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Applications · Time Series

Charalampos Shimillas, Kleanthis Malialis, Konstantinos Fokianos, Marios Polycarpou

Multivariate time series (MTS) anomaly diagnosis, which encompasses both anomaly detection and localization, is critical for the safety and reliability of complex, large-scale real-world systems. The vast majority of existing anomaly diagnosis methods offer limited theoretical insights, especially for anomaly localization, which is a vital but largely unexplored area. The aim of this contribution is to study the learning process of a Transformer when applied to MTS by revealing connections to statistical time series methods. Based on these theoretical insights, we propose the Attention Low-Rank Transformer (ALoRa-T) model, which applies low-rank regularization to self-attention, and we introduce the Attention Low-Rank score, effectively capturing the temporal characteristics of anomalies. Finally, to enable anomaly localization, we propose the ALoRa-Loc method, a novel approach that associates anomalies to specific variables by quantifying interrelationships among time series. Extensive experiments and real data analysis show that the proposed methodology significantly outperforms state-of-the-art methods in both detection and localization tasks. Code is available at: https://github.com/CharisShimillas/ALoRa.

General Machine Learning · Causality

Xiangkun Wu, Qianglin Wen, Yingying Zhang, Hongtu Zhu, Ting Li, Chengchun Shi

A/B testing has become a gold standard for modern technological companies to conduct policy evaluation. Yet, its application to time series experiments, where treatments are sequentially assigned over time, remains challenging. Existing designs suffer from two limitations: (i) they do not fully leverage the entire history for treatment allocation; (ii) they rely on strong assumptions to approximate the objective function (e.g., the mean squared error of the estimated treatment effect) for optimizing the design. We first establish an impossibility theorem showing that failure to condition on the full history leads to suboptimal designs, due to the dynamic dependencies in time series experiments. To address both limitations simultaneously, we next propose a transformer reinforcement learning (RL) approach which leverages transformers to condition treatment allocation on the entire history and employs RL to directly optimize the MSE without relying on restrictive assumptions. Empirical evaluations on synthetic data, a publicly available dispatch simulator, and a real-world ridesharing dataset demonstrate that our proposal consistently outperforms existing designs.

Applications · Time Series

Xiaoda Wang, Kaiqiao Han, Yuhao Xu, Xiao Luo, Yizhou Sun, Wei Wang, Carl Yang

Cardiovascular disease (CVD) is a leading cause of mortality worldwide. Electrocardiograms (ECGs) are the most widely used non-invasive tool for cardiac assessment, yet large, well-annotated ECG corpora are scarce due to cost, privacy, and workflow constraints. Generating ECGs can aid mechanistic understanding of cardiac electrical activity, enable the construction of large, heterogeneous, and unbiased datasets, and facilitate privacy-preserving data sharing. Generating realistic ECG signals from clinical context is important yet underexplored. Recent work has leveraged diffusion models for text-to-ECG generation, but two challenges remain: (i) existing methods often overlook physiological simulator knowledge of cardiac activity; and (ii) they ignore broader, experience-based clinical knowledge grounded in real-world practice. To address these gaps, we propose **SE-Diff**, a physiological simulator- and experience-enhanced diffusion model for comprehensive ECG generation. SE-Diff integrates a lightweight ordinary differential equation (ODE)–based ECG simulator into the diffusion process via a beat decoder and simulator-consistent constraints, injecting mechanistic priors that promote physiologically plausible waveforms. In parallel, we design an LLM-powered, experience retrieval–augmented strategy to inject clinical knowledge, providing stronger guidance for ECG generation. Extensive experiments on real-world ECG datasets demonstrate that SE-Diff improves both signal fidelity and text–ECG semantic alignment over baselines. We further show that simulator-based and experience-based knowledge benefit downstream ECG classification.

Applications · Time Series

Roberto Neglia, Andrea Cini, Michael Bronstein, Filippo Maria Bianchi

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

Applications · Time Series

Zhiyuan Zhao, Haoxin Liu, B. Aditya Prakash

Time-series forecasting finds broad applications in real-world scenarios. Due to the dynamic nature of time series data, it is important for time-series forecasting models to handle potential distribution shifts over time. In this paper, we initially identify two types of distribution shifts in time series: concept drift and temporal shift. We acknowledge that while existing studies primarily focus on addressing temporal shift issues in time series forecasting, designing proper concept drift methods for time series forecasting has received comparatively less attention. Motivated by the need to address potential concept drift, while conventional concept drift methods via invariant learning face certain challenges in time-series forecasting, we propose a soft attention mechanism that finds invariant patterns from both lookback and horizon time series. Additionally, we emphasize the critical importance of mitigating temporal shifts as a preliminary to addressing concept drift. In this context, we introduce ShifTS, a method-agnostic framework designed to tackle temporal shift first and then concept drift within a unified approach. Extensive experiments demonstrate the efficacy of ShifTS in consistently enhancing the forecasting accuracy of agnostic models across multiple datasets, and outperforming existing concept drift, temporal shift, and combined baselines.

Deep Learning · Graph Neural Networks

Zongjiang Shang, Dongliang Cui, Binqing Wu, Ling Chen

Recently, there has been great success in leveraging pre-trained large language models (LLMs) for time series analysis. The core idea lies in effectively aligning the modality between natural language and time series. However, the multi-scale structures of natural language and time series have not been fully considered, resulting in insufficient utilization of LLMs capabilities. To this end, we propose MSH-LLM, a Multi-Scale Hypergraph method that aligns Large Language Models for time series analysis. Specifically, a hyperedging mechanism is designed to enhance the multi-scale semantic information of time series semantic space. Then, a cross-modality alignment (CMA) module is introduced to align the modality between natural language and time series at different scales. In addition, a mixture of prompts (MoP) mechanism is introduced to provide contextual information and enhance the ability of LLMs to understand the multi-scale temporal patterns of time series. Experimental results on 27 real-world datasets across 5 different applications demonstrate that MSH-LLM achieves the state-of-the-art results.

Yanfeng Yang, Siwei Chen, Pingping Hu, Zhaotong Shen, Yingjie Zhang, Zhuoran Sun, Shuai Li, Ziqi Chen, Kenji Fukumizu

Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In this work, we propose Conditionally Whitened Generative Models (CW-Gen), a framework that incorporates prior information through conditional whitening. Theoretically, we establish sufficient conditions under which replacing the traditional terminal distribution of diffusion models, namely the standard multivariate normal, with a multivariate normal distribution parameterized by estimators of the conditional mean and covariance improves sample quality. Guided by this analysis, we design a novel Joint Mean-Covariance Estimator (JMCE) that simultaneously learns the conditional mean and sliding-window covariance. Building on JMCE, we introduce Conditionally Whitened Diffusion Models (CW-Diff) and extend them to Conditionally Whitened Flow Matching (CW-Flow). Experiments on five real-world datasets with six state-of-the-art generative models demonstrate that CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches. Empirical results further demonstrate that CW-Gen can effectively mitigate the effects of distribution shift.

Applications · Time Series

Qingdi Liu, Yan Fu, Lishuo LIU, Yanke LIN, Jin Xin, Jianfeng Zhang, Cheng Liu, Lujia Pan, Dongxu Guo, Yuejiu Zheng 等

With the accelerated popularization of electric vehicles (EV), battery safety issues have become an important research focus. Data-driven battery fault diagnosis algorithms, built on real-world operational data, are critical methods for reducing safety risks. However, existing battery datasets have limitations such as insufficient scale, coarse-grained labels, and lack of coverage of real-world operating conditions, which seriously restrict the development of data-driven fault diagnosis algorithms. To address these issues, this paper introduces a large-scale benchmark dataset named CH-BatteryGen, which is, to the best of our knowledge, the first EV battery system fault diagnosis dataset based on real-world operating conditions. This dataset integrates real on-board operation data with mechanism-constrained generative modeling technology, balancing authenticity and scalability. It covers two mainstream battery chemistries, namely nickel-cobalt-manganese (NCM) lithium batteries and lithium iron phosphate (LFP) batteries, and involves charging, discharging, and operation data of 1000 electric vehicles. It provides four fault labels (normal, self-discharge, high-resistance, low-capacity) and three severity level annotations, supporting two benchmark tasks: fault classification and fault grading. Through systematic validation using traditional machine learning methods (random forest (RF), support vector machine (SVM)) and deep learning models (long short-term memory (LSTM), convolutional neural network (CNN)), the results show that the CNN model performs best in the fault classification task, achieving an F1-score of 0.9280 in the LFP discharging scenario; in the fault grading task, the F1-score reaches 0.8813. The CH-BatteryGen dataset has been open-sourced, aiming to provide a standardized evaluation platform for battery fault diagnosis algorithms, promote research development in this field, and contribute to the transformation of sustainable transportation systems.

Deep Learning · Theory

Nikolaos Tsilivis, Eran Malach, Karen Ullrich, Julia Kempe

Recent advances in reasoning domains with neural networks have primarily been enabled by a training recipe that optimizes Large Language Models, previously trained to predict the next-token in a sequence, with reinforcement learning algorithms. We introduce a framework to study the success of this paradigm, and we theoretically expose the optimization mechanisms by which reinforcement learning improves over next-token prediction in this setting. We study learning from mixture distributions of short and long “chain-of-thought” sequences encoding a single task. In particular, when the task consists of predicting the parity of $d$ bits and long sequences are rare, we show how reinforcement learning after next-token prediction enables autoregressive transformers to generalize, whereas mere next-token prediction requires extreme statistical or computational resources to do so. We further explain how reinforcement learning leverages increased test-time computation, manifested in longer responses, to facilitate this learning process. In a simplified setting, we theoretically prove that autoregressive linear models following this training recipe can efficiently learn to predict the parity of $d$ bits as long as the proportion of long demonstrations in the data mix is not exponentially small in the input dimension $d$. Finally, we demonstrate these same phenomena in other settings, including the post-training of Llama-series models on mixture variations of common mathematical reasoning benchmarks.

Applications · Time Series

Coen Adler, Yuxin Chang, Samar Abdi, Felix Draxler, Padhraic Smyth

The recent development of foundation models for time series data has generated considerable interest in using such models across a variety of applications. Although foundation models achieve state-of-the-art predictive performance, their calibration properties remain relatively underexplored, despite the fact that calibration can be critical for many practical applications. In this paper, we investigate the calibration-related properties of five recent time series foundation models and two competitive baselines. We perform a series of systematic evaluations assessing model calibration (i.e., over- or under-confidence), effects of varying prediction heads, and calibration under long-term autoregressive forecasting. We find that time series foundation models are consistently better calibrated than baseline models and tend not to be either systematically over- or under-confident, in contrast to the overconfidence often seen in other deep learning models.

Applications · Everything Else

Jiahui Chen, Bo Peng, Lianchen Jia, Zeyu Zhang, Tianchi Huang, Lifeng Sun

Content-aware streaming requires dynamic, chunk-level importance weights to optimize subjective quality of experience (QoE). However, direct human annotation is prohibitively expensive while vision-saliency models generalize poorly. We introduce HiVid, the first framework to leverage Large Language Models (LLMs) as a scalable human proxy to generate high-fidelity weights for both Video-on-Demand (VOD) and live streaming. We address 3 non-trivial challenges: (1) To extend LLMs' limited modality and circumvent token limits, we propose a perception module to assess frames in a local context window, autoregressively building a coherent understanding of the video. (2) For VOD with rating inconsistency across local windows, we propose a ranking module to perform global re-ranking with a novel LLM-guided merge-sort algorithm. (3) For live streaming which requires low-latency, online inference without future knowledge, we propose a prediction module to predict future weights with a multi-modal time series model, which comprises a content-aware attention and adaptive horizon to accommodate asynchronous LLM inference. Extensive experiments show HiVid improves weight prediction accuracy by up to 11.5\% for VOD and 26\% for live streaming over SOTA baselines. Real-world user study validates HiVid boosts streaming QoE correlation by 14.7\%.

Applications · Time Series

Huiqiang Wang, Jieming Shi, Qing Li

Modeling the relationships among variables has become increasingly important, particularly in high-dimensional multivariate time series forecasting tasks. However, most existing methods primarily focus on capturing coarse-grained correlations between variables, overlooking a finer and more dynamic aspect: the variable interactions often manifest differently as time progresses. To address this limitation, we propose FACT, an Fine-grained Across-variable Convolution architecture for multivariate Time series forecasting that explicitly models fine-grained variable interactions from both the time and frequency domains. Technically, we introduce a depth-wise convolution block DConvBlock, which leverages a depth-wise convolution architecture with channel-specific kernels to model dynamic variable interactions at each granularity. To further enhance efficiency, we reconfigure the original one-dimensional variables into a two-dimensional space, reducing the variable distance and the required model layers. Then DConvBlock incorporates multi-dilated 2D convolutions with progressively increasing dilation rates, enabling the model to capture fine-grained and dynamic variable interactions while efficiently attaining a global reception field. Extensive experiments on twelve benchmark datasets demonstrate that FACT not only achieves state-of-the-art forecasting accuracy but also delivers substantial efficiency gains, significantly reducing both training time and memory consumption compared to attention mechanism.

Applications · Time Series

Xiannan Huang, Shuhan Qiu, Jiayuan Du, Chao Yang

Time series forecasting is of significant importance across various domains. However, it faces significant challenges due to distribution shift. This issue becomes particularly pronounced in online deployment scenarios where data arrives sequentially, requiring models to adapt continually to evolving patterns. Current time series online learning methods focus on two main aspects: selecting suitable parameters to update (e.g., final layer weights or adapter modules) and devising suitable update strategies (e.g., using recent batches, replay buffers, or averaged gradients). We challenge the conventional parameter selection approach, proposing that distribution shifts stem from changes in underlying latent factors influencing the data. Consequently, updating the feature representations of these latent factors may be more effective. To address the critical problem of delayed feedback in multi-step forecasting (where true values arrive much later than predictions), we introduce ADAPT-Z (Automatic Delta Adjustment via Persistent Tracking in Z-space). ADAPT-Z utilizes an adapter module that leverages current feature representations combined with historical gradient information to enable robust parameter updates despite the delay. Extensive experiments demonstrate that our method consistently outperforms standard base models without adaptation and surpasses state-of-the-art online learning approaches across multiple datasets.

General Machine Learning · Probabilistic Methods

Conor Hassan, Nasrulloh Satrio, Cen-You Li, Daolang Huang, Paul Chang, Yang Yang, Francesco Silvestrin, Samuel Kaski, Luigi Acerbi

Set-based transformer models for amortized probabilistic inference and meta-learning, such as neural processes, prior-fitted networks, and tabular foundation models, excel at single-pass _marginal_ prediction. However, many applications require _joint distributions_ over multiple predictions. Purely autoregressive architectures generate these efficiently but sacrifice flexible set-conditioning. Obtaining joint distributions from set-based models requires re-encoding the entire context at each autoregressive step, which scales poorly. We introduce a _causal autoregressive buffer_ that combines the strengths of both paradigms. The model encodes the context once and caches it; a lightweight causal buffer captures dependencies among generated targets, with each new prediction attending to both the cached context and all previously predicted targets added to the buffer. This enables efficient batched autoregressive sampling and joint predictive density evaluation. Training integrates set-based and autoregressive modes through masked attention at minimal overhead. Across synthetic functions, EEG time series, a Bayesian model comparison task, and tabular regression, our method closely matches the performance of full context re-encoding while delivering up to $20\times$ faster joint sampling and density evaluation, and up to $7\times$ lower memory usage.

Shifeng Xie, Vasilii Feofanov, Jianfeng Zhang, Themis Palpanas, Ievgen Redko

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

Applications · Time Series

Roussel Nzoyem, Nawid Keshtmand, Enrique Crespo Fernandez, Idriss TSAYEM, Raul Santos-Rodriguez, David Barton, Tom Deakin

We introduce WARP (**W**eight-space **A**daptive **R**ecurrent **P**rediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 4 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalization capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Applications · Language, Speech and Dialog

Thinh Pham, Nguyen Nguyen, Pratibha Zunjare, Weiyuan Chen, Yu-Min Tseng, Tu Vu

We introduce SealQA, a challenge benchmark for evaluating SEarch-Augmented Language models on fact-seeking questions where web search yields conflicting, noisy, or unhelpful results. SealQA comes in three flavors: (1) SEAL-0 (main) and (2) SEAL-HARD, both of which assess factual accuracy and reasoning capabilities, where SEAL-0 targets the most challenging questions that frontier non-reasoning models (e.g., GPT-4.1) answer with near-zero accuracy; and (3) LongSeal, which extends SealQA to test long-context, multi-document reasoning in "needle-in-a-haystack" settings. Our evaluation reveals critical limitations in current models. Even frontier reasoning models face significant challenges across SealQA flavors. On SEAL-0, GPT-5 with tools achieves only 43.2% accuracy at its best reasoning effort. We also find that even advanced reasoning models (e.g., DeepSeek-R1) can be vulnerable to noisy search results. Notably, increasing test-time compute does not yield reliable gains across GPT-5 and the o-series of models, with performance often plateauing or even declining early. Finally, while current models are less affected by the "lost-in-the-middle" issue, they still fail to reliably identify relevant documents in LongSeal when faced with numerous distractors. To facilitate future work, we release SealQA at https://huggingface.co/datasets/vtllms/sealqa.

Deep Learning · Generative Models and Autoencoders

Junghwan Lee, Chen Xu, Yao Xie

Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for uncertainty quantification. While conformal prediction has gained attention as a reliable uncertainty quantification method, conformal prediction for time series faces two key challenges: (1) \textbf{leveraging correlations in observations and non-conformity scores to overcome the exchangeability assumption}, and (2) \textbf{constructing prediction sets for multi-dimensional outcomes}. To address these challenges, we propose a novel conformal prediction method for time series using flow with classifier-free guidance. We provide coverage guarantees by establishing exact non-asymptotic marginal coverage and a finite-sample bound on conditional coverage for the proposed method. Evaluations on real-world time series datasets demonstrate that our method constructs significantly smaller prediction sets than existing conformal prediction methods, maintaining target coverage.

General Machine Learning · Probabilistic Methods

Dongze Wu, Feng Qiu, Yao Xie

Time-series forecasting increasingly demands not only accurate observational predictions but also causal forecasting under interventional and counterfactual queries in multivariate systems. We present DoFlow, a flow-based generative model defined over a causal Directed Acyclic Graph (DAG) that delivers coherent observational and interventional predictions, as well as counterfactuals through the natural encoding–decoding mechanism of continuous normalizing flows (CNFs). We also provide a supporting counterfactual recovery theory under certain assumptions. Beyond forecasting, DoFlow provides explicit likelihoods of future trajectories, enabling principled anomaly detection. Experiments on synthetic datasets with various causal DAG structures and real-world hydropower and cancer-treatment time series show that DoFlow achieves accurate system-wide observational forecasting, enables causal forecasting over interventional and counterfactual queries, and effectively detects anomalies. This work contributes to the broader goal of unifying causal reasoning and generative modeling for complex dynamical systems.

Applications · Time Series

Fan Zhang, Sinchee Chin, Jing-Hao Xue, Wenming Yang

Time series anomaly detection (TSAD) faces critical challenges from intrinsic data noisiness and temporal heterogeneity, which undermine the reconstruction fidelity of prevailing generative approaches. While diffusion models offer theoretical advantages in capturing complex temporal dynamics, their inherent stochasticity introduces irreducible variance in reconstructions. We present the ICDiffAD, a novel method that synergizes adaptive noise scheduling with semi-deterministic generation to address these limitations. ICDiffAD introduces two key innovations: (1) an *SNR Scheduler* that governs training through quantifiable noise scales, enabling robust learning of normative patterns across non-stationary regimes; and (2) an *SNR Implicit Conditioning Mechanism* that initializes reverse diffusion from partially corrupted inputs, preserving signal coherence while attenuating anomalous components. This dual strategy ensures high-fidelity reconstructions aligned with the input’s manifold, reconciling generative flexibility with detection accuracy. Across five multivariate benchmarks, ICDiffAD improves the F1 score by 19.57\% and reduces false positives by 60.23\% compared to existing diffusion model-based TSAD methods.