs and degraded accuracy. Existing methods to mitigate this issue remain limited: training-based approaches incur substantial training costs, while training-free methods often rely on well-crafted prompting or unreliable confidence signals. In this work, we study early stopping through attention distributions and propose a simple method, ASAG, that infers the model's reasoning state and adaptively adjusts the generation strategy. The proposed method is training-free and plug-and-play, enabling seamless integration into existing LRMs. Extensive experiments on nine benchmarks demonstrate consistent improvements across mainstream LRMs with varying parameter scales, including the Deepseek-R1-Distill and Qwen3 series. In particular, ASAG achieves a 4.4% relative improvement in accuracy while reducing the number of generated tokens by over 40% across all reasoning tasks on Qwen3-8B.

Applications · Time Series

Kangjia Yan, Chenxi Liu, Hao Miao, Xinle Wu, Yan Zhao, Chenjuan Guo, Bin Yang

Effective time series forecasting enables various real-world applications, benefiting from the proliferation of mobile devices. However, the volume of time series data may vary significantly across domains due to low sampling rates and data regulations. To maximally create value from sparse data, this study focuses on a new problem of source-free time series forecasting, aiming to adapt a pretrained model from sufficient source time series to the sparse target time series without access to the source data, enabling data protection. To achieve this, we propose TimeID, a novel source-free time series forecasting framework with a large language model (LLM) centric proxy denoising inspired by the powerful generalization capabilities of LLMs. Specifically, TimeID consists of three key components: (1) dual-branch invariant disentangled feature learning that enforces representation- and gradient-wise invariance by means of season-trend decomposition; (2) lightweight, parameter-free proxy denoising that dynamically calibrates systematic biases of LLMs; and (3) knowledge distillation that bidirectionally aligns the denoised prediction and the original target prediction. Extensive experiments on real-world datasets demonstrate that TimeID outperforms state-of-the-art baselines, improving MSE and MAE by 10.7\% and 9.3\% on average. The code is publicly available at https://anonymous.4open.science/r/TimeID-6D1D/.

Applications · Chemistry, Physics, and Earth Sciences

Wentao Gao, Jiuyong Li, Lin Liu, Thuc Le, Jixue Liu, Yanchang Zhao, Yun Chen

Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through a single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured multi-scale reasoning for climate forecasting without parameter modification. Our approach combines hierarchical coarse-to-fine prediction refinement with residual-guided error correction; together, they systematically address prediction failures at each resolution level. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR consistently enhances foundation model performance across diverse climate regions within an Australian regional area. Experimental results demonstrate substantial improvements over direct foundation model application, achieving up to 18.9\% reduction in mean squared error, 10.2\% reduction in root mean squared error, and 21.1\% relative gain in $R^2$ when applied to TimesFM, with the largest benefits observed in climatologically complex regions where multi-scale temporal dynamics are most pronounced. The framework's inference-time operation enables immediate deployment on existing operational climate prediction systems without model retraining, offering a practical solution for enhancing foundation model capabilities in specialized forecasting domains.

Deep Learning · Sequential Models, Time series

Wei Shao, Ziquan Fang, Zheqi Lu, Yongfeng Su, Yuzhu Wang, Yunjun Gao

Time-series analysis is critical in real-world applications, yet the explosion of time-series data imposes severe burdens on storage and computational resources. Recently, dataset condensation has emerged as a promising data-centric solution by synthesizing compact yet informative datasets to replace large-scale raw data. However, existing methods are largely vision-centric, failing to capture unique temporal properties of time series, or task-specific, tightly coupling the condensed data to a particular downstream objective. As a result, these approaches suffer from feature mismatch and fail to generalize across diverse time-series tasks. To bridge this gap, we propose UniTSC, the first unified dataset condensation framework for general time-series analysis. UniTSC employs a multi-view hybrid encoder to capture task-invariant representations across temporal, spectral, and topological perspectives. Building upon this representation, we design a tri-space alignment paradigm that jointly aligns optimization trajectories, power spectral densities, and multivariate dependency structures, enabling comprehensive information preservation under extreme compression. Extensive experiments show that UniTSC retains up to 97.9\% of downstream performance using as little as 0.01\% of the original training data, revealing that a single batch-equivalent budget ($\textless$ 128 samples) is sufficient to capture the essential dynamics of complex time-series data.

Deep Learning · Sequential Models, Time series

Xiaohui Zhou, Yijie Wang, Hongzuo Xu, Weixuan Liang, Xiaoli Li, Guansong Pang

Open-set anomaly detection (OSAD) is an emerging paradigm designed to utilize limited labeled data from anomaly classes seen in training to identify both seen and unseen anomalies during testing. Current approaches rely on simple augmentation methods to generate pseudo anomalies that replicate unseen anomalies. Despite being promising in image data, these methods are found to be ineffective in time series data due to the failure to preserve its sequential nature, resulting in trivial or unrealistic anomaly patterns. They are further plagued when the training data is contaminated with unlabeled anomalies. This work introduces $\textbf{IMPACT}$, a novel framework that leverages $\underline{\textbf{i}}$nfluence $\underline{\textbf{m}}$odeling for o$\underline{\textbf{p}}$en-set time series $\underline{\textbf{a}}$nomaly dete$\underline{\textbf{ct}}$ion, to tackle these challenges. The key insight is to $\textbf{i)}$ learn an influence function that can accurately estimate the impact of individual training samples on the modeling, and then $\textbf{ii)}$ leverage these influence scores to generate semantically divergent yet realistic unseen anomalies for time series while repurposing high-influential samples as supervised anomalies for anomaly decontamination. Extensive experiments show that IMPACT significantly outperforms existing state-of-the-art methods, showing superior accuracy under varying OSAD settings and contamination rates.