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Applications · Time Series

Yu Fan, Yang Yang, Yufan Guo, Huazhong Yang, pengjun wang

Real-world time-series data often suffer from missing observations, hindering long-range temporal modeling. However, most existing imputation methods formulate imputation as conditional reconstruction over limited context, which restricts temporal information propagation and fails to explicitly model temporal evolution. To overcome this limitation, we propose the Conditional Temporal Inference Paradigm (CTIP), which formulates time-series imputation as conditional inference along temporal evolution. Under this paradigm, we introduce CBiT, which leverages a history compression mechanism to encode long-range history into a compact latent space for history-conditioned temporal imputation. In addition, we adopt a partitioned modeling strategy that distinguishes historical context and temporal imputation targets with only linear-time complexity. Extensive experiments on multiple public benchmarks show that CBiT improves imputation accuracy by reducing Masked MAE and Masked RMSE by 27.3% and 18.6%, respectively, across different missing rates.

Applications · Time Series

Zexing Zhang, Tianyang Lei, Jichao Li, Yang Kewei

Time-series foundation models (TSFMs) deliver strong cross-domain generalization, but their scale makes deployment costly. Knowledge distillation is a natural compression route, yet prior TSFM distillation typically imitates teacher outputs, features, or pairwise relations, and therefore remains tightly coupled to teacher-specific training trajectories while underutilizing two empirical properties: (i) high-level representations across model scales tend to converge toward a shared, approximately low-rank geometry, and (ii) layer-wise utility follows a long-tail pattern. We propose consensus subspace distillation, which reframes distillation as aligning a student to a model-agnostic geometric object: a scale-invariant low-rank consensus subspace together with its center statistics. Offline, we screen high-contribution layers via drop-layer marginal loss, estimate a shrinkage-stabilized covariance from their embeddings, and derive a truncated eigensubspace that defines a consensus projector. Online, we project student embeddings into this subspace and match the teacher’s projected mean and covariance using a lightweight mean--covariance objective, enabling stable optimization without rigid pointwise feature binding. To mitigate subset-induced bias, we further introduce a frequency-domain uncertainty injection mechanism that inflates spectral density based on characteristic-function discrepancies and injects dispersion only within the consensus directions. Across forecasting and imputation, the distilled student matches or slightly improves upon the teacher, while exhibiting a predictable trade-off under strict zero-shot classification. With MOMENT-Large as teacher, we achieve about 90% parameter reduction and substantial distillation-time savings while retaining comparable performance across multiple time-series tasks. Code and compressed weights are available at anonymous.4open.science/r/CSD-13C3/.

Applications · Time Series

Tao Han, Zhibin Wen, Zhenghao Chen, Dazhao Du, Song Guo, LEI BAI

The development of Time-Series Forecasting (TSF) models is often constrained by the lack of comprehensive datasets, especially in Global Station Weather Forecasting (GSWF), where existing datasets are small, temporally short, and spatially sparse. To address this, we introduce WEATHER-5K, a large-scale observational weather dataset that better reflects real-world conditions, supporting improved model training and evaluation. While recent TSF methods perform well on benchmarks, they lag behind operational Numerical Weather Prediction systems in capturing complex weather dynamics and extreme events. We propose PhysicsFormer, a physics-informed forecasting model combining a dynamic core with a Transformer residual to predict future weather states. Physical consistency is enforced via pressure–wind alignment and energy-aware smoothness losses, ensuring plausible dynamics while capturing complex temporal patterns. We benchmark PhysicsFormer and other TSF models against operational systems across several weather variables, extreme event prediction, and model complexity, providing a comprehensive assessment of the gap between academic TSF models and operational forecasting. The dataset and benchmark implementation are available at: https://anonymous.4open.science/r/WEATHER-5K-BF05.

Applications · Time Series

Hua Wang, Xianhao Jiao, Fan Zhang

Deep forecasting models often suffer from attenuated periodic perception and entangled trend–noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Applications · Time Series

Zongjiang Shang, Chengxi Jin, Binqing Wu, Dongliang Cui, Yue Yu, Haobang Sun, Chuanlin Xu, Ling Chen

Time series forecasting plays a pivotal role in data-driven decision-making across various time series domains. Recently, leveraging their ability to extract semantically rich representations, Large Language Models (LLMs) have achieved promising results in time series forecasting. However, existing LLM-based methods struggle to obtain multi-scale retrieval-augmented representations due to entangled multi-scale representations and redundant multi-scale interference. To address this, we propose TimeMRA, an LLM-empowered Time series forecasting framework via Multi-Scale Retrieval-Augmented representations. Specifically, a scale-aware prompt generation (SAPG) module is designed to decompose time series into multiple scales and generate augmented multi-scale representations. Then, a cross-scale disentanglement constraint (CSDC) mechanism with a router network is designed to obtain the disentangled multi-scale semantic representations while mitigating interference from irrelevant scales. Finally, a cross-modality retrieval module is designed to obtain multi-scale retrieval-augmented representations for time series forecasting. Experiments on 10 real-world datasets demonstrate that TimeMRA achieves state-of-the-art (SOTA) performance.

Applications · Time Series

Jiegang Xu, Fuyuan CAO, Jiye Liang

Federated causal discovery for time series is becoming increasingly important in many application domains. In practice, intervention policies on each client often change over time, causing the local underlying causal mechanisms to drift rather than remain fixed. Moreover, different sampling frequencies across clients yield incompatible time scales in the observed data, making the resulting local causal graphs naturally heterogeneous and difficult to aggregate consistently. Accordingly, we propose Fed-CAW, a Credibility-Aware Weighting Federated causal discovery framework for time series. Specifically, we define edge-level credibility scores that quantify per-edge reliability by summarizing (i) within-client temporal stability across windows and (ii) cross-client temporal consistency after mapping heterogeneous sampling frequencies onto a unified time scale. We then aggregate privatized edge statistics under differential privacy, treating credibility scores as weights to recover a global causal graph while preserving personalized local structures without sharing raw data. Theoretically, we demonstrate the rationale for the unified time scale mapping and establish rigorous differential privacy guarantees. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Deep Learning · Sequential Models, Time series

Michael Menezes, Anastasios Kyrillidis

While Mamba2's expanded state dimension enhances temporal modeling, it incurs substantial inference overhead that saturates bandwidth during autoregressive generation. Standard pruning methods fail to address this bottleneck: unstructured sparsity leaves activations dense, magnitude-based selection ignores runtime dynamics, and gradient-based methods impose prohibitive costs. We introduce GHOST (Grouped Hidden-state Output-aware Selection and Truncation), a structured pruning framework that approximates control-theoretic balanced truncation using only forward-pass statistics. By jointly measuring controllability and observability, GHOST rivals the fidelity of gradient-based methods without requiring backpropagation. As a highlight, on models ranging from 130M to 2.7B parameters, our approach achieves a 50% state-dimension reduction with approximately 1 perplexity point increase on WikiText-2. Code is available at https://anonymous.4open.science/r/mamba2_ghost-7BCB/.

Deep Learning · Sequential Models, Time series

Xuesong Wang, Michael Groom, Rafael Oliveira, He Zhao, Terence O'kane, Edwin V. Bonilla

Recent years have seen a surge in data-driven surrogates for dynamical systems that can be orders of magnitude faster than numerical solvers. However, many machine learning-based models such as neural operators exhibit spectral bias, attenuating high-frequency components that often encode small-scale structure. This limitation is particularly damaging in applications such as weather forecasting, where misrepresented high frequencies can induce long-horizon instability. To address this issue, we propose multi-scale wavelet transformers (MSWTs), which learn system dynamics in a tokenized wavelet domain. The wavelet transform explicitly separates low- and high-frequency content across scales. MSWTs leverage a wavelet-preserving downsampling scheme that retains high-frequency features and employ wavelet-based attention to capture dependencies across scales and frequency bands. Experiments on chaotic dynamical systems show substantial error reductions and improved long-horizon spectral fidelity. On the ERA5 climate reanalysis, MSWTs further reduce climatological bias, demonstrating their effectiveness in a real-world forecasting setting.

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

Dong Huang, Chenyang Tian, Pengkun Yang

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge information, many real-world applications provide informative node features in addition to graph topology. To capture this setting, we introduce the featured correlated Gaussian Wigner model, where two graphs are coupled through an unknown vertex permutation, and the node features are correlated under the same permutation. We characterize the optimal information-theoretic thresholds for exact recovery and partial recovery of the latent mapping. On the algorithmic side, we propose QPAlign, an efficient method based on a quadratic programming relaxation, and demonstrate its strong empirical performance on both synthetic and real datasets. Moreover, we also derive theoretical guarantees for the proposed procedure, supporting its reliability and providing convergence guarantees.

Applications · Time Series

Vincent Zheng, Étienne Marcotte, Arjun Ashok, Andrew Williams, Lijun Sun, Alexandre Drouin, Valentina Zantedeschi

Context-aided forecasting (CAF) holds promise for integrating domain knowledge and forward-looking information, enabling AI systems to surpass traditional statistical methods. However, recent empirical studies reveal a puzzling gap: multimodal models often fail to outperform their unimodal counterparts. We hypothesize that this underperformance stems from poor context quality in existing datasets, as verification is challenging. To address these limitations, we introduce a semi-synthetic data augmentation method that generates contexts both descriptive of temporal dynamics and verifiably complementary to numerical histories. This approach enables massive-scale dataset creation, resulting in CAF-7M, a corpus of 7 million context-augmented time series windows, including a rigorously verified test set. We demonstrate that semi-synthetic pre-training transfers effectively to real-world evaluation, and show clear evidence of context utilization. Our results suggest that dataset quality, rather than architectural limitations, has been the primary bottleneck in context-aided forecasting.

Namjoon Suh, Yuning Yang, Din-Yin Hsieh, Qitong Luan, Shirong Xu, Shixiang Zhu, Guang Cheng

We present \texttt{TimeAutoDiff}, a unified latent-diffusion framework that addresses four fundamental time-series tasks—unconditional generation, missing-data imputation, forecasting, and time-varying-metadata conditional generation—within a single model that natively handles heterogeneous features (continuous, binary, and categorical). We unify these tasks through a simple masked-modeling strategy: a binary mask specifies which time feature cells are observed and which must be generated. To make this work on mixed data types, we pair a lightweight variational autoencoder (i.e., VAE)—which maps continuous, categorical, and binary variables into a continuous latent sequence—with a diffusion model that learns dynamics in that latent space, avoiding separate likelihoods for each data type while still capturing temporal and cross-feature structure.Two design choices give \texttt{TimeAutoDiff} clear speed and scalability advantages. First, the diffusion process samples a single latent trajectory for the full time horizon rather than denoising one timestep at a time; this whole-sequence sampling drastically reduces reverse-diffusion calls and yields an order-of-magnitude throughput gain. Second, the VAE compresses along the feature axis, so very wide tables are modeled in a lower-dimensional latent space, further reducing computational load. Empirical evaluation demonstrates that \texttt{TimeAutoDiff} matches or surpasses strong baselines in synthetic sequence fidelity (discriminative, temporal-correlation, and predictive metrics) and consistently lowers MAE/MSE for imputation and forecasting tasks. Time-varying metadata conditioning unlocks real-world scenario exploration: by editing metadata sequences, practitioners can generate coherent families of counterfactual trajectories that track intended directional changes, preserve cross-feature dependencies, and remain conditionally calibrated—making "what-if" analysis practical. Our ablation studies confirm that performance is impacted by key architectural choices, such as the VAE's continuous feature encoding and specific components of the DDPM denoiser. Furthermore, a distance-to-closest-record (DCR) audit demonstrates that the model achieves generalization with limited memorization given enough dataset. Code implementations of \texttt{TimeAutoDiff} are provided in https://github.com/namjoonsuh/TimeAutoDiff.

Applications · Time Series

Shiyan Hu, Tengxue Zhang, Jianxin Jin, Xiangfei Qiu, Bin Yang, Chenjuan Guo

Multivariate time series anomaly detection remains challenging as it requires the joint modeling of variable relationships and temporal dependencies. Existing methods often struggle to balance channel relationship modeling and overlook the relative importance of different variables within multivariate time series. To address this, we propose TeamWork, an asymmetric role-aware channel modeling framework that decouples variables into dominant and auxiliary roles according to their contributions to uncertainty reduction. Dominant variables drive system evolution and their deviations more strongly disrupt normal patterns, while auxiliary variables provide complementary cues. These variables with different roles are integrated through a role-aware gated interaction module. Moreover, point and subsequence anomalies can exist in multiple periodic systems, and the same anomaly type may behave differently across short- and long-period series. To capture such variations, we introduce a period-aware masked modeling mechanism. It employs multiple specialized masking mechanisms spanning short to long periods to facilitate comprehensive temporal dependency learning. Extensive experiments on multiple real-world datasets demonstrate that TeamWork achieves superior performance compared with state-of-the-art methods.

Applications · Time Series

Huayu Li, ZhengXiao He, Xiwen Chen, Jingjing Wang, Siyuan Tian, Jinghao Wen, Ao Li

Learning meaningful representations from medical time series (MedTS), such as ECG or EEG signals, is a critical challenge. These signals are often high-dimensional, variable-length, and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs), are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact, fixed-size, or semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of $k$ latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are \textit{sufficient statistics} for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically \textit{disentangled} representations. We present the theoretical justification for our method, framing it as a novel \textbf{Disentangled Rate-Distortion} problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.

Applications · Time Series

Dongxun Jiang, Borui Jia, Yuxuan Wang, Dongdong Zhang

Graph-based attention deficit hyperactivity disorder (ADHD) detection methods have been extensively studied, but comparatively less attention has been paid to short-term brain functional reorganization. In this paper, we propose an ADHD disease detection model based on short- and long-term brain function encoding and memory graph network. We first exploit a novel brain map sequence construction method based on short-term windows to extract short-term brain function features. Then, we design a short-term state and temporal dependency encoder to characterize short-term sequence patterns of brain function. Furthermore, a brain function memory is introduced to capture the association of brain activity patterns and historical sequence patterns. Concurrently, GNN-based long-term brain function feature extraction network is used to extract brain structure features, which are fused with short-term features for ADHD detection. Experimental validation on the publicly available neuroimaging datasets ADHD-200 and OpenNeuro-ds002424 demonstrates the superior performance of our model in brain disorder detection.

Applications · Time Series

Yingda Fan, Dan Lu, Xiaowei Jia

Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce—exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach—directly mapping exogenous inputs to targets—can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion—training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://anonymous.4open.science/r/ZeroDiff/.

Applications · Time Series

Zining Qin, Huiling qin, Chenhao Wang, Jianxiong Guo, Tian Wang, Weijia Jia

Diffusion models have achieved remarkable success in generative modeling, yet their application to time series forecasting remains suboptimal. Existing approaches apply uniform Gaussian noise across all time steps, assuming all frequency components should be corrupted at the same rate. However, energy distribution across frequencies in time series is highly non-uniform: when uniform noise is added, high-frequency components are disproportionately overwhelmed while low-frequency trends remain inadequately diffused. We propose EADiff, an energy-adaptive diffusion framework operating in the wavelet domain to address this frequency-energy imbalance. Our key insight is that high-energy components require stronger perturbation while low-energy details need gentler corruption to preserve informative structures. We introduce a learnable modulation mechanism that automatically adjusts noise levels for each frequency band on a per-instance basis. Built upon this adaptive scheduler, we design a conditional diffusion framework where low-frequency trends serve as generation conditions, and noise-level-aware loss weighting naturally emphasizes different frequency components according to their signal characteristics. This cohesive design enables the model to respect the intrinsic multi-scale structure throughout both forward and reverse processes. Extensive experiments demonstrate that EADiff consistently outperforms existing diffusion-based and state-of-the-art deterministic methods.

Applications · Health / Medicine

Xiaoda Wang, Ching Chang, Defu Cao, Kaiqiao Han, Fang Sun, Yue Huang, Minxiao Wang, Chang Xu, Xiao Luo, Runze Yan 等

Physiological waveforms (e.g., ECG, PPG, EEG) encode clinically meaningful information in fine-grained morphology, precise timing, and cross-channel dynamics, yet most machine learning systems still treat them as generic time series and optimize end-to-end prediction. In this position paper, **we argue for verifiable physiological waveform reasoning: extracting localized, measurable signal evidence from raw signals, interpreting that evidence into physiological semantics, and supporting clinically grounded decisions.** Waveform reasoning is challenging due to acquisition heterogeneity, signal fidelity, complex semantics and cross-channel coupled dynamics. We analyze why existing model families remain insufficient: physiological foundation models learn strong perceptual representations but remain weak at verifiable reasoning, while LLM-based adaptations have limited waveform understanding. To bridge this gap, **we advocate verifiable, closed-loop systems that unify waveform semantics with language intelligence.** Concretely, we propose a dual-process architecture that System 1 aligns physiological waveforms with language, and System 2 provides agentic reasoning via a Plan--Act--Verify loop, together enabling verifiable physiological waveform reasoning. We further propose evaluations beyond accuracy, emphasizing traceability, replayability, counterfactual robustness, and calibrated abstention.

Social Aspects · Security

Quang Duc Nguyen, Siyuan Liang, Yiming Li, Fushuo Huo, Dacheng Tao

Time Series Forecasting (TSF) plays a critical role across many domains, yet it is vulnerable to backdoor attacks. However, backdoor defenses tailored to TSF remain underexplored, due to data entanglement and task-formulation shift challenges. To fill this gap, we conduct a systematic evaluation of thirteen representative backdoor defenses across the TSF life cycle and analyze their failure modes. Our results reveal two fundamental issues: (1) data entanglement induces *channel-level signal dilution*, rendering sample-filtering and trigger-synthesis defenses ineffective at localizing backdoors; and (2) task-formulation shift leads to *training-loss degeneration*, causing poisoned and clean windows to become indistinguishable at training stages. Based on these findings, we propose a training-time backdoor defense for TSF, termed TimeGuard. Our method adopts channel-wise pool training as the core paradigm and initializes a high-confidence pool using time-aware criteria to mitigate signal dilution. Moreover, we introduce distance-regularized loss selection to progressively expand the reliable pool during training and ease loss degeneration. Extensive experiments across multiple datasets, forecasting architectures, and TSF backdoor attacks demonstrate that TimeGuard substantially improves robustness, boosting $\mathrm{MAE}\_\mathrm{P}$ by 1.96× over the leading baseline, while preserving clean performance within 5% $\mathrm{MAE}\_\mathrm{C}$.

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

Kun Zeng, Wu Binquan, Qianli Ma

Integrating Large Language Models (LLMs) into time series tasks has yielded impressive performance. While some works aim to enhance accuracy by explicitly designing step-by-step reasoning into prompts, such explicit Chain-of-Thought (CoT) approaches are difficult to generalize to time series. This is because it is difficult to clearly define the reasoning trajectories of time series. In addition, the high heterogeneity across time series often requires specialized prompt designs, limiting the model's scalability. To address these challenges, we propose **Time-CoT** (**Time** Series **C**hain-**o**f-**T**hought), a hierarchical reasoning framework based on temporal semantic codes for multivariate time series classification. This framework automatically constructs scenario-specific reasoning trajectories based on the characteristics of time series, thereby better eliciting the LLM's reasoning capability for time-series data. Specifically, Time-CoT, we first perform temporal representation pre-training with a multi-view temporal representation fusion to acquire high-quality temporal embeddings. We then discretize these temporal embeddings into hierarchical temporal semantic codes as the reasoning trajectory. Finally, the LLM predicts temporal semantic codes in a stepwise manner and then infers the final labels, thereby establishing a coarse-to-fine decision process. Experiments on ten public multivariate time series datasets demonstrate that the Time-CoT effectively adapts to diverse datasets and outperforms state-of-the-art methods. Our code is available at .

Deep Learning · Sequential Models, Time series

Tian Lan, Hao Le, Jinbo Li, Wenjun He, Meng Wang, Chenghao Liu, Chen Zhang

TSAD is a critical task, but developing models that generalize to unseen data in a zero-shot manner remains a major challenge. Prevailing foundation models for TSAD predominantly rely on reconstruction-based objectives, which suffer from a fundamental objective mismatch and representation conflict: they tend to memorize static patterns from training data, struggling to identify subtle anomalies while often misinterpreting complex normal patterns in unseen domains. To overcome these limitations, we introduce TimeRCD, a novel foundation model for TSAD built upon a new pre-training paradigm: Relative Context Discrepancy (RCD). Instead of reconstructing inputs based on fixed priors, TimeRCD is explicitly trained to adaptively identify anomalies by contrasting the query with its surrounding context. This relational approach, implemented with a standard Transformer architecture, enables the model to infer normality on-the-fly and capture contextual shifts indicative of anomalies that reconstruction-based methods often miss. To empower this paradigm, we develop a large-scale, diverse synthetic corpus with context-dependent anomaly labels, providing the rich supervisory signal necessary for effective pre-training. Extensive experiments demonstrate that TimeRCD significantly outperforms existing general-purpose and anomaly-specific foundation models in zero-shot TSAD across diverse datasets. Our results validate the superiority of the RCD paradigm and establish a new, effective path toward building robust and generalizable foundation models for time series anomaly detection. The code is available in \url{https://anonymous.4open.science/r/TimeRCD-5BE1/}