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Renjun Huang, Han Xiao, Bingqing Li, Baili Zhang, Jianhua Lyu

Time series forecasting plays a critical role across a wide range of domains. Recently, an increasing number of Transformer-based forecasting models have emerged, achieving remarkably competitive performance. However, real-world time series data often exhibit complex multi-scale periodicities, which are not well-suited for modeling by the original Transformer architecture originally developed for NLP tasks. To address this limitation, we propose the Hierarchical Multi-scale Time Series Transformer (HMformer), employing a novel and sophisticated framework specifically designed for multi-scale time series forecasting. Specifically, HMformer incorporates a hierarchical cross-scale mixing mechanism that progressively aggregates temporal information from fine to coarse granularities, a scale-adaptive feature expansion design enhancing the extraction of high-level temporal semantics, and a multi-branch complementary prediction strategy for effectively integrating diverse temporal patterns. Collectively, these components enable HMformer to capture intricate, multi-scale temporal dynamics while retaining the Transformer’s inherent strength in modeling long-range dependencies. Extensive experiments conducted on multiple real-world benchmark datasets—encompassing both long-term and short-term forecasting tasks—demonstrate that HMformer achieves state-of-the-art performance.

Junji Hou, Junzhou Zhao, Shuo Zhang, Pinghui Wang

Motivated by the increasing risks of data misuse and fabrication, we investigate the problem of identifying synthetic time series generated by Time-Series Large Models (TSLMs) in this work. While there are extensive researches on detecting model generated text, we find that these existing methods are not applicable to time series data due to the fundamental modality difference, as time series usually have lower information density and smoother probability distributions than text data, which limit the discriminative power of token-based detectors. To address this issue, we examine the subtle distributional differences between real and model-generated time series and propose the contraction hypothesis, which states that model-generated time series, unlike real ones, exhibit progressively decreasing uncertainty under recursive forecasting. We formally prove this hypothesis under theoretical assumptions on model behavior and time series structure. Model-generated time series exhibit progressively concentrated distributions under recursive forecasting, leading to uncertainty contraction. We provide empirical validation of the hypothesis across diverse datasets. Building on this insight, we introduce the Uncertainty Contraction Estimator (UCE), a white-box detector that aggregates uncertainty metrics over successive prefixes to identify TSLM‑generated time series. Extensive experiments on 32 datasets show that UCE consistently outperforms state-of-the-art baselines, offering a reliable and generalizable solution for detecting model-generated time series.

Seungha Hong, Sanghwan Jang, Wonbin Kweon, Suyeon Kim, Gyuseok Lee, Hwanjo Yu

Time Series forecasting (TSF) in the modern era faces significant computational and storage cost challenges due to the massive scale of real-world data. Dataset Distillation (DD), a paradigm that synthesizes a small, compact dataset to achieve training performance comparable to that of the original dataset, has emerged as a promising solution. However, conventional DD methods are not tailored for time series and suffer from architectural overfitting and limited scalability. To address these issues, we propose Harmonic Dataset Distillation for Time Series Forecasting (HDT). HDT decomposes the time series into its sinusoidal basis through the FFT and aligns the core periodic structure by Harmonic Matching. Since this process operates in the frequency domain, all updates during distillation are applied globally without disrupting temporal dependencies of time series. Extensive experiments demonstrate that HDT achieves strong cross-architecture generalization and scalability, validating its practicality for large-scale, real-world applications.

Zelin He, Sarah Alnegheimish, Matthew Reimherr

Time-series anomaly detection (TSAD) has played a vital role in a variety of fields, including healthcare, finance, and sensor-based condition monitoring. Prior methods, which mainly focus on training domain-specific models on numerical data, lack the visual–temporal reasoning capacity that human experts have to identify contextual anomalies. To fill this gap, we explore a solution based on vision language models (VLMs). Recent studies have shown the ability of VLMs for visual reasoning tasks, yet their direct application to time series has fallen short on both accuracy and efficiency. To harness the power of VLMs for TSAD, we propose a two-stage solution, with (1) ViT4TS, a vision-screening stage built on a relatively lightweight pre-trained vision encoder, which leverages 2-D time series representations to accurately localize candidate anomalies; (2) VLM4TS, a VLM-based stage that integrates global temporal context and VLM's reasoning capacity to refine the detection upon the candidates provided by ViT4TS. We show that without any time-series training, VLM4TS outperforms time-series pre-trained and from-scratch baselines in most cases, yielding a 24.6% improvement in F1-max score over the best baseline. Moreover, VLM4TS also consistently outperforms existing language model-based TSAD methods and is on average 36× more efficient in token usage.

Chandan Gautam, Lew Choon Hean, Ankit Das, Xiaoli Li, Savitha Ramasamy

Generalized Category Discovery (GCD) aims to classify labeled instances from known categories while discovering novel categories from unlabeled data. Despite recent progress in GCD for computer vision, existing GCD approaches largely rely on static final-step representations (in the visual domain), overlooking the temporally evolving nature of time-series data. In this paper, we introduce TGCD, the first framework specifically designed for GCD in time-series data. TGCD leverages both the dynamics of latent representations and the heterogeneity of predictions across multiple temporal segments to disover unknown (i.e., novel) categories, based on a pre-trained time-series foundation model. We propose a unified learning objective for TGCD that integrates the following three components: (i) a Stochastic Temporal Segment Dropout (STeSD) objective that regularizes the model by selectively penalizing high-entropy segments to encourage confident predictions on uncertain regions of the time-series, and (ii) a Known–Unknown Temporal Discriminability (KUTD) objective that promotes representational separation between known and unknown categories within unlabeled data and (iii) a margin-aware classification objective to improve generalization. Empirical evaluation on six multivariate time-series data sets demonstrates that the TGCD substantially outperforms existing GCD methods, particularly in discovering unknown categories. We further conduct ablation studies to highlight the individual contributions of each component. Additionally, we provide the first comprehensive benchmarking of recent GCD approaches on time-series data, revealing the limitations of naive transfer and underscoring the benefits of temporal modeling.

Luca-Andrei Fechete, Mohamed Sana, Fadhel Ayed, Nicola Piovesan, Wenjie Li, Antonio De Domenico, Tareq Si Salem

Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that enables forecasting models to adapt their focus to application-specific regions of interest at inference time, without retraining. The approach partitions the prediction space into fine-grained segments during training, which are dynamically reweighted and aggregated to emphasize the target range specified by the application. Unlike prior methods that predefine these ranges, our framework supports flexible, on-demand adjustments. Experiments on standard benchmarks and a newly collected wireless communication dataset demonstrate that our method not only improves forecast accuracy within regions of interest but also yields measurable gains in downstream task performance. These results highlight the potential for closer integration between predictive modeling and decision-making in real-world systems.

Yuhang Duan, Lin Lin, Xiaoshuai Wu

Time series generation is essential for advancing data-driven modeling and decision-making across a wide range of domains. However, existing approaches primarily focus on global patterns, often failing to capture local key patterns such as abrupt changes or anomalies. These key patterns are crucial for interpretability and operational decision making, as they frequently represent intervention points with significant real-world impact. To bridge this gap, we propose Key Prototypes-Guided Diffusion (K-ProtoDiff) for time series generation , a new model that learns the global data distribution while preserving localized key patterns critical for temporal dynamics. In K-ProtoDiff, we first derive time series prototype representations through adaptive self-supervised learning. Then, a key prototype assignment module is used to extract prototype weights, forming key prototype-aware representations that serve as conditional guidance for generation. During sampling, to further enhance the fidelity of key patterns during the denoising process, we propose Reflection Sampling (R-Sampling), a step-wise refinement strategy that encourages the reverse trajectory to better align with key prototype constraints. Experiments on nine real-world datasets demonstrate that K-ProtoDiff significantly outperforms state-of-the-art baselines in key pattern retention, achieving an average 77.6% improvement in key pattern preservation.

Dazhao Du, Tao Han, Song Guo

Deep learning models such as MLP, Transformer, and TCN have achieved remarkable success in univariate time series forecasting, typically relying on sliding window samples from historical data for training. However, while these models implicitly compress historical information into their parameters during training, they are unable to explicitly and dynamically access this global knowledge during inference, relying only on the local context within the lookback window. This results in an underutilization of rich patterns from the global history. To bridge this gap, we propose Predicting the Future by Retrieving the Past (PFRP), a novel approach that explicitly integrates global historical data to enhance forecasting accuracy. Specifically, we construct a Global Memory Bank (GMB) to effectively store and manage global historical patterns. A retrieval mechanism is then employed to extract similar patterns from the GMB, enabling the generation of global predictions. By adaptively combining these global predictions with the outputs of any local prediction model, PFRP produces more accurate and interpretable forecasts. Extensive experiments conducted on seven real-world datasets demonstrate that PFRP enhances the average performance of advanced univariate forecasting models by 8.4%.

Kuiye Ding, Fanda Fan, Chunyi Hou, Zheya Wang, Lei Wang, Zhengxin Yang, Jianfeng Zhan

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

Hang Ding, Xue Wang, Tian Zhou, Tao Yao

Diffusion models have recently shown promise in time series forecasting, particularly for probabilistic predictions. However, they often fail to achieve state-of-the-art point estimation performance compared to regression-based methods. This limitation stems from difficulties in providing sufficient contextual bias to track distribution shifts and in balancing output diversity with the stability and precision required for point forecasts. Existing diffusion-based approaches mainly focus on full-distribution modeling under probabilistic frameworks, often with likelihood maximization objectives, while paying little attention to dedicated strategies for high-accuracy point estimation. Moreover, other existing point prediction diffusion methods frequently rely on pre-trained or jointly trained mature models for contextual bias, sacrificing the generative flexibility of diffusion models. To address these challenges, we propose SimDiff, a single-stage, end-to-end framework. SimDiff employs a single unified Transformer network carefully tailored to serve as both denoiser and predictor, eliminating the need for external pre-trained or jointly trained regressors. It achieves state-of-the-art point estimation performance by leveraging intrinsic output diversity and improving mean squared error accuracy through multiple inference ensembling. Key innovations, including normalization independence and the median-of-means estimator, further enhance adaptability and stability. Extensive experiments demonstrate that SimDiff significantly outperforms existing methods in time series point forecasting.

Henggang Deng, Yuchao Tang, Wenjie Fu, Huandong Wang, Kun Chen, Tao Jiang

In real-world time-series modelling, graph structures are widely adopted because they explicitly encode node topology and capture complex network dynamics. In practice, however, a complete graph is often partitioned across multiple parties; each party can access only its local sub-graph and, owing to privacy regulations, cannot share topology or data, creating pervasive data silos. Federated Graph Learning (FGL) offers a privacy-preserving collaborative-learning paradigm, yet current methods still face two key challenges: (1) the graph topology itself contains sensitive structural information, which can lead to privacy leakage if directly shared during FGL; (2) cross-party edges are crucial for accurate modeling, yet exploiting them without compromising privacy remains a significant challenge. To overcome these obstacles, we propose FedSkeleton, a privacy-preserving framework for time-series prediction that comprises a Skeleton Construction Module and a Dual-stream Forecasting Module, enabling global dependency capture without revealing the topology. Extensive experiments show that FedSkeleton consistently outperforms existing baselines and even surpasses models trained in a centralized setting with full-graph access in certain cases. In addition, we conduct comprehensive security analysis, communication-cost evaluation and scalability experiments, demonstrating that FedSkeleton effectively resists common attacks, keeps communication overhead manageable, and remains robust with respect to key hyper-parameters and the number of participating parties.

Ibrahim Delibasoglu, Sanjay Chakraborty, Fredrik Heintz, Mattias Tiger

Understanding how localized changes in one variable affect others in multivariate time series is essential for diagnostics and decision-making in complex systems. Existing models often fail to capture realistic inter-feature dynamics when simulating "what-if" scenarios, leading to inaccurate or uncorrelated reconstructions. We propose CFORVAE, a variational autoencoder framework that explicitly addresses this limitation by combining temporal decomposition with frequency-domain feature correlation modeling. Our architecture uses a dual-path encoding of trend and seasonal components, each projected into attention-pooled latent spaces, and applies Fourier Neural Operators (FNO) to capture cross-feature dependencies in the spectral domain. This decomposition-correlation design enables component-specific latent manipulation and ensures that local modifications propagate realistically across correlated variables. Through extensive experiments, we show that CFORVAE outperforms state-of-the-art baselines in preserving temporal and feature-level dependencies, especially under adjustment-based reconstructions, making it a powerful tool for interpretable "what-if" analysis and diagnostics.

Abdul Monaf Chowdhury, Rabeya Akter, Safaeid Hossain Arib

Multivariate time series forecasting (MTSF) seeks to model temporal dynamics among variables to predict future trends. Transformer-based models and large language models (LLMs) have shown promise due to their ability to capture long-range dependencies and patterns. However, current methods often rely on rigid inductive biases, ignore intervariable interactions, or apply static fusion strategies that limit adaptability across forecast horizons. These limitations create bottlenecks in capturing nuanced, horizon-specific relationships in time-series data. To solve this problem, we propose T3Time, a novel trimodal framework consisting of time, spectral, and prompt branches, where the dedicated frequency encoding branch captures the periodic structures along with a gating mechanism that learns prioritization between temporal and spectral features based on the prediction horizon. We also proposed a mechanism which adaptively aggregates multiple cross-modal alignment heads by dynamically weighting the importance of each head based on the features. Extensive experiments on benchmark datasets demonstrate that our model consistently outperforms state-of-the-art baselines, achieving an average reduction of 3.28% in MSE and 2.29% in MAE. Furthermore, it shows strong generalization in few-shot learning settings: with 5% training data, we see a reduction in MSE and MAE by 4.13% and 1.91%, respectively; and with 10% data, by 3.62% and 1.98% on average. Code will be released upon publication.

Xinyang Chen, Huidong Jin, Yu Huang, Zaiwen Feng

Despite the prevalent assumption of uniform variable importance in long-term time series forecasting models, real-world applications often exhibit asymmetric causal relationships and varying data acquisition costs. Specifically, cost‐effective exogenous data (e.g., local weather) can unilaterally influence dynamics of endogenous variables, such as lake surface temperature. Exploiting these links enables more effective forecasts when exogenous inputs are readily available. Transformer-based models capture long-range dependencies but incur high computation and suffer from permutation invariance. Patch-based variants improve efficiency yet can miss local temporal patterns. To efficiently exploit informative signals across both the temporal dimension and relevant exogenous variables, this study proposes XLinear, a lightweight time series forecasting model built upon Multi-Layer Perceptrons (MLPs). XLinear uses a global token derived from an endogenous variable as a pivotal hub for interacting with exogenous variables, and employs MLPs with sigmoid activation to extract both temporal patterns and variate-wise dependencies. Its prediction head then integrates these signals to forecast the endogenous series. We evaluate XLinear on seven standard benchmarks and five real-world datasets with exogenous inputs. Compared with state-of-the-art models, XLinear delivers superior accuracy and efficiency for both multivariate forecasts and univariate forecasts influenced by exogenous inputs.

Zhongde An, Jinhong You, Jiyanglin Li, Yiming Tang, Wen Li, Heming Du, Shouguo Du

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the spectral entanglement and the computational burden of complex-valued learning. The spectral entanglement refers to the overlap of trends, periodicities, and noise across the spectrum due to spectral leakage and the presence of non-stationarity. However, existing decompositions are not suited to resolving spectral entanglement. To address this, we propose the Frequency Decomposition Network (FreDN), which introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain. Furthermore, we propose a theoretically supported ReIm Block to reduce the complexity of complex-valued operations while maintaining performance. We also re-examine the frequency-domain loss function and provide new theoretical insights into its effectiveness. Extensive experiments on seven long-term forecasting benchmarks demonstrate that FreDN outperforms state-of-the-art methods by up to 10%. Furthermore, compared with standard complex-valued architectures, our real-imaginary shared-parameter design reduces the parameter count and computational cost by at least 50%.

Pingping Pan, Yunjian Zhang, Jinyi Liu

Time-frequency analysis (TFA) and mode decomposition for non-stationary signals are research hotspots in the field of signal processing. Current optimization-based decomposition methods require a good initial IF estimate. However, due to the Heisenberg uncertainty, achieving accurate ridge extraction from the time-frequency representation (TFR) necessitates empirical parameter adjustments. In this paper, we propose the TFD-Net framework, which takes time-series signals as inputs and adaptively conducts TFR construction and mode decomposition. Specifically, the framework integrates a physically interpretable TFA encoder and a query-based mode decomposition decoder. The highlights of this study include exploring the mathematical equivalence between deep convolutional operators and classical TFA methods. This enables the extraction of multi-scale features for TFR construction and mode separation in a data-driven manner, eliminating the need for signal-specific manual tuning and enhancing adaptability. Finally, simulated and real-world experiments demonstrate TFD-Net's superior performance over several state-of-the-art methods in complex signal processing.

Sebastian Hagedorn Gaete, Martín Muñoz, Cristian Riveros, Rodrigo Toro Icarte

Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the L* algorithm, introduced by Angluin (1987). The L* algorithm learns deterministic finite-state automata (DFAs) in polynomial time when provided with a minimally adequate teacher. Unfortunately, the L* algorithm can only learn DFAs over finite alphabets, which limits its applicability. In this paper, we extend L* to learn symbolic automata whose transitions use predicates over rational numbers, i.e., over infinite and dense alphabets. Our result makes the L* algorithm applicable to new settings like (real) RGX, and time series. Furthermore, our proposed algorithm for learning each predicate is optimal in the sense that it asks a number of queries to the teacher that is at most linear with respect to the size of their representation.

Alan Gabriel Paredes Cetina, Kaouther Benguessoum, Raoni Lourenco, Sylvain Kubler

Recent advances in deep learning have improved multivariate time series (MTS) classification and regression by capturing complex patterns, but their lack of transparency hinders decision-making. Explainable AI (XAI) methods offer partial insights, yet often fall short of conveying the full decision space. Counterfactual Explanations (CE) provide a promising alternative, but current approaches typically prioritize either accuracy, proximity or sparsity -- rarely all -- limiting their practical value. To address this, we propose CONFETTI, a novel multi-objective CE method for MTS. CONFETTI identifies key MTS subsequences, locates a counterfactual target, and optimally modifies the time series to balance prediction confidence, proximity and sparsity. This method provides actionable insights with minimal changes, improving interpretability, and decision support. CONFETTI is evaluated on seven MTS datasets from the UEA archive, demonstrating its effectiveness in various domains. CONFETTI consistently outperforms state-of-the-art CE methods in its optimization objectives, and in six other metrics from the literature, achieving ≥ 10% higher confidence while improving sparsity in ≥ 40%.

Xueyi Zhou, Zhenyu Li, Dong-Kyu Chae

In large-scale sensor networks, Multivariate Time Series Classification (MTSC) is a pivotal task for identifying events dependent on longitudinal data at the edge. However, existing methods focus on neither the inherent ability of convolutional networks to perceive subsequence features, nor the prolonged processing pipeline and the model deployment overhead brought by the highly parameterized models. To resolve these difficulties, we present EdgeMTSC, a lightweight large-kernel ConvNet for MTSC, which naturally extracts and learns features of diverse subsequences. Specifically, a novel module named Inter-channel Message Passing-driven Kernel Block (IMP-KB) is proposed, which maintains a learnable correlation matrix to propagate and merge inter-channel messages, and fuses miscellaneous patterns learned by parallel conv kernels of different sizes. EdgeMTSC sequences two modules of different receptive fields to aggregate local features using small kernels and study long-term representation provided by large kernels, respectively. For inference parameter reduction and accelerating inference without performance loss, the conv blocks in IMP-KBs are structurally reparameterizable. The performance of our model (76.2%) is benchmarked on 26 UEA MTSC datasets and is superior to the SOTA model (MPTSNet, 75%). At the same time, EdgeMTSC uses the fewest parameters and achieves the minimum inference time, applicable on any machine (8 devices ranging from large-scale distributed AI computing servers to resource-constrained edge devices) and in any application scenario.

Tong Zhao, Junping Du, Zhe Xue, Meiyu Liang, Aijing Li, Xiaolong Meng, Dandan Liu

Spatial-temporal prediction plays a crucial role in various domains, including intelligent transportation and environmental monitoring. Although large language model has shown advantages in long-range dependency modeling and excellent generalization ability for forecasting, it has limited understanding of spatial-temporal features. Especially for spatial features, most existing methods still simplify the spatial-temporal prediction task into multiple independent temporal prediction tasks, failing to effectively encode the dynamic evolution of spatial relations. To address these problems, we propose ST-VLM (Spatial-Temporal Forecasting with Vision-Language Model), a novel framework that leverages visual representations to encode the dynamic spatial dependencies within spatial-temporal data and integrates multi-modal information to enhance prediction. This framework transforms spatial-temporal features into three modalities: vision, text, and time series, enhances cross-modal fusion through an attention-aware fusion mechanism in the first-layer of Vision-Language Model (VLM), optimizes multi-modal feature interaction via adaptive fine-tuning strategies. After fusion, the multi-modal embeddings are subsequently used for the final spatial-temporal prediction task. Extensive experiments demonstrate that ST-VLM achieves state-of-the-art performance across various datasets. In particular, the framework exhibits promising results in few-shot scenarios, verifying its strong generalization ability.