Time Series

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.

Time series foundation models (TSFMs) are increasingly pretrained on large corpora, raising concerns that evaluation datasets may have been exposed during pretraining and thus yield overly optimistic performance estimates. Auditing such contamination is challenging in time series because signals are continuous and heterogeneous, and often lack corpus documentation. To the best of our knowledge, this is the first work to study pretraining contamination auditing for TSFMs. We formalize the problem of pretraining contamination auditing for TSFMs and propose TSFMAudit, a method based on probe adaptation dynamics. Our key intuition is that contamination manifests as unusually efficient adaptation: after a fine tuning probe, contaminated datasets tend to exhibit faster loss reduction with smaller backbone movement. We evaluate TSFMAudit on 6 TSFMs and 187 datasets using documented training source evidence as supervision, and compare against 10 competitive baselines adapted from the LLM literature.

Medical time series are central to healthcare, enabling continuous monitoring and supporting timely clinical decisions. Despite recent progress, existing methods struggle to jointly model local-global dynamics and handle nonstationarities like baseline drift, while often failing to capture latent channel interactions. To address these challenges, we propose MedMamba, an end-to-end architecture that integrates state space models with domain-specific inductive biases. Specifically, MedMamba first employs multi-scale convolutional embeddings to capture discriminative local morphology. Second, to mitigate nonstationarity, we introduce a tri-branch differential state space encoder that processes raw, temporal-difference, and frequency-domain views, fusing them to emphasize informative patterns while suppressing drift. Furthermore, to uncover latent channel correlations, we design a spatial graph Mamba module that learns a directed dependency structure regularized toward sparsity and acyclicity, which obviates the need for predefined graphs. Extensive experiments on five real-world datasets demonstrate that MedMamba achieves state-of-the-art performance while maintaining linear computational complexity, and ablation studies validate each component's contribution.Code is available at https://github.com/zhangda1018/MedMamba.

Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction. However, our empirical analysis reveals a non-trivial limitation of retrieval-based forecasting: retrieval tends to induce more oscillatory predictions, improving performance on highly fluctuating series while degrading accuracy on smoother, trend-dominated ones. This suggests that retrieved information may be fused into prediction without explicitly distinguishing stable temporal structure from instance-specific variations, which can reduce robustness under distribution shifts. We propose a Retrieval-guided Invariant-Dynamic DEcomposition framework for time series forecasting. Rather than using retrieval as auxiliary predictive context, we leverage retrieved sequences as implicit samples from related environments to guide representation decomposition. Specifically, we first construct a retrieval-aware representation via attention-based aggregation, and then introduce a retrieval-guided routing mechanism to decompose it into an invariant component capturing stable shared structure and a dynamic component modeling context-dependent variations. These two components are forecast separately and fused for final prediction, enabling the model to preserve transferable patterns while remaining adaptive to evolving dynamics. We further design training objectives that encourage invariant learning and disentanglement, and provide theoretical insight showing that retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment supervision. Extensive experiments demonstrate that our method consistently improves robustness under distribution shifts and outperforms existing TSFMs and retrieval-based baselines in zero-shot forecasting settings.

Temporal surrogate models are effective for predicting chaotic dynamical systems where computational cost can be prohibitive. Several deep neural network architectures can be used for such purposes. In this work, a few commonly used architectures are compared using a common training protocol. The objective is to fairly assess the impact of model architectures for long-horizon prediction stability. Experiments are carried out for three problems, the double pendulum, the Kuramoto-Sivashinsky equations, and the Kolmogorov flow. The experiments are carried out with matching model capacity. Analysis is also carried out for a scenario where each model is individually optimized. It is observed that in both scenarios, the models exhibit categorical differences in long-horizon rollouts. For a concrete quantification, stepwise error injections and perturbation amplifications are analyzed using metrics such as local jacobian, relative one-step bias, and finite-time Lyapunov growth. Additionally, an attractor analysis is also conducted to assess how well the learned models replicate the underlying system geometry. An ablation study to isolate the impact of each component of a continuous-update architecture is also carried out. It is concluded that models that having integrator-like updates show lower bias and perturbation amplification yielding stable long-horizon rollout and more accurate predictions.

Large language models (LLMs) and time-series language models (TSLMs) are increasingly applied to time-series question answering (TSQA). Unlike text-only QA, TSQA requires models to ground answers in temporal signals whose patterns may occur at different scales, specific time locations, or across separated intervals. However, existing benchmarks are typically organized by task types or high-level reasoning categories, making it difficult to diagnose the underlying signal-level capabilities driving model performance. We introduce TS-Skill, a controlled benchmark for evaluating three composable analytical skills in TSQA: temporal scale selection (SK1), temporal localization (SK2), and cross-interval integration (SK3). TS-Skill provides timestamp-aware questions, broad domain coverage, and human-validated QA quality. To construct the benchmark at scale, we develop SKEvol, a skill-guided agentic framework that combines domain-aware time-series seed generation, skill-controlled question generation, metadata- and code-assisted answer construction, multi-phase signal-grounded verification, and human-in-the-loop curation. Experiments on ten state-of-the-art LLMs and TSLMs reveal substantial and uneven capability gaps across SK1-SK3. In particular, SK3 remains consistently challenging for non-agent models, whereas tool-augmented agents show a selective advantage on standalone SK3. These findings demonstrate that skill-level evaluation can uncover temporal reasoning failures that are obscured by aggregate TSQA scores.

Time series forecasting drives operational decisions in areas like finance, transportation, and energy. While supervised learning approaches achieve strong performance, they require domain-specific training, feature engineering, and ongoing maintenance. Large-scale foundation models have recently emerged as a zero-shot alternative, avoiding task-specific training much like LLMs. In this work, we evaluate foundation models against standard supervised approaches. Rather than focusing solely on aggregate accuracy, we analyze performance across four operational regimes: periodic human-centric systems, physically constrained processes, stochastic financial markets, and heterogeneous demand forecasting. Our results characterize optimal deployment areas. Foundation models perform well in domains with transferable periodic structures and are efficient for cold-start or long-tail scenarios. Conversely, supervised specialists maintain higher precision in systems governed by strict physical constraints. In financial domains, newer foundation models are rapidly closing the performance gap with supervised specialists. We further quantify trade-offs in inference latency, data drift adaptability, and deployment constraints. Finally, we propose a Complexity Router that assigns each series to the optimal model class using empirical features. We demonstrate that this selective routing achieves higher accuracy and significantly lower inference costs compared to deploying a universal foundation model, providing a practical framework for balancing generalization and efficiency.

We introduce CopFITi, a copula model for probabilistic forecasting of irregular multivariate time series (IMTS). Our model combines the expressivity of normalizing flows for univariate marginals with the consistency and flexibility of a Gaussian Mixture Copula for the joint dependency structure. Our experiments show that copula-based approaches, which decouple the marginals from the joint, yield better marginal models than architectures that directly fit the full joint. With CopFITi, we propose the first IMTS copula that is marginalization-consistent by construction and establish a new state of the art in joint IMTS density modeling.

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack flexibility, whereas deep generative models struggle to capture complex temporal dependencies without extensive data and computation. We introduce Parametric Prior Mapping (PPM), a framework that injects parametric structural priors into a generative modeling process. Specifically, PPM utilizes a parametric estimator to derive a dynamic, adaptive prior that guides the learning of a complex predictive distribution via a learnable mapping. This design allows the model to retain the efficiency of parametric methods while exploiting the expressive power of generative models. Trained with a hybrid objective, PPM yields precise forecasts with well-calibrated uncertainty estimates. Empirical results show that PPM outperforms existing baselines in handling non-stationary data, offering a superior trade-off between accuracy and computational efficiency. The code is available at https://github.com/ljl8336/PPM.

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient alternative to diffusion models, but practical implementations typically rely on a single finite-capacity global vector-field estimator. In such heterogeneous temporal distributions, distinct regimes may pass through nearby flow states while requiring incompatible conditional velocities. A monolithic estimator trained with the standard $\ell_2$ velocity-matching objective may therefore learn an overly smoothed approximation of the local transport field. This estimator-level smoothing can attenuate branch-specific dynamics, leading to spectral distortion and poor mode coverage. To address this, we propose PrismFlow, a new FM method with Koopman-inspired dynamical experts. Each expert learns residual corrections in a latent space where local nonlinear temporal evolution can be approximated by linear transitions. We further propose a confidence-aware Winner-Take-All (WTA) objective that updates only the expert best aligned with each sample while masking gradients to the others, encouraging mode-specific specialization. During sampling, the selected expert adds a residual dynamical correction to the global transport field, preserving FM stability while recovering fine-grained and high-frequency temporal structures. Across various benchmarks, PrismFlow effectively mitigates the spectral contraction in standard FM and achieves state-of-the-art performance, with a 15.6% gain in Context-FID and a 38.6% improvement in Discriminative Score, while remaining robust in low-data settings and effective for forecasting and imputation.

Token-based time series large language models (TS-LLMs) have emerged as a promising direction for time series analysis and reasoning. However, prior studies largely overlook the inherent continuity and ordinality of time series tokens, which substantially limits model performance. In this paper, we argue that preserving these properties in time series token embeddings is crucial for the effectiveness of token-based TS-LLMs. To this end, we propose COM (Continuity and Ordinality Matter), a continuity- and ordinality-aware strategy that integrates geometric constraints into both the initialization and training stages. Empirical results on multiple time series analysis benchmarks demonstrate that COM consistently improves the performance of token-based TS-LLMs, achieving competitive results and strong generalizability. Code is available at https://anonymous.4open.science/r/COM .

Diagnosing Major Depressive Disorder (MDD) from functional magnetic resonance imaging (fMRI) using functional connectivity (FC) analysis requires large amounts of labeled data that are scarce in clinical settings. Existing augmentation methods synthesize FC matrices, which compress fMRI recordings into static pairwise summaries and discard temporal information. We propose fMRI-Diffusion, a framework that synthesizes region-of-interest (ROI)-level fMRI time series rather than FC matrices. A Temporal Transformer serves as the denoising network within a denoising diffusion probabilistic model, treating each time point as a token to capture temporal dependencies through self-attention. A supervised pretraining strategy initializes the Transformer with task-relevant representations before diffusion training, and FC matrices are derived from the synthesized time series for classification. Experiments on the REST-meta-MDD dataset show that augmenting training data with synthetic time series consistently improves diagnostic accuracy across ten classifiers, six parcellation atlases, and three acquisition sites. The method outperforms five recent FC-based synthesis approaches, with accuracy gains of up to 3.7 percentage points over the strongest baseline. Ablation studies confirm the contributions of both the Transformer-based denoiser and the pretraining strategy. Distributional fidelity metrics remain below 0.06 across all conditions, indicating close agreement between real and synthetic distributions. These findings suggest that synthesizing fMRI time series before FC computation preserves temporal information lost in matrix-level augmentation and provides a practical strategy for MDD diagnosis under limited data.

Time series forecasting plays a central role in many real-world applications and has been extensively studied. Most existing approaches rely on deterministic models. However, real-world environments exhibit inherently uncertain and complex future behaviors, making single-point predictions insufficient. This highlights the need for probabilistic forecasting methods that can quantify and represent uncertainty. In this work, we propose PaP-NF, a probabilistic forecasting framework that aligns continuous time series representations with a frozen large language model (LLM) using a Prefix-as-Prompt mechanism, and conditions a normalizing flow decoder on the global context extracted by the LLM. The quality of the resulting predictive distributions is evaluated using the Continuous Ranked Probability Score (CRPS), a standard metric in probabilistic forecasting. Across a variety of long-term forecasting benchmarks, PaP-NF robustly captures multi-modal uncertainty while maintaining competitive point forecasting accuracy. The official implementation is available at: https://github.com/democracy04/PaP-NF

World models represent a paradigm shift in generative AI, pursuing predictive understanding and controllable simulation of environments in a structured and generalizable way. We present World Machine, a generative world-modeling architecture for time series. It is a transformer-based architecture with latent states that enables adaptation to different amounts of observed data and contexts. This shows an improvement over traditional transformers, which have a computational and memory cost that scales quadratically with the context. Experiments on a proposed synthetic dataset, Toy1D, validate the approach's feasibility, demonstrate capabilities not found in conventional transformers, and highlight the contributions of each component of the training protocol.

Time Series Foundation Models (TSFMs) have become a new component of the state-of-the-art in general time series forecasting. However, adapting them to specialized classification tasks remains constrained by two interconnected challenges: the quadratic cost of standard attention mechanisms and the inability to disentangle the structural components underlying time series variability. This technical report introduces ChronoVAE-HOPE, a next-generation TSFM that reconciles massive generalization with structured latent representation for time series classification. The core of the proposal is a Variational Autoencoder (VAE) framework built upon the HOPE Block, which replaces quadratic attention with a dual-memory system: Titans modules for dynamic short-term retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. A key architectural novelty is the disentangled latent space, which factorizes representations into independent trend and seasonal components via dedicated encoder heads and separate decoder pathways. ChronoVAE-HOPE undergoes self-supervised pre-training on the Monash archive, combining a Masked Time Series Modeling (MTSM) auxiliary objective with a disentangled VAE reconstruction loss. The pre-trained encoder is subsequently frozen and used to generate fixed-length embeddings for downstream classification on the UCR benchmark datasets. Empirical results demonstrate strong performance across diverse temporal domains, particularly in settings characterized by strict causal structure. ChronoVAE-HOPE establishes a robust and interpretable framework for the adaptation of foundation models to time series classification through structured generative representations.

Artificial intelligence (AI) is increasingly embedded in scientific discovery, yet whether it can anticipate scientific progress remains unclear. To study this question, we introduce a temporally grounded evaluation framework for forecasting scientific progress under controlled knowledge constraints. We present CUSP (Cutoff-conditioned Unseen Scientific Progress), a multi-disciplinary and event-level benchmark that evaluates scientific forecasting in AI systems through feasibility assessment, mechanistic reasoning, generative solution design, and temporal prediction. Across 4,760 scientific events, we observe systematic and domain-dependent limitations in current frontier models. While models can identify plausible research directions from competing candidates, they fail to reliably predict whether scientific advances will be realized and systematically misestimate when they will occur. Performance is highly heterogeneous across domains, with the timing of AI progress more predictable than advances in biology, chemistry, and physics. Performance is largely insensitive to whether events occur before or after the training cutoff, suggesting these limitations cannot be explained solely by knowledge exposure in training data. Under controlled information access, additional pre-cutoff knowledge improves performance but does not close the gap to full-information settings, which becomes more pronounced for high-citation advances. Models also exhibit systematic overconfidence and strong response biases, indicating unreliable uncertainty estimation. Taken together, current AI systems fall short as predictive tools for scientific progress. Access to prior knowledge does not translate into reliable forecasting, and performance benefits more from post-event information than from forward-looking prediction.

We document inverse scaling in LLMs on forecasting problems whose underlying time series exhibit superlinear growth and tail risk of regime change, a structure common in finance and epidemiology. On these tasks, more capable models produce worse distributional forecasts. The pattern appears on ForecastBench-Sim (FBSim), a contamination-free, simulated-world benchmark we release, in forecasting synthetic SIR epidemics with a matched linear control, and replicates in real-world datasets on COVID-19, measles, housing markets, and hyperinflation. A per-quantile decomposition shows the failure concentrates at the upper tail, which more capable models shift upward to track aggressive extrapolations of growth, while the lower tail stays put. A within-family study of Llama-3.1 shows that both model scale and post-training independently contribute to this effect. Domain knowledge does not reliably rescue calibration. This inverse scaling does not appear on single-threshold metrics common in LLM forecasting benchmarks, reversing the sign of the capability--accuracy relationship on identical outputs. Single-threshold scoring at conventional cutoffs misses the upper-tail cost; tail-inclusive scoring reverses the sign of the capability--accuracy relationship on the same outputs. We recommend that LLM forecasting evaluations use continuous (and unbounded) measures of accuracy alongside bounded binary threshold metrics.

Time Series Classification (TSC) is a long-standing research problem that has gained increasing attention in recent years with the rapid growth of large-scale temporal data. Despite substantial progress enabled by deep learning, designing TSC models that are both accurate and interpretable remains a challenging task. Many existing approaches adopt a direct feature-to-label classification paradigm, by collapsing high-dimensional temporal embeddings into class logits via a single linear projection (often after global pooling), the paradigm conflates feature extraction and decision logic into an inseparable mapping. To address these limitations, we propose PDFTime, a prototype-guided framework that reformulates time series classification as a multi-stage decision process. Instead of direct feature-to-label mapping, PDFTime leverages learned prototypes to approximate class-conditional feature distributions in the latent space, enabling progressive discrimination through classification sub-tasks of varying granularity. To our knowledge, PDFTime is the first framework to reformulate time series classification as a decoupled, multi-stage similarity-based reasoning process, breaking the long-standing paradigm of direct, black-box feature-to-label mapping. Extensive evaluations demonstrate that PDFTime achieves state-of-the-art (SOTA) performance across UEA and UCR benchmarks. Notably, it secures the top-$1$ accuracy on 80 out of 128 datasets in the UCR archive, significantly outperforming recent strong baselines in both consistency and generalization.

Multivariate time series (MTS) classification is foundational to pervasive computing and financial analysis, yet existing multi-scale paradigms are often constrained by suboptimal representation fidelity. We identify two critical bottlenecks: temporal non-causality in standard encoders that induces temporal confounding in non-stationary dynamics, and the absence of explicit channel saliency mechanisms that allows noise to contaminate the latent space. To address these challenges, we propose the Causal Attention and Spatio-temporal Encoder Network (CASE-NET), an architecture designed for structural manifold pre-conditioning. CASE-NET synergizes a Causal Temporal Encoder, which enforces physical arrow-of-time constraints via masked self-attention and causal convolutions, with an Adaptive Channel Recalibration module functioning as an information bottleneck to suppress detrimental noise. Comprehensive evaluations across six heterogeneous domains demonstrate that CASE-NET establishes new state-of-the-art benchmarks on four tasks, achieving a peak accuracy of 98.6% on the AWR dataset and superior robustness in non-stationary regimes.

Financial markets are characterized by extreme non-stationarity, low signal-to-noise ratios, and strong dependence on external information such as news, company fundamentals, and macroeconomic signals. Yet, existing approaches either abstract time-series into text or decouple forecasting from language-based reasoning, leading to a fundamental mismatch between qualitative reasoning and quantitative outcomes. To address this, we introduce StockR1, a time-series-enhanced LLM that unifies stock forecasting and financial reasoning through a verifiable forecast action. Based on a tool-call design, the model first emits a forecast action, which is a structured and interpretable representation of its qualitative market outlook. It then invokes a time-series decoder conditioned on this action to generate distributional future trajectories, leading to more informed question answering and financial reasoning. We optimize the full pipeline with reinforcement learning, where rewards jointly reflect answer validity, forecast accuracy, and consistency between generated actions and observed time-series dynamics. In addition, rewards are reweighted by a sample-level uncertainty scalar, encouraging the model to accommodate varying uncertainty in market dynamics. We evaluate StockR1 on financial question answering and stock forecasting over a large-scale 10-year benchmark. Our method consistently outperforms time-series baselines and general-purpose LLMs, improving reasoning accuracy by 17.7% (4B) and 25.9% (8B). These findings demonstrate that structuring the forecast actions establishes a powerful synergy between language reasoning and temporal prediction, enabling LLMs to reason through verifiable, interpretable, and numerically grounded decisions.

Self-supervised learning for time-series representation aims to reduce reliance on labeled data while maintaining strong downstream performance, yet many existing approaches incur high computational costs or rely on assumptions that do not hold across diverse temporal dynamics. In this work, we introduce Divide and Contrast (Di-COT), an unsupervised framework that avoids data augmentation and multiple encoder passes by contrasting informative substructures within a window rather than individual timesteps. Di-COT stochastically partitions each window into a small number of overlapping sub-blocks per iteration, enabling efficient and meaningful contrast while mitigating false positives during temporal transitions. To further improve scalability, we adopt a contrastive objective whose computation depends on the batch size and the number of sub-blocks, making loss computation independent of sequence length. Extensive experiments on six large-scale real-world datasets, as well as the UCR and UEA benchmarks, demonstrate that Di-COT learns semantically structured and transferable representations, achieving state-of-the-art performance on classification, clustering, $k$NN, and cross-dataset transfer, while substantially reducing training time. The source code is publicly available at https://github.com/sfi-norwai/Di-COT.

Public events on social media generate large volumes of discussion whose collective dynamics carry direct value for opinion forecasting and crisis response. Capturing how these dynamics evolve across an event's lifecycle requires organizing fragmented posts into event-level time series. Existing datasets cover only a small number of events within a single category, and typically discard the interaction structure between posts when constructing time series, which restricts both transfer across event types and controlled study of how interactions shape the resulting collective dynamics. We present SURGE, a multi-event social media benchmark that pairs event-level time series with aligned text and interaction structure linking posts within an event. SURGE is built through an automated pipeline that produces calendar-aligned time series at three temporal granularities, covering 67 events and more than 800K posts across five event categories. Each time bin is paired with flat and structured textual views derived from the same selected posts, enabling controlled evaluation of whether social interaction structure affects forecasting behavior. On top of SURGE we define benchmark protocols for numerical-only forecasting, text-augmented forecasting, high-interaction evaluation, and leave-one-category-out generalization. Experiments with representative time-series and multimodal forecasting models reveal three properties of the benchmark: a strong local-persistence regime in which naive baselines remain hard to beat under absolute error, limited transfer of existing text-augmented forecasters to event-driven social-media data, and increased difficulty on reply-dense periods that aggregate metrics tend to obscure. We further include a lightweight structure-aware probe as a reference implementation, illustrating how SURGE can support interaction-aware forecasting research.

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

Country-level temporal panels are widely used in empirical analysis. Researchers often need to audit how different entities respond to historical signals over different time horizons. Current approaches typically do not provide directly auditable entity-specific lag summaries. We formulate entity-conditioned heterogeneous lag discovery as a temporal panel mining task and propose AC-GATE, an Adaptive-Conditioning Encoder with a Scale-Invariant Lag Gate. It instantiates conditional Moderated Distributed Lag by using observable entity-level proxies to condition lag-weight distributions over historical observations, thereby making effective lags structural outputs of the model rather than post-hoc explanations. The evaluation is based on a layered audit protocol that separates predictive calibration from lag discovery. A synthetic panel with known ground-truth lags is used for mechanism recovery testing, and two real-world country-level panels are used for external audit and stress testing. The results show that AC-GATE can recover heterogeneous lag structure in synthetic data, and generates non-degenerate, externally structured effective lags in real data.

Can language-pretrained transformers become effective time-series forecasters, and why? In this paper, we show that cross-modal transfer arises because language pretraining preconditions time series training with a reusable manifold. A linear probe on frozen LLM states decodes realistic time-series trajectories without paired supervision, and retrieval in this projected space yields competitive forecasts, showing that structure and dynamics exist before finetuning. Pretrained initialization also improves optimization, producing coherent gradients and a highly anisotropic loss landscape unlike random initialization. Finetuning then acts as low-dimensional alignment, reusing existing directions rather than learning temporal primitives from scratch, as evidenced by low-rank updates, subspace alignment, and shared features for periodicity, trend, and repetition. Together, these results support a geometric account of LLM-to-time-series transfer: language pretraining builds the manifold, and finetuning projects numerical dynamics onto task-relevant directions.

We show that time series foundation models scale: a single training recipe produces reliable forecast-quality improvements from 4M to 2.5B parameters. We release Toto 2.0, a family of five open-weights forecasting models trained under this recipe. The Toto 2.0 family sets a new state of the art on three forecasting benchmarks: BOOM, our observability benchmark; GIFT-Eval, the standard general-purpose benchmark; and the recent contamination-resistant TIME benchmark. This report describes our experimental results and details the design decisions behind Toto 2.0: its architecture and training recipe, training data, and the u-muP hyperparameter transfer pipeline. All five base checkpoints are released under Apache 2.0.

Discovering shapelets -- i.e., discriminative temporal patterns within time series -- has been widely studied to address the inherent complexity of time-series classification (TSC) and to make model decision-making processes more transparent. However, existing methods primarily focus on population-level shapelets optimized across the entire dataset, which leads to two fundamental limitations: (i) population-level patterns often misalign with instance-specific features, resulting in suboptimal performance and potentially misleading interpretations, and (ii) most methods treat shapelets as independent entities, overlooking important temporal dependencies and interactions among multiple patterns. To address these limitations, we propose INSHAPE, an interpretable TSC framework that discovers variable-length, discriminative temporal patterns specific to each time series. INSHAPE identifies these patterns as non-overlapping segments and models their temporal dependencies, thereby providing clear instance-level interpretations while achieving strong predictive performance. Furthermore, INSHAPE bridges local and global interpretability through a bottom-up approach, aggregating instance-level shapelets into prototypical (population-level) shapelets. Extensive experiments on 128 UCR and 30 UEA benchmark datasets show that INSHAPE consistently outperforms state-of-the-art shapelet-based methods while providing more intuitive and interpretable insights.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced multivariate forecasting, they often suffer from a "normality bias" when trained end-to-end, sacrificing marginal calibration for joint coherence and consistently underestimating tail risk. To address this, we propose a Diffusion-Copula framework that explicitly decouples the learning of marginal distributions from their dependence structure. We employ deep Mixture Density Networks to capture heavy-tailed asset dynamics, followed by a Classification-Diffusion Copula to model the joint dependence. Applied to cryptocurrency markets, our approach demonstrates superior performance over state-of-the-art baselines in forecasting systemic extremes of both marginal and joint events. Crucially, we demonstrate that while baseline models classify simultaneous market crashes as statistically impossible "Black Swans" (high surprise), our framework identifies them as "Expected Crashes" (low surprise), successfully preserving the correlation structure necessary for robust risk management during contagion events.

Numerical time-series models can effectively process irregular electronic health record (EHR) trajectories, but they do not naturally expose the measurements and temporal patterns supporting each risk estimate as readable evidence. Existing text-based interfaces improve readability, but typically rely on either raw serialization, which is lengthy and redundant, or patient-level free-form summaries, which are difficult to trace to source measurements and time windows. To bridge this gap, we introduce TreeText-CTS (Clinical Time-Series), which converts irregular EHR trajectories into human-readable, compact, source-traceable tree-path evidence units without patient-level summarization or inference-time autoregressive decoding. TreeText-CTS routes multi-scale window summaries through frozen XGBoost models and verbalizes activated tree paths as deterministic, source-traceable evidence units composed of threshold conditions. An evidence selector assembles an informative subset of these units, which a language-model encoder then integrates for prediction. Across PhysioNet 2012 mortality, MIMIC-III mortality, and PhysioNet 2019 sepsis-onset forecasting, TreeText-CTS achieves the best AUROC and AUPRC among evaluated text-based EHR time-series interfaces, improving AUPRC by 6.0 to 9.7 absolute percentage points over the strongest prior text-based interface while remaining competitive with numerical time-series models. Ablations show that tree-path evidence construction, evidence selection, and language-model composition each contribute to performance. Because every span passed to the language-model encoder is constructed from activated tree-path threshold conditions, TreeText-CTS makes the evidence supplied to the final predictor inspectable and source-traceable.

The success of self-supervised learning (SSL) in vision and NLP has motivated its rapid adoption for time series. However, research has focused primarily on Generative paradigms and forecasting tasks, leaving the broader utility of learned representations unquantified. We establish a controlled framework to evaluate the "pre-training dividend": the value added by SSL across diverse temporal tasks. We systematically compare Generative paradigms against Latent Alignment architectures, introducing adaptations of LeJEPA and DINO for time series. These adaptations utilize Discrete Wavelet Transform (DWT) augmentations to enforce invariance to local fluctuations. Our analysis reveals that the pre-training dividend is highly asymmetric: SSL yields gains of up to 375% for anomaly detection and classification, yet remains marginal for forecasting. We demonstrate that representational utility is non-universal, governed by a precision-invariance trade-off where the specific signal resolution required by the task must align with the objective. Finally, we show that representation quality is largely independent of data origin and saturates at moderate architectural depths, suggesting a path to scaling via massive synthetic generation. Our code is available at: https://github.com/noammajor/Models

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models.

The rapid adoption of deep learning has increasingly led to data-driven models replacing classical model-based algorithms, even in domains governed by well-understood physical laws. While data-driven models, such as long short-term memory (LSTM) networks, have become a popular choice for time-series analysis, their performance relative to model-based approaches in structured environments is rarely evaluated objectively. This paper presents a performance evaluation framework comparing an LSTM classifier against a model-based expectation maximization (EM) classifier for binary time-series classification. The evaluation is conducted on two scalar linear Gaussian state space models differing only in their noise statistics, where the Kalman filter likelihood ratio test with true parameters serves as a reference for the best achievable classification performance.Through Monte Carlo simulations, the classifiers are evaluated across three axes: task difficulty, controlled by the separation in process or measurement noise between the two models; sequence length; and training dataset size. The results show that the EM classifier, which exploits the known model structure, performs strongly when the data conform to the assumed model class. The LSTM classifier requires a larger separation in noise statistics to achieve reliable classification, and its performance saturates below the reference classifier when the models differ only in measurement noise, regardless of sequence length or training dataset size.

Real-world time series come with text: metadata, descriptions, news, reports. Yet time series foundation models process numerical sequences in isolation, and the multimodal text-and-time-series models that attempt to bridge the two all adapt a pretrained language model post hoc, inheriting representations shaped without ever seeing temporal data. These models are also evaluated almost exclusively against other multimodal baselines, not against the strongest unimodal foundation models in either domain, leaving open whether joint training is needed at all. We present Chronicle, a compact 324M-parameter decoder-only transformer trained from scratch on natural language and time series within a single unified architecture. Both modalities share the same transformer blocks, attention mechanism, and residual stream; the bulk of pretraining uses unimodal batches so cross-modal capability emerges purely from shared parameters, with a short alignment stage that interleaves the two. To our knowledge, Chronicle is the first model jointly pretrained on text and time series from scratch, and the first multimodal model evaluated against dedicated foundation models in both domains. It matches Gemma-3-270M-PT on 19 NLU tasks, sets a new bar for frozen-embedding time series classification on 24 UCR/UEA datasets, and produces multimodal forecasts on Time-MMD that beat every supervised fusion baseline, all from a single backbone.

The rapid global expansion of solar photovoltaic (PV) capacity-reaching a record 597 GW in 2024-highlights the urgent need for robust forecasting models to mitigate the grid instability caused by the intermittent nature of solar irradiance. While deep learning-based direct forecasting using ground-based sky images (GSI) has emerged as a dominant approach, existing literature is often constrained by single-architecture evaluations and an exclusive focus on single-horizon (point) prediction. This paper proposes a transition from traditional single-horizon estimation toward a multi-horizon forecasting framework, leading to an architecture-independent improvement in accuracy. We hypothesize and demonstrate experimentally that joint optimization over a sequence of future values allows deep neural networks to better capture latent inter-step temporal dependencies by avoiding precocious convergence of the network in terms of both weight gradients and filter diversity. Leveraging this architecture-independent improvement that integrates sequential sky imagery with historical PV generation data, we evaluate the models' abilities to predict power output across multiple discrete future time steps simultaneously. Our methodology is validated through a comparative analysis across diverse deep learning architectures. The results demonstrate that this multi-horizon approach significantly enhances predictive accuracy and robustness across the entire forecast horizon while maintaining computational parsimony. By achieving superior performance with negligible overhead compared to single-horizon models, this work provides a scalable and efficient solution to improve the resilience of modern power grids.

Time Series Foundation Models (TSFMs) have demonstrated notable success in general-purpose forecasting tasks; however, their adaptation to specialized classification problems remains constrained by the computational bottleneck of standard attention and the systematic omission of classical statistical knowledge. This technical report introduces KairosHope, a next-generation TSFM designed to reconcile massive generalization with analytical precision in classification tasks. The core of the proposal is the HOPE block, an architecture that replaces quadratic attention with a dual-memory system: Titans modules for dynamic short-term retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. To enrich the inductive bias, a Hybrid Decision Head is introduced, which fuses deep latent representations with deterministic statistical features extracted via tsfeatures package. KairosHope undergoes self-supervised pre-training on the massive Monash archive, combining Masked Time Series Modeling (MTSM) and contrastive learning (InfoNCE). Its subsequent adaptation to the UCR benchmark datasets is conducted through a rigorous Linear Probing and Full Fine-Tuning (LP-FT) protocol to prevent catastrophic forgetting. Empirical results demonstrate superior performance in domains characterized by strict temporal causality such as HAR or Sensor data. Consequently, KairosHope establishes a robust and efficient framework for the adaptation of foundation models to time series analysis.

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Time series classification (TSC) of biological signals has progressed from handcrafted, modality-specific approaches to deep architectures capable of representing the diverse waveform structures of underlying physiological processes (i.e., morphology). This review introduces a unified morphology--modality framework that connects waveform structure to a methodological design, revealing how spikes, bursts, oscillations, slow drift, and hierarchical rhythms inform model design. By analyzing electroencephalography, electromyography, electrocardiography, photoplethysmography, and ocular modalities (electrooculography, pupillometry, eye-tracking), the review demonstrates how morphology determines preprocessing and modeling strategies. Integrating evidence across these biological signals, the framework reveals that morphology, not model class, most strongly determines performance and interpretability. This provides insight into why deep models succeed when their inductive biases align with underlying waveform dynamics. This review also identifies future work including morphological data augmentation and evaluation metrics to improve generalization. Together, these insights position morphology-aware modeling as a unifying principle for developing generalizable, interpretable, and physiologically meaningful TSC models across biological signals.

Anomaly detection in batch processes is hindered by transient dynamics, scarce fault labels, and reliance on single-modality sensor data. This work introduces UTOPYA (Unified Temporal Observation for Physics-Informed Anomaly Detection and Time-Series Prediction), a 15.2M-parameter multimodal framework that jointly addresses anomaly detection, time-series prediction, and phase classification in batch distillation by fusing eight data modalities through Feature-wise Linear Modulation (FiLM) conditioned cross-modal attention and gated fusion. A physics-informed regularisation scheme introduced in this work enforces temporal smoothness and thermodynamic monotonicity, while curriculum learning introduces training samples in order of physical difficulty. On the 119-experiment multimodal batch distillation dataset of Arweiler et al. (2026), UTOPYA achieves a window-level test AUROC of 0.832 and 0.874 under multi-signal experiment-level scoring, substantially outperforming four external baselines (PCA, autoencoder, Isolation Forest, and LSTM autoencoder) evaluated under identical conditions (+0.147 window-level AUROC over the best baseline). A multimodal ablation over 15~architectural configurations shows that static context via FiLM conditioning is the key enabler, lifting experiment-level multi-signal AUROC by +0.145 over the unimodal baseline (0.729 to 0.874). Separately, a training ablation across 14 design choices reveals that several widely-adopted techniques, including instance normalisation, Mixup, ensembling, test-time augmentation, and stochastic weight averaging, fail to improve or actively degrade generalisation in this data-scarce setting. These negative results expose a fundamental tension between smoothing-based regularisation and anomaly detection, providing practical guidance for multimodal process monitoring deployment.

Long-horizon prediction of three-dimensional (3D) wall-bounded turbulence with machine-learning methods remains a challenging task, due to the rapid accumulation of autoregressive errors and the substantially computational cost. To address these challenges, we present a hybrid machine-learning framework, in which a channel-time-attention Swin-UNet (CTA-Swin-UNet) and a multi-time-scale fusion correction (MTFC) strategy are developed to predict the turbulent flow fields in a wall-parallel plane, with affordable computational cost. Then, 3D flow fields are reconstructed via a resolvent-based spectral linear stochastic estimation (SLSE), rooting from the predicted planar flow. Results show that the CTA-Swin-UNet outperforms the baseline models (LSTM, FNO and traditional Swin-UNet) in both single-step prediction and autoregressive rollouts, indicating the effectiveness of introducing the CTA module into the Swin-UNet architecture. At the same temporal interval, the CTA-Swin-UNet remains stable for approximately 150 rollout steps, while the baseline models fail within 20 to 50 rollout steps. After introducing the MTFC strategy, a longer horizon upto 300 steps is achieved. Using the resolvent-based SLSE reconstruction further recovers the 3D flow structures and energy spectral distributions from the predicted planar inputs, which demonstrates that the proposed framework provides an effective and computationally efficient approach for long-horizon autoregressive prediction of 3D wall-bounded turbulence.

Small-scale data is a critical problem in time-series forecasting tasks. Data augmentation is an effective strategy for this task, but it has a limitation in generating meaningful data. To address this limitation, we propose DAD4TS, a diffusion-model-based data augmentation method with reinforcement learning, designed for time-series forecasting with small-scale data. In DAD4TS, a data generator is simultaneously trained with a time-series model and controlled by a reinforcement learning model to efficiently generate samples that improve the forecast accuracy of the time-series model. To support small-scale data, we use mathematical methods instead of conventional VAE methods to train the diffusion model by projecting the time-series data into the geometric space. We validated the effectiveness of DAD4TS with seven comparative methods through qualitative and quantitative experiments on six real-world datasets and eight time-series models. As a result, DAD4TS was validated on five datasets.

Generative models have demonstrated remarkable potential in time series analysis tasks, like synthesis, forecasting, imputation, etc. However, offering limited coverage for generative models, existing time series libraries are mainly engineered for discriminative models, with standardized workflows for specific tasks, such as optimizing Mean Squared Errors for time series forecasting. This rigid structure is fundamentally incompatible with the distinct and often complex paradigms of generative models (e.g., adversarial training, diffusion processes), which learn the underlying data distribution rather than a direct input-output mapping. To this end, we proposed GenTS, a comprehensive and extensible benchmark library designed for systematic assessment on generative time series models. GenTS features a unified data preprocessing pipeline, a collection of versatile models, and panoramic evaluation metrics. Its modular design also enables the researchers to flexibly customize beyond our built-in datasets and models. Based on GenTS, we conducted benchmarking experiments under diverse tasks, accordingly offering suggestions for model selection and identifying potential directions for future research. Our codes are open-source at https://github.com/WillWang1113/GenTS. The official tutorials and document are available at https://willwang1113.github.io/GenTS/.

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Time series foundation models rely on large-scale pretraining over diverse datasets across domains, yet their heterogeneity in temporal patterns could hinder the effectiveness of training and learning transferable time series representations. Inspired a fundamental concept, normalized power spectral density (PSD) in signal processing, we assume harmonizing datasets via PSDs in the spectral domain could reduce mismatches and enhance pretraining. We then go beyond the direct intractable minimization optimization and innovatively reformulate it as a principled harmonization approach. Specifically, we propose Harmonizer, a module that reshapes spectral structures and implicitly harmonizing PSDs across datasets, which theoretically corresponds to a shared reparameterization of second-order temporal correlations. Our theoretical analysis further reveals token interactions with Harmonizer can be efficiently mediated by a compact set of resonators, motivating a HarmonicAttention design that performs self-attention in a low-dimensional interaction space. Then, we propose Olivia, a novel time series foundation model built upon these harmonization mechanisms. Extensive experiments on two large-scale benchmarks (TSLib and GIFT-Eval) and extra 6 datasets from GluonTS, demonstrate Olivia consistently achieves state-of-the-art performance under zero-shot, few-shot, and full-shot forecasting scenarios. Our code is available at https://github.com/TSTS13/Olivia.

Test-time adaptation (TTA) has recently emerged as a promising approach for improving time series forecasting (TSF) under distribution shift. Existing TSF-TTA methods differ in how they utilize revealed targets, yet the resulting adaptation protocols remain heterogeneous and lack a clearly unified formulation. To address this issue, we revisit TSF-TTA from the perspective of protocol cleanliness and propose an adaptation protocol based solely on matured ground truth, yielding a more principled setting for adaptation. Under this protocol, we further diagnose existing adapters in the frequency domain and find that their prediction corrections often exhibit limited and weakly structured spectral modifications. Motivated by this diagnosis, we propose Frequency-Aware Calibration (FAC), a lightweight calibration method that directly parameterizes prediction corrections in the frequency domain. Across diverse datasets, forecasting horizons, and source forecasters, FAC achieves competitive and consistent performance while requiring substantially fewer trainable parameters than the compared TSF-TTA adapters.

Scientific forecasting typically relies on direct state prediction, an approach that grows brittle under data scarcity, extended horizons, non-stationary dynamics, or high-dimensional complexity. While raw state trajectories are highly sensitive in these regimes, underlying local evolution rules often exhibit robust reusability. We introduce mechanism learning, a framework that forecasts future states by estimating the currently active local mechanism. Our method compresses local spatiotemporal fragments into mechanism descriptors, forming a data-driven, structured mechanism space where proximity reflects similar local evolution rules. To ground these estimates in observed data, we utilize prototype anchors, a set of representative mechanisms that sparsely cover the space of local rules. We evaluate this approach on Burgers dynamics, WeatherBench2, and Lorenz96. Empirically, the learned mechanism spaces resist collapse and maintain strong local consistency. Compared to direct prediction and other models including FNO, NODE, LSTM, and reservoir-family methods, our framework demonstrates predictive gains in fragile regimes: it significantly improves switching stability in Burgers dynamics and achieves state-of-the-art performance both under the scarce-data fixed-horizon WeatherBench2 protocol and in intermediate-complexity Lorenz96. Ablation studies and drift diagnostics confirm that these improvements are driven by finite prototype anchoring rather than sheer latent capacity. Together, these results establish mechanism learning as a principled, robust alternative to direct state prediction in forecasting complex systems.

Recent advances in Time Series Foundation Models (TSFMs) promise zero-shot forecasting capabilities with minimal task-specific training. While these models have shown strong performance across generic benchmarks, their applicability in volatile, complex electricity markets remains underexplored. Addressing this gap, this study provides a systematic empirical evaluation of several TSFMs, specifically Chronos-2 and Chronos-Bolt (developed by Amazon), and TimesFM 2.5 (provided by Google), for forecasting Belgian day-ahead and imbalance electricity prices. For both considered markets, Chronos-2 in ARX mode produces the most accurate forecasts. Compared with the best ensemble prediction from other machine learning methods, Chronos-2's Mean Absolute Error (MAE) is 5% lower for the day-ahead market. In contrast, the model yields 10% higher MAE predicting imbalance prices across all forecast horizons, except for the two-hour-ahead horizon. Moreover, we find that TSFMs exhibit genuine zero-shot forecasting skills but still struggle under extreme market conditions.

Electrocardiogram (ECG) foundation models pretrained on typical diagnostic 10-second ECG segments, have demonstrated strong transferability across a range of clinical applications. However, many real-world applications produce recordings that are typically longer, and are varied in duration during inference time. These 10-second models have no built-in way to combine information across time. Extending them to longer horizons introduces two challenges: structural incompatibilities arising from input-length disparities, and semantic challenges that limit meaningful temporal aggregation. We propose a parameter-efficient framework that extends pretrained ECG foundation models to longer and variable-length ECGs without retraining the backbone. Guided by a frozen pretrained 10-second model, we introduce a lightweight plug-in module that extends the model in two complementary ways: (i) structurally compatible long-sequence processing and (ii) semantically informed temporal modeling. Experiments on multiple long-horizon ECG tasks, datasets, and foundation model backbones demonstrate that our method enables robust long-horizon extension from pretrained snapshot models, consistently outperforming sliding-window and pooling-based baselines with strong parameter efficiency.

Many decision-facing stochastic systems are observed through aggregate distributions rather than scalar trajectories: queue occupancies, mobility shares, public-health mixtures, generation-source shares, ecological compositions, and air-quality severity profiles all live on the probability simplex and evolve over time. We study causal (online) forecasting for these distribution-valued time series and argue that the transition operator itself should be structured around the simplex. We introduce CAST (Causal Anchored Simplex Transport), a successor-local operator that (i) retrieves empirical successors from causal context, (ii) stabilizes them with a persistence anchor, and (iii) applies a bounded local stochastic transport on ordered supports; every stage preserves the simplex by construction. We identify a structural failure mode, latent transition-kernel aliasing, where similar observed distributions evolve differently under different contextual regimes, and prove that any forecaster depending only on an aliased summary incurs an irreducible weighted Jensen-Shannon excess-risk lower bound, while the CAST hypothesis class contains the regime-aware Bayes successor; for ordered supports an additional Pinsker separation holds whenever the transported successor lies outside the no-transport anchor hull. On eleven public and simulated benchmarks spanning ecology, energy, diet, mortality, employment, air quality, severe weather, mobility, and G/G/1, G_t/G/1 queue occupancy, CAST attains the best average rank on both one-step KL (1.27) and autoregressive rollout JSD (1.91), winning 8/11 sections on each metric against a broad statistical, compositional, recurrent, convolutional, and Transformer baseline set, and top-2 on all 11 sections for offline KL. Component ablations and a controlled synthetic aliasing experiment corroborate the theory.

Accurate long-horizon glucose forecasting is critical for automated insulin delivery systems, which help people with type 1 diabetes (T1D) manage their glucose and avoid dangerous hypoglycemia. However, standard recursive long short-term memory (LSTM) networks suffer from systematic negative bias at longer horizons due to error compounding, while purely mechanistic ordinary differential equation (ODE) models fail to generalize across individuals when parameterized at the population level. We propose PhysioSeq2Seq, a hybrid architecture that combines patient-specific physiological modeling with a sequence-to-sequence (Seq2Seq) LSTM. For each glucose segment, twin matching searches a population of 300 parameterized digital twins to identify the best-fitting physiological match from a 3-hour continuous glucose monitoring (CGM) history. The 10 internal ODE state variables of the matched twin are injected as exogenous covariates into both the encoder and decoder of the Seq2Seq LSTM. This simultaneous 48-step prediction strategy eliminates recursive error compounding, while the ODE features provide a physics-grounded constraint that bounds long-horizon drift within physiologically plausible ranges. PhysioSeq2Seq was trained on CGM and insulin data from 348 participants in the Type 1 Diabetes Exercise Initiative (T1DEXI) dataset and evaluated on 74 held-out participants. At the 240-minute horizon, PhysioSeq2Seq achieves a mean absolute error of 39.28 mg/dL and a mean error of -10.62 mg/dL, reducing bias by 13.89 mg/dL over the recursive LSTM and reducing mean absolute error by 28.62 mg/dL over the ODE-based digital twin. These results show that eliminating architectural feedback and injecting patient-matched physiological states is an effective and clinically meaningful strategy for long-horizon glucose forecasting in T1D.

Skillful medium-range precipitation forecasting at kilometer scale remains challenging over complex terrain because precipitation arises from multiscale nonlinear processes that global models cannot explicitly resolve at affordable cost. Global AI weather models can produce skillful medium-range forecasts, but their native 0.25 degrees resolution limits direct use for local hazard applications. Statistical downscaling can help bridge this gap, yet existing approaches often struggle with state-dependent, and especially lead-time-dependent, biases in global forecasts. We introduce SwAIther-Precip, a lead-time-aware downscaling framework that converts coarse-resolution AIFS forecasts into probabilistic km-scale precipitation fields over Switzerland. First, a U-Net conditioned on lead time via feature-wise linear modulation deterministically corrects systematic biases at coarse resolution. This targeted correction enables a cheaper super-resolution stage conditioned only on corrected precipitation, allowing direct training on observations rather than on the full atmospheric state. A diffusion-based model then generates fine-scale spatial variability independently of lead time. Using AIFS forecasts and CombiPrecip radar-gauge observations, SwAIther-Precip reduces CRPS by 48% relative to raw AIFS. The generated fields reproduce observed spatial variability with spectral fidelity above 0.85 at large scales and 0.88 at small scales, corresponding to an effective resolution of approximately 4 km on a 1 km grid for lead times up to 5 days. Training across lead times further improves long-range performance, yielding a 13% CRPS reduction at 6 days relative to lead-time-specific models. These results show that explicitly correcting lead-time-dependent biases before generative super-resolution is key to efficient km-scale probabilistic downscaling of global AI precipitation forecasts.

Timeseries regression models often struggle to leverage large volumes of labeled multimodal data, particularly when the data are irregularly sampled or contain missing values. This is common in domains like healthcare and predictive maintenance, where data are collected from unreliable sources, and labeling requires expert knowledge or costly equipments. Transformer-based large language models have proven effective on structured data such as text through self-supervised learning (SSL) and generative pretraining (GPT) frameworks. However, such models lack the flexibility to efficiently process irregularly sampled multimodal timeseries data. In this paper, we introduce ITGPT, an attention-based architecture designed for handling multimodal, irregularly sampled timeseries by allowing training with both SSL losses and GPT-like objectives. We evaluate its performance on a healthcare task with the TIHM dataset, and a predictive maintenance task with the CompX dataset. Our results demonstrate that ITGPT achieves state-of-the-art performance without requiring resampling, feature fusion or explicit data imputation. Furthermore, when labels are scarce, ITGPT effectively leverages unlabeled data through SSL and GPT training, outperforming the purely supervised approach. This represents an important step towards efficiently using large and unstructured timeseries datasets for practical inference tasks.

State Space Models (SSMs) are inherently recurrent along the sequence dimension, yet depth-recurrence - reusing the same block repeatedly across layers, as recently applied in looped transformers - has not been explored in this model family. We show that a looped SSM with $k$ parameters iterated $L$ times consistently closely matches or outperforms a standard SSM with $k \cdot L$ independent parameters across four architectures (LRU, S5, LinOSS, LrcSSM) and six time series classification benchmarks, despite operating within a strictly smaller hypothesis space, as we formally establish. Since the larger model contains the looped model as a special case, this dominance cannot be explained by expressivity and instead points to parameter sharing across depth as a beneficial inductive bias that simplifies optimization. These results demonstrate that depth-recurrence is orthogonal to sequence-recurrence and independently beneficial. We further show that input reshaping is an equally neglected design axis: concatenating timesteps for low-dimensional inputs, or flattening and rechunking the joint feature-time dimension for high-dimensional ones, yields accuracy gains of 1-6% across all models, confirmed over 5 random seeds. Both techniques provide standalone improvements that compound when combined, suggesting that depth and input reshaping are two independent and underexplored design axes for SSMs on time series.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

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.

Long-horizon vessel trajectory forecasting under real ocean conditions is critical for collision avoidance, traffic management, and route planning. However, achieving accurate predictions is challenging due to long-range temporal dependencies and dynamic environmental factors such as currents, wind, and waves. To address these issues, we propose a hierarchical two-stage framework that combines a coarse long-term predictor with a grid-aware short-term predictor through a hierarchical fusion mechanism. The short-term branch leverages a Spatio-Temporal Graph Transformer on discretized maritime cells to capture localized dynamics, while the long-term branch encodes overarching navigational intent. An integrated environmental module incorporates oceanographic parameters, including surface currents, wind vectors, and significant wave height, using cross-modal attention and feature-wise modulation for adaptive response to varying sea conditions. Additionally, a learnable Savitzky-Golay smoothing layer enhances temporal coherence in fused trajectories. We evaluate our approach on Australian Craft Tracking System (CTS) data from the North West region, aligned with Copernicus Marine Service products, using a 3-hour input and a 10-hour prediction horizon. Experimental results show that our framework outperforms the state-of-the-art by 25% in Average Displacement Error (ADE) and 17% in Final Displacement Error (FDE). Ablation studies further validate the contribution of each component.

Reconstructing precise clinical timelines is essential for modeling patient trajectories and forecasting risk in complex, heterogeneous conditions like sepsis. While unstructured clinical narratives offer semantically rich and contextually complete descriptions of a patient's course, they often lack temporal precision and contain ambiguous event timing. Conversely, structured electronic health record (EHR) data provides precise temporal anchors but misses a substantial portion of clinically meaningful events. We introduce a retrieval-augmented multimodal alignment framework that bridges this gap to improve the temporal precision of absolute clinical timelines extracted from text. Our approach formulates timeline reconstruction as a graph-based multistep process: it first extracts central anchor events from narratives to build an initial temporal scaffold, places non-central events relative to this backbone, and then calibrates the timeline using retrieved structured EHR rows as external temporal evidence. Evaluated using instruction-tuned large language models on the i2m4 benchmark spanning MIMIC-III and MIMIC-IV, our multimodal pipeline consistently improves absolute timestamp accuracy (AULTC) and improves temporal concordance across nearly all evaluated models over unimodal text-only reconstruction, without compromising event match rates. Furthermore, our empirical gap analysis reveals that 34.8% of text-derived events are entirely absent from tabular records, demonstrating that aligning these modalities can produce a more temporally faithful and clinically informative reconstruction of patient trajectories than either source alone.

We introduce TopoPrimer, a framework that makes the global topological structure of the series population an explicit input to any forecasting model. TopoPrimer improves accuracy across diverse domains, stabilizes forecasts under seasonal demand spikes, and closes the cold-start gap. Precomputed once per domain via persistent homology and spectral sheaf coordinates, TopoPrimer deploys per token for fully-trained models and as a lightweight adapter for pre-trained backbones. Of these two components, sheaf coordinates are the primary accuracy driver. Across four public benchmarks on Chronos and TimesFM, TopoPrimer consistently improves forecasting accuracy, with gains of up to 7.3% MSE on ECL. The topology advantage persists with near-identical magnitude across zero-shot and fine-tuned backbones, suggesting topology and per-series training capture complementary signals. The gains are most pronounced in difficult regimes. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10%. At cold start with no item history, TopoPrimer reduces MAE by 27% over a topology-free baseline.

Instance normalization (IN) is widely used in non-stationary multivariate time series forecasting to reduce distribution shifts and highlight common patterns across samples. However, IN can over-smooth instance-specific structural information that is essential for modeling temporal and cross-channel heterogeneity. While prior methods further suppress distribution discrepancies or attempt to recover temporal specific dependencies, they often ignore a central tension: how to adaptively model common and instance-specific dependency based on each instance's non-stationary structures. To address this dilemma, we propose SeesawNet, a unified architecture that dynamically balances common and instance-specific dependency modeling in both temporal and channel dimensions. At its core is Adaptive Stationary-Nonstationary Attention (ASNA), which captures common dependencies from normalized sequences and specific dependencies from raw sequences, and adaptively fuses them according to instance-level non-stationarity. Built upon ASNA, SeesawNet alternates dedicated temporal and channel relationship modeling to jointly capture long-range and cross-variable dependencies. Extensive experiments on multiple real-world benchmarks demonstrate that SeesawNet consistently outperforms state-of-the-art methods.

Time series forecasting is not just numerical extrapolation, but often requires reasoning with unstructured contextual data such as news or events. While specialized Time Series Foundation Models (TSFMs) excel at forecasting based on numerical patterns, they remain unaware to real-world textual signals. Conversely, while LLMs are emerging as zero-shot forecasters, their performance remains uneven across domains and contextual grounding. To bridge this gap, we introduce Nexus, a multi-agent forecasting framework that decomposes prediction into specialized stages: isolating macro-level and micro-level temporal fluctuations, and integrating contextual information when available before synthesizing a final forecast. This decomposition enables Nexus to adapt from seasonal signals to volatile, event-driven information without relying on external statistical anchors or monolithic prompting. We show that current-generation LLMs possess substantially stronger intrinsic forecasting ability than previously recognized, depending critically on how numerical and contextual reasoning are organized. Evaluated on data strictly succeeding LLM knowledge cutoffs spanning Zillow real estate metrics and volatile stock market equities, Nexus consistently matches or outperforms state-of-the-art TSFMs and strong LLM baselines. Beyond numerical accuracy, Nexus produces high-quality reasoning traces that explicitly show the fundamental drivers behind each forecast. Our results establish that real-world forecasting is an agentic reasoning problem extending well beyond only sequence modeling.