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Zhanye Luo, Yuefeng Han, Xiufan Yu

This paper studies the problem of dimension reduction, tailored to improving time series forecasting with high-dimensional predictors. We propose a novel Supervised Deep Dynamic Principal component analysis (SDDP) framework that incorporates the target variable and lagged observations into the factor extraction process. Assisted by a temporal neural network, we construct target-aware predictors by scaling the original predictors in a supervised manner, with larger weights assigned to predictors with stronger forecasting power. A principal component analysis is then performed on the target-aware predictors to extract the estimated SDDP factors. This supervised factor extraction not only improves predictive accuracy in the downstream forecasting task but also yields more interpretable and target-specific latent factors. Building upon SDDP, we propose a factor-augmented nonlinear dynamic forecasting model that unifies a broad family of factor-model-based forecasting approaches. To further demonstrate the broader applicability of SDDP, we extend our studies to a more challenging scenario when the predictors are only partially observable. We validate the empirical performance of the proposed method on several real-world public datasets. The results show that our algorithm achieves notable improvements in forecasting accuracy compared to state-of-the-art methods.

Junkai Lu, Peng Chen, Chenjuan Guo, Yang Shu, Meng Wang, Bin Yang

Time series forecasting is critical for decision making across dynamic domains such as energy, finance, transportation, and cloud computing. However, real-world time series often exhibit non-stationarity, including temporal distribution shifts and spectral variability, which poses significant challenges for existing long-term time series forecasting methods. In this paper, we propose DTAF, a dual-branch framework that addresses non-stationarity in both the temporal and frequency domains. For the temporal domain, the Temporal Stabilizing Fusion (TFS) module employs a non-stationary mix of experts (MOE) filter to disentangle and suppress temporal non-stationary patterns while preserving long-term dependencies. For the frequency domain, the Frequency Wave Modeling (FWM) module applies frequency differencing to dynamically highlight components with significant spectral shifts. By fusing the complementary outputs of TFS and FWM, DTAF generates robust forecasts that adapt to both temporal and frequency domain non-stationarity. Extensive experiments on multiple real-world benchmarks demonstrate that DTAF outperforms state-of-the-art baselines, yielding significant improvements in forecasting accuracy under non-stationary conditions.

Zhixin Liu, Xuanlin Liu, Sihan Xu, Yaqiong Qiao, Ying Zhang, Xiangrui Cai

Existing backdoor attacks on multivariate time series (MTS) forecasting enforce strict temporal and dimensional coupling between triggers and target patterns, requiring synchronous activation at fixed positions across variables. However, realistic scenarios often demand delayed and variable-specific activation. We identify this critical unmet need and propose TDBA, a temporally decoupled backdoor attack framework for MTS forecasting. By injecting triggers that encode the expected location of the target pattern, TDBA enables the activation of the target pattern at any positions within the forecasted data, with the activation position flexibly varying across different variable dimensions. TDBA introduces two core modules: (1) a position-guided trigger generation mechanism that leverages smoothed Gaussian priors to generate triggers that are position-related to the predefined target pattern; and (2) a position-aware optimization module that assigns soft weights based on trigger completeness, pattern coverage, and temporal offset, facilitating targeted and stealthy attack optimization. Extensive experiments on real-world datasets show that TDBA consistently outperforms existing baselines in effectiveness while maintaining good stealthiness. Ablation studies confirm the controllability and robustness of its design.

Zhen Liu, Yucheng Wang, Boyuan Li, Junhao Zheng, Emadeldeen Eldele, Min Wu, Qianli Ma

Foundation models pre-trained on large-scale source datasets are reshaping the traditional training paradigm for time series classification. However, existing time series foundation models primarily focus on forecasting tasks and often overlook classification-specific challenges, such as modeling interpretable shapelets that capture class-discriminative temporal features. To bridge this gap, we propose UniShape, a unified shape-aware foundation model designed for time series classification. UniShape incorporates a shape-aware adapter that adaptively aggregates multiscale discriminative subsequences (shapes) into class tokens, effectively selecting the most relevant subsequence scales to enhance model interpretability. Meanwhile, a prototype-based pretraining module is introduced to jointly learn instance- and shape-level representations, enabling the capture of transferable shape patterns. Pre-trained on a large-scale multi-domain time series dataset comprising 1.89 million samples, UniShape exhibits superior generalization across diverse target domains. Experiments on 128 UCR datasets and 30 additional time series datasets demonstrate that UniShape achieves state-of-the-art classification performance, with interpretability and ablation analyses further validating its effectiveness.

Yu Liu, Haoqin Yang, Jinping Sui, Hui Wang, Haipeng Li, Weimin Wang, Qi Jia

Class-incremental learning (CIL) has recently gained great attention in the field of time series classification. Existing CIL methods based on knowledge distillation exhibit impressive ability to retain prior knowledge and overcome catastrophic forgetting, however, their effectiveness faces major challenges posed by time series data. Since temporal data is more susceptible to sensor errors and electronic noise, the distillation process may be significantly affected by noisy knowledge transfer. To address this issue, we propose a novel confidence-guided mask distillation (CMD) framework, to prevent the noisy inheritance during distillation. The core of CMD lies in a dynamic masking mechanism guided by prediction confidence, capable of allocating higher weights to high-confidence time series and substantially suppressing the influence of low-confidence ones. Additionally, different from prior work simply passing a set of feature prototypes to the classifier, we develop prototype-guided contrastive learning (PCL) to alleviate the classifier bias on new classes, through extra contrastive constraints to push away the feature distributions of old feature prototypes from those of new classes features. Extensive experiments on three time-series datasets demonstrate that, our method significantly outperforms other replay-free CIL approaches in raising average accuracy, as well as decreasing forgetting rate.

Ying Liu, Bo Liu, Sheng Huang, Gang Luo, Wenbo Hu, Meng Wang, Richang Hong

Time series forecasting (TSF) plays a crucial role in many real-world applications, such as weather prediction and economic planning. While Transformer-based models have shown strong capabilities in modeling long-range dependencies, effectively capturing the multi-scale temporal dynamics inherent in time series remains a major challenge. Existing methods often adopt time-windows of varying sizes, which may introduce noisy or irrelevant representations when mismatched with the underlying temporal patterns, potentially leading to overfitting. In this paper, we propose Sparse-Scale Transformer (SSformer) with Bidirectional Awareness for Time Series Forecasting to enhance the multi-scale modeling for time series. Specifically, we propose a novel Sparse-Scale Convolution (SSC) block that imposes sparsity on scales to obtain the informative representations by evaluating the intra-scale segment similarity of time series, and utilizes scale-specific convolutions to extract local patterns. Furthermore, we design a Bidirectional-Scale Interaction (BSI) block to explicitly model scale correlations in both coarse-to-fine and fine-to-coarse directions. Finally, scale predictions are ensembled to fully exploit the complementary forecasting capabilities across scales. Extensive experiments on various real-world datasets demonstrate that SSformer achieves state-of-the-art performance with superior efficiency.

Xvyuan Liu, Xiangfei Qiu, Xingjian Wu, Zhengyu Li, Chenjuan Guo, Jilin Hu, Bin Yang

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main factors. First, the inherent irregularity and data missingness in irregular time series make modeling difficult. Second, most existing methods are typically complex and resource-intensive. In this study, we propose a general framework called APN to address these challenges. Specifically, we design a novel Time-Aware Patch Aggregation (TAPA) module that achieves adaptive patching. By learning dynamically adjustable patch boundaries and a time-aware weighted averaging strategy, TAPA transforms the original irregular sequences into high-quality, regularized representations in a channel-independent manner. Additionally, we use a simple query module to effectively integrate historical information while maintaining the model's efficiency. Finally, predictions are made by a shallow MLP. Experimental results on multiple real-world datasets show that APN outperforms existing state-of-the-art methods in both efficiency and accuracy.

Shikang Liu, Ziyu Tang, Xiren Zhou, Huanhuan Chen

Multivariate time series classification (MTSC) has broad applications in numerous domains. Existing MTSC methods typically focus on either temporal dynamics or variable interactions of the data, often overlooking cross-scale couplings among different variables. To bridge this gap, we propose Scale-Variable Graph Learning (SVGL), a novel framework that effectively captures data-inherent scale-variable interactions for MTSC. SVGL begins with spectral analysis to adaptively identify key periodic scales for each variable. A period-aware reservoir computing network is then incorporated to fit the variable at these scales, encoding the sequential and periodic dynamics into multi-scale dynamic representations. Subsequently, we construct a scale-variable graph to model interactions of the encoded temporal dynamics, where nodes represent scale-variable pairs and edges denote their correlations. After sparsely initializing the graph via nearest neighbors, a parallel graph learning architecture is integrated in SVGL, combining global graph convolutional and sample-specific graph attention to aggregate effective features for classification. Extensive experiments on 30 UEA datasets demonstrate that SVGL outperforms state-of-the-art baselines in accuracy and maintains low training overhead.

Jiexi Liu, Meng Cao, Songcan Chen

Irregularly sampled time series (ISTS), characterized by non-uniform time intervals with natural missingness, are prevalent in real-world applications. Existing approaches for ISTS modeling primarily rely on observed values to impute unobserved ones or infer latent dynamics. However, these methods overlook a critical source of learning signal: the reconstruction error inherently produced during model training. Such error implicitly reflects how well a model captures the underlying data structure and can serve as an informative proxy for unobserved values. To exploit this insight, we propose iTimER, a simple yet effective self-supervised pre-training framework for ISTS representation learning. iTimER models the distribution of reconstruction errors over observed values and generates pseudo-observations for unobserved timestamps through a mixup strategy between sampled errors and the last available observations. This transforms unobserved timestamps into noise-aware training targets, enabling meaningful reconstruction signals. A Wasserstein metric aligns reconstruction error distributions between observed and pseudo-observed regions, while a contrastive learning objective enhances the discriminability of learned representations. Extensive experiments on classification, interpolation, and forecasting tasks demonstrate that iTimER consistently outperforms state-of-the-art methods under the ISTS setting.

Li Lin, Xinrui Zhang, Qi Zhang, Shuai Wang, Kaiwen Xia

Time Series Foundation Models (TSFMs) have emerged as a promising approach in time series analysis. Due to the large-scale parameters of TSFMs and pretraining cost, how to adapt TDFMs in streaming data is always the key factor constraining their application effectiveness. Because streaming data often experiences data distribution and task drifts, which cannot be learnt by offline training. Existing methods typically address streaming data modeling with continuous learning through model fine-tuning or model editing. However, fine-tuning incurs significant computational costs, while editing methods can lead to shifts in the original feature space during streaming updates. To address these limitations, we propose a novel Orthogonal Rotation Transformation-based Continuous Learning method, called ORTCL, for TSFMs. Our key insight is to apply orthogonal matrix rotations to the input and output feature spaces of the TSFMs during model editing. This preserves the metric structure of the original feature space and enables new data to be directly mapped into the existing feature space of the TSFMs. Specifically, we obtain the orthogonal matrix for the input layer via singular value decomposition and derive the corresponding transformation matrix for the output layer through least squares optimization. Extensive experimental results demonstrate that ORTCL outperforms existing methods in both single-domain and cross-domain streaming time series forecasting tasks, effectively mitigating catastrophic forgetting.

Huaizhang Liao, Zhixiong Yang, Jingyuan Xia, Yuheng Sun, Yue Zhang, Shengxi Li, Yongxiang Liu

Despite the remarkable success of semantic token learning in NLP and vision domains, token-level representation mechanisms face fundamental challenges when extended to continuous time series analysis. We identify a core limitation lies in the intrinsic absence of semantically meaningful tokenization boundaries within time-series, which differs substantially from discrete text tokens and presents unique complexities compared to spatially coherent image patches. While existing works mechanically apply fixed-length partitioning, recent evidence from time series foundation models reveals performance ceilings in prediction tasks under such paradigms. This paper introduces a novel tokenization framework known as physics-aware tokenization (PATK), designed to implement adaptive time-frequency tokenization via distribution-sensitive sampling strategies. Key innovations include: 1) A Rate-of-Variation (RoV) distribution is meticulously structured to encompass multi-scale temporal dynamics in the time domain, alongside a Spectral Energy Intensity (SEI) distribution devised to reveal global seasonal patterns within the frequency domain; 2) A physics-aware hidden Markov modeling (PA-HMM) is then established to adaptively breaks down continuous time-series into distinct tokens with elastic lengths, responding to physics-aware probabilities sampled from RoV and SEI distributions. The proposed PATK allows steady integration with both conventional Transformers and advanced large-scale time series models (including LLM-transferred methods and pretrained time series foundation models). Simulations across various datasets demonstrate that PATK excels in classification and forecasting tasks, showing notable adaptability to model long-term dependencies, strengthening resilience against disturbances, and robustness to missing data events.

Daojun Liang, Jing Chen, Xiao Wang, Yinglong Wang, Shuo Li

Time-Series (TS) exhibits pronounced non-stationarity. Consequently, most forecasting methods display compromised robustness to concept drift, despite the prevalent application of instance normalization. We tackle this challenge by first analysing concept drift through a bias-variance lens and proving that weighted ensemble reduces variance without increasing bias. These insights motivate DeepBooTS, a novel end-to-end dual-stream residual-decreasing boosting method that progressively reconstructs the intrinsic signal. In our design, each block of a deep model becomes an ensemble of learners with an auxiliary output branch forming a highway to the final prediction. The block‑wise outputs correct the residuals of previous blocks, leading to a learning‑driven decomposition of both inputs and targets. This method enhances versatility and interpretability while substantially improving robustness to concept drift. Extensive experiments, including those on large-scale datasets, show that the proposed method outperforms existing methods by a large margin, yielding an average performance improvement of 15.8% across various datasets, establishing a new benchmark for TS forecasting.

Xingwang Li, Fei Teng, Xin Wu, Qiang Duan

Hidden degenerations in industrial time series often precede observable failures, they remain undetected by standard monitoring systems until anomalies become apparent. This gap between microscopic degradation and macroscopic observation renders conventional predictors inherently reactive, as they rely on correlations in sensor data rather than uncovering the underlying, physics‑consistent degradation states. Crucially, the microscopic mechanisms governing system evolution depend on macroscopic state variables—whose measurements are expectations over microscopic probability distributions—so purely data‑driven “top‑down” or purely physics‑guided “bottom‑up” approaches cannot forecast degeneration‑entangled industrial faults. To address these challenges, we propose a Physics-Guided Bidirectional Inference Framework that represents hidden microscopic states from macroscopic measurements. Our approach uniquely combines: (1) bottom-up physics-based simulation using Continuum Damage Mechanics to model micro-scale damage evolution under environmental stressors, and (2) top-down probabilistic inference via maximum entropy formalism to estimate latent microstate distributions from sparse sensor data. This bidirectional mechanism enables early failure prediction by bridging observable measurements with unobservable degeneration. Validation on real-world railway infrastruc datasets demonstrates significant improvements in early fault prediction compared to state-of-the-art baselines. Our method establishes a new paradigm for safety-critical industrial applications requiring reliable prediction of hidden degeneration processes.

Kanxue Li, Yibing Zhan, Hua Jin, Chongchong Qi, Xu Lin, Baosheng Yu

Intraoperative hypotension (IOH) poses significant surgical risks, but accurate prediction remains challenging due to patient-specific variability. While test-time adaptation (TTA) offers a promising approach for personalized prediction, the rarity of IOH events often leads to unreliable test-time training. To address this, we propose CSA-TTA, a novel cross-sample augmented test-time adaptation framework that enhances training by incorporating hypotension events from other individuals. Specifically, we first construct a cross-sample bank by segmenting historical data into hypotensive and non-hypotensive samples. Then, we introduce a coarse-to-fine retrieval strategy for building test-time training data: we initially apply K-Shape clustering to identify representative cluster centers and subsequently retrieve the top-K semantically similar samples based on the current patient signal. Additionally, we integrate both self-supervised masked reconstruction and retrospective sequence forecasting signals during training to enhance model adaptability to rapid and subtle intraoperative dynamics. We evaluate the proposed CSA-TTA on both the VitalDB dataset and a real-world in-hospital dataset by integrating it with state-of-the-art time series forecasting models, including TimesFM and UniTS. CSA-TTA consistently enhances performance across settings—for instance, on VitalDB, it improves Recall and F1 scores by +1.33% and +1.13%, respectively, under fine-tuning, and by +7.46% and +5.07% in zero-shot scenarios—demonstrating strong robustness and generalization.

Jonghun Lee, YongKyung Oh, Sungil Kim, Dong-Young Lim

Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, making them susceptible to overfitting. To address this research gap, we introduce Continuum Dropout, a universally applicable regularization technique for NDEs built upon the theory of alternating renewal processes. Continuum Dropout formulates the on-off mechanism of dropout as a stochastic process that alternates between active (evolution) and inactive (paused) states in continuous time. This provides a principled approach to prevent overfitting and enhance the generalization capabilities of NDEs. Moreover, Continuum Dropout offers a structured framework to quantify predictive uncertainty via Monte Carlo sampling at test time. Through extensive experiments, we demonstrate that Continuum Dropout outperforms existing regularization methods for NDEs, achieving superior performance on various time series and image classification tasks. It also yields better-calibrated and more trustworthy probability estimates, highlighting its effectiveness for uncertainty-aware modeling.

Linghao Kong, Xiaopeng Hong

Deep neural network-based time series prediction models have recently demonstrated superior capabilities in capturing complex temporal dependencies. However, it is challenging for these models to account for uncertainty associated with their predictions, because they directly output scalar values at each time step. To address such a challenge, we propose a novel model named interleaved dual-branch Probability Distribution Network (interPDN), which directly constructs discrete probability distributions per step instead of a scalar. The regression output at each time step is derived by computing the expectation of the predictive distribution on a predefined support set. To mitigate prediction anomalies, a dual-branch architecture is introduced with interleaved support sets, augmented by coarse temporal-scale branches for long-term trend forecasting. Outputs from another branch are treated as auxiliary signals to impose self-supervised consistency constraints on the current branch's prediction. Extensive experiments on multiple real-world datasets demonstrate the superior performance of interPDN.

Shuning Jia, Baijun Song, Canming Ye, Chun Yuan

Multivariate Time Series Forecasting (MTSF) aims to capture the dependencies among multiple variables and their temporal dynamics to predict future values. In recent years, Large Language Models (LLMs) have set a new paradigm for MTSF, incorporating external knowledge into the modeling process through textual prompts. However, we observe that current LLM-based methods fail to exploit these priors due to their coarse-grained representation of time series data, which hinders effective alignment of the two modals. To address this, we propose M3Time, a multi-modal, multi-scale, and multi-frequency framework for multivariate time series forecasting. It enhances the quality of time series representations and facilitates the integration of LLM semantic priors with fine-grained temporal features. Additionally, M3Time further improved training stability and model robustness with an adaptive mixed loss function, which dynamically balances L1 and L2 error terms. Experiment results on seven real-world public datasets show that M3Time consistently outperforms state-of-the-art methods, underscoring its effectiveness.

Haoyi Jia

While Transformers have revolutionized time series forecasting, they remain trapped by manual architecture design—every model uses the same attention mechanism, normalization, and activation choices. What if we could automatically discover the perfect architectural recipe for each dataset? This work introduces STrans (Spontaneous Transformer), a comprehensive neural architecture search framework for time series Transformers that simultaneously explores attention variants, normalization techniques, activation functions, and encoding operations. Using differentiable architecture search, STrans automatically discovers architectures that outperform manually designed baselines. However, the experiments reveal a surprising and counterintuitive finding: complex searched architectures often fail catastrophically, while simpler configurations generalize better. This "search overfitting" phenomenon challenges fundamental assumptions about automated architecture design in time series domains. The work not only advances automated model design but uncovers critical insights that will reshape how we think about neural architecture search for temporal data.

Yaohui Huang, Runmin Zou, Yun Wang, Laeeq Aslam, Ruipeng Dong

Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events' complex temporal dynamics. To address these limitations, we propose M²FMoE, an extreme-adaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multi-view frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances long-term trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M²FMoE outperforms state-of-the-art baselines without requiring extreme-event labels.

Shuokang Huang, Julie McCann

Human sensing with radio signals has emerged as a non-intrusive and occlusion-robust alternative to vision-based approaches, and WiFi signals further support device-free sensing. However, current approaches deeply rely on neural networks, whose black-box nature hinders model transparency and explainability, limiting the use of WiFi-based human sensing in critical fields. For model explainability, recent works have studied saliency methods which attribute model outputs to important features, but they mostly bias in favor of common modalities (e.g., images, time series). This paper proposes a Matryoshka-like saliency method, MatryMask, an initial exploration of feature attribution for human sensing with radio signals. Compared to existing methods that require empirical knowledge about the sparsity of important features, MatryMask regularizes multiple masks to highlight salient areas at different scales, adapting to the uncertain and varying sparsity of important features in radio signals. To effectively perturb radio signals, we devise a novel frequency-removal perturbation beyond existing spatial/time-domain perturbations. Experimentally, MatryMask outperforms state-of-the-art saliency methods and significantly improves the attribution performance by up to 38.1~70.6% for three tasks.