Time Series

The key problem facing ChatGPT-like AI's use across society is that its behavior can shift, unnoticed, from desirable to undesirable -- encouraging self-harm, extremist acts, financial losses, or costly medical and military mistakes -- and no one can yet predict when. Shifts persist in even the newest AI models despite remarkable progress in AI modeling, post-training alignment and safeguards. Here we show that a vector generalization of fusion-fission group dynamics observed in living and active-matter systems drives -- and can forecast -- future shifts in the AI's behavior. The shift condition, which is also derivable mathematically, results from group-level competition between the conversation-so-far (C) and the desirable (B) and undesirable (D) basin dynamics which can be estimated in advance for a given application. It is neither model-specific nor driven by stochastic sampling. We validate it across six independent tests, including: 90 percent correct across seven AI models spanning two orders of magnitude in parameter count (124M-12B); production-scale persistence across ten frontier chatbots; and a priori time-stamped prediction eleven months before the Stanford 'Delusional Spirals' corpus appeared, and independently confirmed by that corpus of 207,443 human-AI exchanges. Because it sits architecturally below the current safety stack, the same formula provides a real-time warning signal that current alignment does not supply, portable across current and future ChatGPT-like AI architectures and instantiable in application domains where competing response classes can be defined.

Irregularly sampled multivariate event streams remain a difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude. We (i) propose \textbf{SurF}, a generative model that uses the Time Rescaling Theorem (TRT) as a learnable bijection between event sequences and i.i.d.\ unit-rate exponential noise, enabling a single model to be trained across heterogeneous event-stream datasets; (ii) three efficient parameterizations of the cumulative intensity that scale to long sequences; and (iii) a Transformer-based encoder for multi-dataset pretraining. On six real-world benchmarks, SurF achieves the best reported time RMSE on Earthquake, Retweet, and Taobao, and is within trial-level noise of the strongest specialist on the remaining three. Under a strict leave-one-out protocol, the held-out checkpoint beats every classical and neural-autoregressive baseline on $5/6$ datasets and beats every baseline on Amazon and Earthquake, an initial step toward foundation models over asynchronous event streams (Code is available at https://github.com/MrRezaeiUofT/SurF).

Multimodal irregular time series (MITS) consist of asynchronous and irregularly sampled observations from heterogeneous numerical and textual channels. In healthcare, for example, patients' electronic health records (EHR) include irregular lab measurements and clinical notes. The irregular timing and channel patterns of observations carry predictive signal alongside the numerical values and textual content. LLMs are natural candidates for processing such heterogeneous data, given their extensive pretrained knowledge spanning textual and numerical domains. We introduce MILM (Multimodal Irregular time series Language Model), which represents MITS as time-ordered triplets in Extensible Markup Language (XML) format and fine-tunes an LLM through a two-stage strategy for MITS classification. The first stage trains on value-redacted MITS to predict from sampling patterns alone, and the second stage trains on full MITS to jointly model sampling patterns and observed values. Our two-stage model (MILM-2S) and its single-stage counterpart (MILM-Direct) achieve the best and second-best average performance on multiple EHR datasets. Further value redaction evaluations confirm that sampling patterns carry predictive signal and that MILM-2S learns to exploit them. In the value pending evaluation we introduce, where some values are unavailable at prediction time, MILM-2S outperforms MILM-Direct by a larger margin compared to standard evaluation. For MILM-2S, preserving the time and channel of value-pending observations as additional sampling information further improves in-hospital mortality prediction.

Existing precipitation nowcasting methods typically adopt an autoregressive formulation, where future states are predicted from previous outputs. However, such an approach accumulates errors over long rollouts, causing forecasts to drift away from physically plausible evolution trajectories. Although various studies have attempted to alleviate this problem by improving step-wise prediction accuracy, they largely neglect the global temporal evolution of meteorological systems and lack mechanisms to actively correct drift during rollouts. To address this issue, we propose McCast, a memory-guided latent drift correction method for precipitation nowcasting. Rather than treating memory as an unordered dictionary of latent states for passive conditioning, McCast leverages temporally organized memory to actively correct autoregressive latent evolution. Specifically, McCast introduces a Drift-Corrective Memory Bank (DCBank) that explicitly estimates the temporally consistent drift corrections to calibrate the divergent trajectory. DCBank performs drift correction in two stages: a Corrective Latent Extractor first predicts an initial correction from the current prediction and a reference latent state, and a Correction-Aware Memory Retrieval module then refines the initial correction using temporally organized historical memory. By explicitly correcting latent evolution, instead of improving step-wise prediction accuracy only, McCast produces more temporally coherent and reliable long-horizon forecasts. Experiments on two widely used benchmarks, SEVIR and MeteoNet, show that McCast achieves state-of-the-art performance, particularly in challenging long-horizon forecasting scenarios.

Explainability methods have progressed rapidly, but global explanations for time-series models remain underdeveloped, with most approaches focusing on local, instance-level attributions. We introduce INSIGHTS, a model-agnostic, user-centric approach for providing global explanations of time series models. Our approach prioritizes simplicity, efficiency, and transparency in its design, ensuring that stakeholders can readily adopt its outputs. While current methods focus on local explanations, INSIGHTS generates sample summaries that offer a comprehensive overview of model behavior. It balances the importance and diversity of time series samples to create informative subsets using utility functions that capture domain-specific aspects of time series behavior, such as exceeding domain norms. We evaluate INSIGHTS through experiments, interviews, and a user study. Our results indicate INSIGHTS effectively constructs comprehensive, diverse time series subsets, producing summaries manageable for individual evaluation. It is preferred by domain experts for its ability to provide a stable understanding of model behavior and the quality of the samples identified. Moreover, user study participants presented with INSIGHTS-based summaries exhibit an enhanced understanding of the model's overall behavior.

Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such \emph{approximately periodic} behavior poses a challenge for Gaussian Processes (GP) modeling: strictly periodic models suppress inter-repetition variability, while non-periodic models fail to capture the strong structural regularities required for generation. In this work, we propose a stochastic generative model for approximately periodic time series. The model is based on a GP whose posterior is modulated by a novel kernel. Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction which yields a generative distribution with a identical mean function across repetitions, while allowing smooth variation between repetitions. The modeling choices are supported by an implementation in which realistic synthetic trajectories are generated from toy datasets.

This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed framework reduces reliance on conventional clustering methods, such as $K$-means, $K$-medoids, or hierarchical clustering, and their associated objective functions and heuristics. Leveraging statistical features, such as autocorrelations and quantile autocorrelations, the approach learns a data-driven affinity structure from which clustering partitions can be recovered, without requiring explicit prior specification of cluster shapes or structures. In addition, one version of the method can automatically determine the number of clusters, avoiding ad-hoc selection procedures. Comprehensive empirical studies show that the proposed framework achieves competitive or superior clustering accuracy relative to traditional methods, even in challenging scenarios where competing techniques are provided with the true number of clusters. An application to financial time series of stock returns illustrates its practical utility. By reducing the need for algorithm selection and calibration, the proposed framework opens new possibilities for automated, adaptive, and data-driven clustering of temporal data across scientific and industrial domains.

Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with interpretable, user-configurable parameters and modular topology, demand, and control rules. The simulator advances a directed routing graph in discrete time: demand is served from inventory or recorded as backlog and triggers replenishment throughout the network. The state tracks inventory, outstanding orders, in-transit shipments, and a smoothed demand estimate, yielding Markovian dynamics on a tractable state space. The released data reproduces the bullwhip effect at empirically consistent magnitudes, while three conservation laws provide verification tools for simulator extensions. We release datasets at two catalogue scales ($C=50$ and $C=200$), six scenario sweeps, and 20 Latin-hypercube perturbations. These datasets exhibit dynamics largely absent from fixed TSF benchmarks, including variance amplification, cascading bottlenecks, regime shifts, and cross-channel coupling through shared macro shocks. Zero-shot evaluation of four foundation models (Chronos, Moirai, TimesFM, and Lag-Llama) yields MASE values exceeding public GIFT-Eval references at low-to-moderate horizons, supporting incorporation into existing benchmark suites. The same models provide forecast confidence bands through Latin-hypercube perturbations of demand-side parameters, enabling forward uncertainty quantification (UQ) unavailable on standard TSF datasets and demonstrating that foundation models can serve as fast surrogates for digital-twin-based UQ. Code (MIT): https://github.com/tuhinsahai/ISOMORPH. Interactive demo: https://huggingface.co/spaces/HyeminGu/ISOMORPH-demo.

Reinforcement learning agents for portfolio management are typically trained and deployed as static policies, with no mechanism for using price forecasts at inference time. We propose $\text{FPILOT}$ (Financial Plugin Inference-time Learning for Optimal Trading), a plugin inference-time optimization framework inspired by Model Predictive Control (MPC). Our key structural insight is that future prices mostly do not depend on one agent's portfolio allocation, so a suitable predictive model can produce a multi-step price trajectory without iterative action-conditioned rollouts as in typical reinforcement learning. At each decision step, we use the forecaster's predicted price trajectory to construct an allocation-based imagined return objective, and optimize the policy at inference-time before executing one step of the trade. Our framework is compatible with any pre-trained agent and adapts the policy to the forecaster's predictions without any retraining. Evaluated across five policy learning algorithms on the TradeMaster DJ30 benchmark, $\text{FPILOT}$ produces consistent improvements in total return and return-based risk-adjusted metrics (Sharpe, Sortino, Calmar), with stochastic policies benefiting more than deterministic ones. Further, using synthetic forecasts at calibrated quality levels, we show that gains consistently improve with forecaster quality, suggesting that our performance will improve based on advances in financial forecasting.

Time Series Foundation Models (TSFMs) have recently achieved state-of-the-art performance, often outperforming supervised models in zero-shot settings. Recent TSFM architectures, such as Chronos-2 and TabPFN-TS, aim to integrate covariates. In this paper, we design controlled experiments based on simple target-covariate relationships to assess this integration capability. Our results show that TabPFN-TS captures these relationships more effectively than Chronos-2, especially for short horizons, suggesting that the strong benchmark performance of Chronos-2 does not automatically translate into optimal modeling of simple covariate-target dependencies.

Accurate ultra-short-term wind power forecasting is critical for grid dispatch and reserve management, yet remains challenging due to the non-stationary, condition-dependent nature of wind generation. Meteorological exogenous variables carry substantial predictive information, but the most informative variable combination varies across sites, operating conditions, and prediction horizons. Existing deep learning approaches either treat exogenous inputs as generic auxiliary channels through uniform mixing or soft gating, or rely on fixed preprocessing steps such as PCA, without exploiting the physical structure of meteorological variables. We propose ECTO (Exogenous-Conditioned Temporal Operator), a unified framework that decomposes exogenous variable modeling into two complementary modules. Physically-Grounded Variable Selection (PGVS) performs hierarchical, group-aware sparse selection over exogenous variables using a domain-informed physical prior and sparsemax activations, producing a compact, condition-adaptive exogenous context. Exogenous-Conditioned Regime Refinement (ECRR) routes the forecast through learned regime experts that apply gain--bias calibration and horizon-specific corrections via a mixture-of-experts paradigm. Experiments on three wind farms spanning different climates, capacities (66--200 MW), and exogenous dimensions (11--13 variables) demonstrate that ECTO achieves the lowest MSE across all sites, with relative improvements over the strongest baseline ranging from 2.2% to 5.2%, widening to 8.6% at the longer prediction horizon ($H=32$). Ablation analysis confirms that each exogenous-related component contributes positively (PGVS +1.84%, ECRR +2.86%), and interpretability analysis reveals that PGVS learns physically meaningful, site-specific variable selection patterns, while ECRR converges to well-separated calibration strategies consistent across sites.

The efficient operation of modern cellular networks hinges on the accurate analysis of spatio-temporal traffic data. Mastering these patterns is essential for core network functions, chiefly forecasting future load to pre-empt congestion and imputing missing values caused by sensor failures or transmission errors to ensure data continuity. While deeply connected, forecasting and imputation have historically evolved as separate sub-fields. The dominant paradigm, Spatio-Temporal Graph Neural Networks (STGNNs), while effective, are often specialized, computationally intensive, and exhibit limited generalization. Concurrently, adapting large pre-trained language models (LLMs) offers a powerful alternative for sequence modeling, yet existing approaches provide weak structural guidance, leading to unstable convergence and a narrow focus on forecasting. To bridge these gaps, we propose U-STS-LLM, a unified framework built on a spatio-temporally steered LLM. Our core innovation is a Dynamic Spatio-Temporal Attention Bias Generator that synthesizes a persistent functional graph with transient nodal states to explicitly steer the LLM's attention. Coupled with a partially frozen backbone tuned via Low-Rank Adaptation (LoRA) and a Gated Adaptive Fusion mechanism, the model achieves stable, parameter-efficient adaptation. Trained under a unified multi-task objective, U-STS-LLM learns a holistic data representation. Extensive experiments on real-world cellular datasets demonstrate that U-STS-LLM establishes new state-of-the-art performance in both long-horizon forecasting and high-missing-rate imputation, while maintaining remarkable training efficiency and stability, offering a novel blueprint for harnessing foundation models in structured, non-linguistic domains.

The increasing adoption of data-driven decision-making in public health has established epidemic forecasting as a critical area of research. Recent advances in multivariate forecasting models better capture complex temporal dependencies than conventional univariate approaches, which model individual series independently. Despite this potential, the development of robust epidemic forecasting methods is constrained by the lack of high-quality benchmarks comprising diverse multivariate datasets across infectious diseases and geographical regions. To address this gap, we present EpiCastBench, a large-scale benchmarking framework featuring 40 curated (correlated) multivariate epidemic datasets. These publicly available datasets span a wide range of infectious diseases and exhibit diverse characteristics in terms of temporal granularity, series length, and sparsity. We analyze these datasets to identify their global features and structural patterns. To ensure reproducibility and fair comparison, we establish standardized evaluation settings, including a unified forecasting horizon, consistent preprocessing pipelines, diverse performance metrics, and statistical significance testing. By leveraging this framework, we conduct a comprehensive evaluation of 15 multivariate forecasting models spanning statistical baselines to state-of-the-art deep learning and foundation models. All datasets and code are publicly available on Kaggle (https://www.kaggle.com/datasets/aimltsf/epicastbench) and GitHub (https://github.com/aimltsf/EpiCastBench).

While traditional time-series classifiers assume full sequences at inference, practical constraints (latency and cost) often limit inputs to partial prefixes. The absence of class-discriminative patterns in partial data can significantly hinder a classifier's ability to generalize. This work uses knowledge distillation (KD) to equip partial time series classifiers with the generalization ability of their full-sequence counterparts. In KD, high-capacity teacher transfers supervision to aid student learning on the target task. Matching with teacher features has shown promise in closing the generalization gap due to limited parameter capacity. However, when the generalization gap arises from training-data differences (full versus partial), the teacher's full-context features can be an overwhelming target signal for the student's short-context features. To provide progressive, diverse, and collective teacher supervision, we propose Generative Diffusion Prior Distillation (GDPD), a novel KD framework that treats short-context student features as degraded observations of the target full-context features. Inspired by the iterative restoration capability of diffusion models, we learn a diffusion-based generative prior over teacher features. Leveraging this prior, we posterior-sample target teacher representations that could best explain the missing long-range information in the student features and optimize the student features to be minimally degraded relative to these targets. GDPD provides each student feature with a distribution of task-relevant long-context knowledge, which benefits learning on the partial classification task. Extensive experiments across earliness settings, datasets, and architectures demonstrate GDPD's effectiveness for full-to-partial distillation.

Critical events in multivariate time series, from turbine failures to cardiac arrhythmias, demand accurate prediction, yet labeled data is scarce because such events are rare and costly to annotate. We introduce HEPA (Horizon-conditioned Event Predictive Architecture), built on two key principles. First, a causal Transformer encoder is pretrained via a Joint-Embedding Predictive Architecture (JEPA): a horizon-conditioned predictor learns to forecast future representations rather than future values, forcing the encoder to capture predictable temporal dynamics from unlabeled data alone. Second, we freeze the encoder and finetune only the predictor toward the target event, producing a monotonic survival cumulative distribution function (CDF) over horizons. With fixed architecture and optimiser hyperparameters across all benchmarks, HEPA handles water contamination, cyberattack detection, volatility regimes, and eight further event types across 11 domains, exceeding leading time-series architectures including PatchTST, iTransformer, MAE, and Chronos-2 on at least 10 of 14 benchmarks, with an order of magnitude fewer tuned parameters and, on lifecycle datasets, an order of magnitude less labeled data.

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While Lévy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepLévy, a neural framework that learns mixtures of Lévy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLévy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.

Time series forecasting serves as an essential tool for many real-world applications, supporting tasks such as resource optimization and decision-making. Despite significant architectural advancements, most modern models still treat forecasting task as a fixed mapping from history to target horizons. This induces temporal decoupling across future time points and limits the model's ability to adapt to the evolving context as forecasting progresses. In this work, we present LeapTS, a novel framework that reformulates time series forecasting as a dynamic scheduling process over the prediction horizon. Specifically, LeapTS organizes the forecasting process into multi-level decisions using: (1) the hierarchical controller to dynamically select the optimal prediction scale and advancement length at each step, and (2) continuous-time state evolution driven by neural controlled differential equations. Within this process, the controlled update mechanism explicitly couples the irregular temporal dynamics with discrete scheduling feedback. Extensive evaluations on both real-world and synthetic datasets demonstrate that LeapTS improves overall forecasting performance by at least 7.4% while achieving a 2.6$\times$ to 5.3$\times$ inference speedup over representative Transformer-based models. Furthermore, by explicitly tracing the scheduling trajectories, we reveal how the model autonomously adapts its forecasting behavior to capture non-stationary dynamics.

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward-backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.

Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn implicit finite-time transitions from discrete observations. When deployed autoregressively, such propagators often suffer from rapid error accumulation and dynamic drift. To address this, we propose a neural forecasting framework that reformulates PDE rollout as learning a Structured Spectral Propagator (SSP) in a propagation-oriented latent space. Following an analysis-propagation-synthesis design, our framework: (i) maps physical states into a shared, time-consistent spatial representation; (ii) projects this space into a compact propagation state to isolate recurrent dynamics from fine-grained spatial details, thereby decoupling reconstruction fidelity from rollout regularity; and (iii) evolves retained spectral modes using a frequency-conditioned linear backbone complemented by a nonlinear spectral closure to account for truncated interactions. This explicit structuring endows the propagator with a strong inductive bias for coherent modal evolution. Extensive experiments demonstrate that SSP significantly outperforms state-of-the-art baselines, reducing relative $L_2$ errors by up to 48.9% and exhibiting improved stability in temporal extrapolation beyond the supervised horizon.

Short-term air traffic flow prediction in terminal airspace is essential for proactive air traffic management. Existing approaches predominantly model traffic flow as aggregated time series. However, traffic dynamics are governed by aircraft states and their interactions in continuous airspace. Such aggregation obscures fine-grained information, including aircraft kinematics, boundary interactions, and control intent. Here we present AeroSense, a state-to-flow modeling paradigm that predicts future traffic flow directly from instantaneous airspace situations represented as dynamic sets of aircraft states derived from ADS-B trajectories. By establishing an end-to-end mapping from microscopic aircraft states to future regional traffic flow, AeroSense preserves aircraft-level dynamics while naturally accommodating varying traffic density without relying on historical look-back windows. Experiments on a large-scale real-world dataset show that AeroSense exhibits admirable predictive accuracy and robustness over aggregation-based forecasting approaches, particularly during high-density traffic periods. These findings suggest that aircraft-state situation modeling provides a promising alternative to conventional time-series forecasting in air traffic flow management.

Clinical time-series data are difficult to model with methods designed for regular sequences because they exhibit irregular sampling, frequent missing values, and heterogeneous observation patterns across variables. Existing approaches commonly use observation masks and time-gap information, but they do not continuously capture the decaying reliability of past observations or consistently organize multi-resolution information within a coherent temporal context during aggregation. To address these limitations, we propose Reliability-aware Temporal Aggregation with Mamba (ReTAMamba), which reconstructs clinical time series as time-variable token sequences, estimates observation reliability from missingness and elapsed time, and augments interval summaries with statistical descriptors. Chronological Weaving is used to integrate short- and long-term temporal information within a coherent temporal context, and a budgeted token router is applied to constrain sequence length while preserving informative summaries. Experiments on MIMIC-IV, eICU, and PhysioNet 2012 show that ReTAMamba consistently improves AUPRC over strong baselines, with average relative gains of 7.51%, 7.80%, and 10.15%, respectively. Cohort-level and patient-level analyses on eICU further showed that the learned mean decay for more dynamic signals, such as heart rate and blood pressure, was 24.3% larger than that for relatively static signals, such as laboratory test variables. These findings suggest that effective prediction in irregular clinical time series requires modeling not only what was measured, but also when and how it was observed, including information freshness and observation timeliness.

Large language models (LLMs) exhibit a strong capacity for in-context learning: Given labeled examples, they can generate good predictions without parameter updates. However, many interactive settings go beyond static prediction to online decision-making, in which effective behavior demands adaptation over long multi-turn horizons in response to feedback, and efficient algorithms in these domains must use compact representations of what they have learned. Recently, continuous transformer architectures with latent chain of thought have shown promise for offline iterative tasks such as directed graph-reachability. Motivated by this, we study whether continuous latent context tokens equip transformers to more effectively realize online learning. We give explicit constructions of constant-depth transformers that implement two foundational online decision-making procedures -- the weighted majority algorithm and $Q$-learning -- by storing their algorithmic state as linear combinations of feature embeddings, using a small number of latent context tokens. We further train a small GPT-2-style transformer with latent contexts using a multi-curriculum objective that does not directly supervise the latent states. On long synthetic online prediction sequences, this model outperforms larger and more complex LLMs, including Qwen-3-14B and DeepSeek-V3. Our results suggest that continuous latent contexts provide a simple and effective persistent state for transformers to implement online learning algorithms.

While machine learning has revolutionized many fields such as natural language processing (NLP) and computer vision, its impact on time-series forecasting is still widely disputed, especially in the finance domain. This paper compares forecasting performance on U.S. Treasury yield curve data across econometrics/time-series analysis, classical machine learning, and deep learning methods, using daily data over 47 years. The Treasury yield curve is important because it is widely used by every participant in the bond markets, which are larger than equity markets. We examine a variety of methods that have not been tested on yield curve forecasting, especially deep learning algorithms. The algorithms include the Autoregressive Integrated Moving Average (ARIMA) model and its extensions, naive benchmarks, ensemble methods, Recurrent Neural Networks (RNNs), and multiple transformers built for forecasting. ARIMA and naive econometric models outperform other models overall, except in one time block. Of the machine learning methods, TimeGPT, LGBM and RNNs perform the best. Furthermore, the paper explores whether stationary or nonstationary data are more appropriate as input to deep learning models.

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step $\TildeΔ$ a learned function of the input. However, in doing so, $\TildeΔ$ ceases to represent a physical sampling interval, limiting its irregular time series modeling capability. Continuous-time SSMs, such as S5, preserve the physical meaning of $\TildeΔ$ and handle irregular timestamps natively ($\TildeΔ\equivΔ)$, but their dynamics remain linear time-invariant (LTI), limiting per-token expressivity. We propose \textbf{TIDES}, a selective SSM variant that reconciles selective and continuous architectures by moving input-dependence off the step size and onto the diagonal state matrix. As a result, $\TildeΔ$ retains its physical meaning, tied to the state discretization, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel \emph{Fading Flash} experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input-dependence and extrapolation to out-of-distribution $Δ$ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new state-of-the-art average rank on UEA time-series classification and the Physiome-ODE regression benchmark. Code available at: https://github.com/TaylanSoydan/TIDES.

Spatio-temporal graph neural networks (STGNNs) are widely used for short-term forecasting in dynamic physical systems such as traffic and weather. However, the prevailing evaluation practice uses real world benchmark data sets in a single domain with a single fixed holdout splits, making it difficult to compare architectures across different dynamical regimes. We introduce ChaosNetBench (CNB), a synthetic benchmark dataset and evaluation framework for studying STGNN performance under controlled multidimensional chaotic dynamics. CNB is built on a lattice of coupled standard maps with independently tunable local chaos ($K$), coupling strength ($\varepsilon$), and system size ($N$), providing known topology and known dynamics across 96 system instances and 9{,}600 trajectories. We introduce chaos indicators, evaluation metrics and a protocol to analyze and compare the capacity of STGNN architectures to deal with different levels of local and global chaos. We illustrate the usage of the framework by analyzing 13 architectures (5 STGNNs and 8 non-graph baselines). The results reveal a regime dependent transition in which non-graph baselines (TCN, N-BEATS, iTransformer) remain competitive when there is low local chaos, while STGNNs (e.g., Graph WaveNet, D2STGNN, STAEformer) are generally more resilient to higher levels of local and global chaos. CNB provides a practical, reusable testbed for systematically comparing and analyzing the capacity of STGNN architectures to handle different levels of local and global chaos.

In this paper, we propose the first VL$\underline{\textbf{M}}$ $\underline{\textbf{a}}$gentic $\underline{\textbf{r}}$easoning framework for few-$\underline{\textbf{s}}$hot multimodal $\underline{\textbf{T}}$ime $\underline{\textbf{S}}$eries $\underline{\textbf{C}}$lassification ($\textbf{MarsTSC}$), which introduces a self-evolving knowledge bank as a dynamic context iteratively refined via reflective agentic reasoning. The framework comprises three collaborative roles: i) Generator conducts reliable classification via reasoning; ii) Reflector diagnoses the root causes of reasoning errors to yield discriminative insights targeting the temporal features overlooked by Generator; iii) Modifier applies verified updates to the knowledge bank to prevent context collapse. We further introduce a test-time update strategy to enable cautious, continuous knowledge bank refinement to mitigate few-shot bias and distribution shift. Extensive experiments across 12 mainstream time series benchmarks demonstrate that $\textbf{MarsTSC}$ delivers substantial and consistent performance gains across 6 VLM backbones, outperforming both classical and foundation model-based time series baselines under few-shot conditions, while producing interpretable rationales that ground each classification decision in human-readable feature evidence.

Large vision models (LVMs) have recently proven to be surprisingly effective time series forecasters, simply by rendering temporal data as images. This success, how ever, rests on a largely unexamined premise: the rendered time series images are sufficiently close to natural images for knowledge in pre-trained models to transfer effectively. We argue that two gaps still remain, i.e., spectral and structural gaps, fundamentally limiting the potential of LVMs for time series forecasting. Spectrally, we systematically reveal that rendered time series images exhibit a markedly shallower power spectrum than the natural images LVMs are pre-trained to recognize. Structurally, reshaping 1D temporal sequences into 2D grids fabricates spurious spatial adjacencies while severing genuine temporal continuities, misleading the spatial inductive biases of pre-trained LVMs. To bridge these gaps, we propose SSDA, a dual-branch network that spectrally and structurally adapts to unlock the full potential of LVMs for time series forecasting. At the data level, a Spectral Magnitude Aligner (SMA) applies 2D FFT to selectively enhance the magnitude spectrum toward natural-image statistics while preserving phase. At the model level, a Structural-Guided Low-Rank Adaptation (SG-LoRA) injects position-aware temporal encodings into patch embeddings and adapts at tention via low-rank updates. The two branches are further adaptively fused to produce the final forecast. Extensive experiments on seven real-world benchmarks demonstrate that SSDA consistently outperforms strong LVM- and LLM-based baselines under both full-shot and few-shot settings. Code is publicly available at https://anonymous.4open.science/r/SSDA-8C5B.

Although many complex models were proposed to analyze time series data, some studies have demonstrated remarkable performance with simpler structures. A recent study proposed a non-parametric framework for 3D point cloud classification, which has the potential to be adapted for time series forecasting and enable interpretability. Inspired by the previous works, we present TSNN, a non-parametric and interpretable framework for traffic time series forecasting. TSNN consists of multiple layers that decouple the time series by matching the entries in a memory bank, where the memory bank is constructed using a similar matching process within the training set. It leverages the periodicity in traffic data to enhance forecasting accuracy while maintaining a simple model architecture. The proposed model operates without trainable parameters, preserving its inherent interpretability. In the experiments, TSNN achieves competitive performance compared to the typical deep learning models in four real-world traffic flow datasets. We also visualize the decoupling process to show the effectiveness of the components. Finally, we demonstrate the interpretability of the model and illustrate the contribution of each time step within the memory bank.

Wearable sensors enable the continuous acquisition of high-resolution physiological waveforms, such as photoplethysmography and accelerometry, under free-living conditions. However, inferring health-related phenotypes from these signals presents significant challenges due to high sampling frequencies, multimodal dependencies, and extreme sequence lengths (e.g., weeks of recordings), compounded by a scarcity of ground-truth labels. To address these challenges, existing self-supervised learning (SSL) methodologies typically follow two paradigms: (1) learning rich morphological representations from short waveform segments while collapsing longitudinal dynamics through simple aggregation, or (2) modeling behavioral patterns from coarse, hand-crafted features (e.g. heart rate, step counts) spanning longer horizons but foregoing subtle, predictive signatures in raw waveforms. To bridge this gap, we propose WavesFM, a foundation model utilizing a two-stage SSL framework for longitudinal physiological data. Specifically, we decompose the learning problem into two stages: first, a segment-level encoder is pretrained to extract local embeddings from short waveforms; subsequently, a temporal encoder is trained to model the sequence of these embeddings across a multi-day horizon. This hierarchical approach overcomes the computational complexity of high-resolution, long-sequence data, allowing the overall model to capture both local signal semantics and the complex circadian and inter-day variations governing physiological dynamics. Pretrained on over 6.8M hours (N=324k individuals) of recordings for the first stage and 5.3M hours (N=10k) for the second stage, WavesFM demonstrates superior performance across 58 diverse tasks spanning demographics, lifestyle, health conditions, and medications.

We introduce the first universal pretraining corpus for industrial time-series data: FactoryNet. 51M datapoints across 23k end-to-end task executions (13.3k real, 9.8k synthetic) on six embodiments, unified by a shared schema that enables robust zero-shot cross-embodiment transfer and highly parameter-efficient anomaly detection. We introduce a novel schema: Setpoint, Effort, Feedback, Context (S-E-F-C) underlying the whole pipeline that maps any actuated system into a common representational frame. The corpus spans 27 annotated anomaly types alongside healthy baselines and counterfactual pairs across robotic manipulation and machining domains. Cross-embodiment transfer experiments yield positive results: under bias-aware metrics our model demonstrates fair cross-embodiment transfer capabilities on the evaluated source-target pair, while 24 schema-aligned signals achieves competitive anomaly detection performance compared to high-dimensional baselines. We release FactoryNet as a growing, multi-embodiment dataset to drive progress toward industrial foundation models.

Reliable short horizon forecasting of solar and wind generation is a structural prerequisite of any modern power system yet most published forecasters are tuned and evaluated on a single climatic regime and most algorithmic novelty has been concentrated either on classical recurrent networks or on monolithic foundation models that combine forecasting and explanation We develop a four stage hybrid framework that separates these concerns The first stage acquires hourly generation irradiance and surface weather records through public application programming interfaces The second stage trains three classical baselines autoregressive integrated moving average gradient boosted regression trees and a two layer long short term memory network and produces a strong point forecast together with a residual error series The third stage corrects the residual through a quantum inspired variational kernel built on a six qubit hardware efficient ansatz with three repeated entangling layers The fourth stage uses generative artificial intelligence strictly as an explainability layer that reads the measured benchmark numbers and produces a structured natural language interpretation Across three regions drawn from open public archives Iberian solar North Sea wind and a mixed Texas trace the proposed configuration stays within one percentage point of the strongest classical baseline on the in domain forecasting task and the quantum inspired kernel separates calm and stormy weather regimes with a Fisher discriminant ratio approximately fifteen fold higher than a tuned radial basis kernel

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

This paper introduces a framework specifically designed for sparse and irregular time series {risk estimation}. It is based on a Transformer Autoencoder with local attention, which leverages the powerful pattern identification capabilities of transformers complemented by traditional data cleaning and normalization methods. It efficiently captures relevant patterns within irregular sequences suffering from sparse data collection, benefiting from the discriminative ability of the local attention mechanism. The proposed framework is applied to a real-world case study, on the risk estimation of non-technical losses in electrical power systems in a wide area in Greece. Non-technical losses in electrical power systems, primarily stemming from electricity theft, pose significant economic and operational challenges. Detecting these anomalies is particularly challenging due to the inherent sparse and irregular nature of real-world data collection practices. Traditional risk estimation methods struggle with effectively capturing long-range dependencies and robustly handling such data characteristics. We demonstrate that our approach effectively yields highly discriminative latent features, which results in more consistent risk estimation compared with existing state-of-the-art and widely used methods. It achieves high recall and precision, meeting the critical objectives of the problem. As such, our solution offers a robust and effective tool for risk detection in irregular time series datasets.

Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.

We propose a new class of waveform foundation models that departs from conventional sequence based representations by modeling physiological time series as realizations of latent event processes. Rather than treating signals as collections of local tokens or patches, our approach assumes that clinically meaningful structure arises from temporally extended, interacting events whose boundaries and dynamics are not directly observed. To capture this structure, we introduce a self supervised learning framework that enforces consistency across stochastic segmentations and time frequency projections of the same waveform, encouraging representations that are invariant to signal level perturbations while preserving event level organization. The resulting model combines a segmentation aware encoder with a latent interaction operator that captures dependencies among inferred events, and naturally extends to multimodal settings by aligning modalities through shared event representations. Across a range of physiological benchmarks, including arrhythmia classification, hemodynamic prediction, and waveform retrieval, the proposed method improves performance, robustness, and label efficiency relative to strong sequence based baselines. These results suggest that shifting from signal centric to event centric representations provides a more appropriate inductive bias for modeling physiological dynamics and offers a complementary path to scaling foundation models in healthcare.

Large Language Models (LLMs) are increasingly applied to forecasting. To evaluate this capability while mitigating pre-training data contamination, several living benchmarks have been proposed. However, existing benchmarks either lack the multidimensional events essential for accurate forecasting due to data scarcity, or focus on relatively closed environments. To assess the predictive capabilities of LLMs in complex, real-world scenarios, we propose LEAF, the first living benchmark for event-augmented forecasting tasks, including future event probabilities, trend and time series forecasting. LEAF utilizes a recursive retrieval agent system paired with dual-agent cross-validation to provide comprehensive and relevant auxiliary text for forecasting. Evaluating state-of-the-art proprietary and open-weight LLMs, we find that these models can leverage signals extracted from complex events to enhance predictive performance. In the stock domain, we find that LLMs achieve better performance on equities they confidently identify as more predictable. Furthermore, the events demonstrate a strong correlation with the target equities. To this end, LEAF provides a necessary, dynamically updating testbed to continuously track and drive progress in event-driven forecasting tasks.

Time Series Foundation Models (TSFMs) excel at numerical forecasting but operate as black boxes lacking qualitative reasoning. Conversely, applying LLMs directly to temporal data introduces a modality gap: text tokenizers fragment continuous numerical values, degrading mathematical relationships and exploding sequence lengths, leading to computational overhead. To resolve this, we introduce STRIDE (Strategic Time-series Reasoning Injected via Distilled Embeddings), a novel framework natively integrating LLM reasoning into the continuous embedding space of TSFMs. Instead of discrete tokens, STRIDE distills reasoning traces into a lightweight LLM, dynamically projecting its mean-pooled hidden states as a cross-modal prior into the target numerical encoder. The architecture is jointly optimized using cross-entropy and quantile losses. Evaluations demonstrate STRIDE establishes state-of-the-art numerical forecasting on GIFT-Eval (0.674 MASE, 0.454 CRPS) compared to TSFMs and exhibits superior in-domain and out-of-domain numerical as well as reasoning performance on TFRBench. Specifically, STRIDE acts as a plug-and-play enhancement, consistently improving diverse TSFMs (e.g., Chronos-2, Timer-S1) across various LLM configurations. Thus, injecting semantic reasoning as a continuous prior equips TSFMs with human-interpretable reasoning while fundamentally improving predictive accuracy.

Using Chronos-2, an open-source time-series foundation model, we evaluate pretrained time-series models for economic and financial forecasting with an emphasis on whether multivariate (MV) inputs improve accuracy relative to univariate (UV) baselines. The study covers two panels -- the Magnificent-7 equities and U.S. Treasury interest rates -- as well as a combined panel, using rolling monthly evaluations from 2000--2025. We vary input window lengths and forecast horizons and report RMSE and MAPE. Across datasets, MV forecasts consistently outperform UV forecasts, with especially strong gains for interest rates and meaningful improvements for equities. Series-level comparisons show MV improvements in every case, and error dispersion is generally lower under MV inputs. We also provide parameter-heatmap and time-series visualizations. However, mixing time series across equity and interest rate markets reduces forecast accuracy, indicating that adding noisy context degrades model performance. Overall, the results indicate that foundation models can leverage cross-series information to improve forecast accuracy in finance, and that the benefits are strongest when related series are modeled jointly under disciplined rolling protocols. Other than using an open-source foundation model, this paper also showcases how AI may be used for financial research.

Test-Time Adaptation (TTA) aims to improve time series forecasting under distribution shifts by using limited observations revealed during inference. However, forecasting TTA must operate in a source-free online setting, where the adaptation signal is short, temporally correlated, and potentially noisy. Existing methods can therefore suffer from weak identifiability, error accumulation, and unstable long-horizon corrections when the revealed prefix is sparse or contaminated. To address these issues, we propose STEPS, a Smooth Temporal Error Propagation Solver for TTA in time-series forecasting. STEPS reformulates forecasting TTA as a Dirichlet Boundary Value Problem on a temporal manifold, where the revealed prefix error serves as the boundary condition for the unknown future error field. Then, STEPS solves a smooth and bounded correction field in prediction space: a Local Solver propagates prefix errors under temporal smoothness, a Global Solver retrieves stable cross-window error memory and Spatiotemporal Manifold Fusion (SMF) integrates both solutions into the final correction. Across six standard benchmarks and four frozen backbones, STEPS achieves an average relative MSE reduction of 26.82% over the zero-shot backbone, exceeding the strongest compared TTA baseline by 12.77%. Additional sparse prefix and contamination tests confirm the robustness of STEPS under limited and noisy prefixes.

Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex optimization landscapes and overfitting risks, particularly in regression. Recent advances have introduced differentiable formulations that enable gradient-based training and joint optimization of decision boundaries and leaf regressors. Yet, existing approaches typically rely on approximations, either through probabilistic softening of boundaries (soft DTs) or quantized gradients such as the Straight-Through Estimator (STE). To overcome these limitations, we propose DTSemNet, a novel, semantically equivalent, and invertible representation of hard oblique DTs as neural networks. DTSemNet enables end-to-end training with standard gradient descent, eliminating the need for approximations in both classification and regression. While classification aligns naturally with this formulation, regression remains challenging due to the joint optimization of internal nodes and leaf regressors. To address this, we analyze the limitations of STE and introduce an annealed Top-k method that provides accurate gradient signals without approximation. Extensive experiments on classification and regression benchmarks show that DTSemNet-trained oblique DTs outperform state-of-the-art differentiable DTs. Furthermore, we demonstrate that DTSemNet can serve as programmatic DT policies in reinforcement learning environments, thereby broadening their applicability.

Time-series anomaly detection is critical for ensuring safety in high-stakes applications, where robustness is a fundamental requirement rather than a mere performance metric. Addressing the vulnerability of these systems to adversarial manipulation is therefore essential. Existing defenses are largely heuristic or provide certified robustness only under $\ell_p$-norm constraints, which are incompatible with time-series data. In particular, $\ell_p$-norm fails to capture the intrinsic temporal structure in time series, causing small temporal distortions to significantly alter the $\ell_p$-norm measures. Instead, the similarity metric \emph{Dynamic Time Warping} (DTW) is more suitable and widely adopted in the time-series domain, as DTW accounts for temporal alignment and remains robust to temporal variations. To date, however, there has been no certifiable robustness result in this metric that provides guarantees. In this work, we introduce the first \emph{DTW-certified robust defense} in time-series anomaly detection by adapting the randomized smoothing paradigm. We develop this certificate by bridging the $\ell_p$-norm to DTW distance through a lower-bound transformation. Extensive experiments across various datasets and models validate the effectiveness and practicality of our theoretical approach. Results demonstrate significantly improved performance, e.g., up to 18.7% in F1-score under DTW-based adversarial attacks compared to traditional certified models.

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 ($71.4\%$) evaluated experimental setups for MSE.

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from "more interaction" to "more effective interaction".

A latent world model may achieve accurate short-horizon prediction while still inducing a latent space that is poorly aligned with planning. A key issue is spatiotemporal mismatch: these models are often trained with local predictive supervision, but deployed for long-horizon goal-directed search in latent spaces where Euclidean distance may not reflect what is reachable within a finite action budget. We present the Reachability-Correction auxiliary objective (RC-aux), a lightweight correction for this mismatch in reconstruction-free latent world models. RC-aux keeps the world-model backbone unchanged and adds planning-aligned supervision along two axes. Along the time axis, multi-horizon open-loop prediction trains the model beyond one-step consistency. Along the space axis, budget-conditioned reachability supervision, together with temporal hard negatives, encourages the latent space to distinguish states that are eventually reachable from those reachable within the current planning horizon. At test time, the learned reachability signal can also be used by a reachability-aware planner to favor trajectories that are both goal-directed and attainable under the available budget. We instantiate RC-aux on LeWorldModel and evaluate it under both continuation-training and matched-from-scratch settings. Across goal-conditioned pixel-control tasks and a LIBERO-Goal extension, RC-aux improves LeWM-style planning with modest additional cost. These results suggest that planning with latent world models depends not only on predictive accuracy, but also on whether the learned representation encodes the temporal and geometric structure required by downstream search. The code is available at https://github.com/Guang000/RC-aux.

Scientific foundation models are expected to reuse representations under changes in dataset, acquisition protocol, and deployment domain, yet many sequence backbones treat scientific temporal structure as an unconstrained pattern to be fitted. We argue that this misses a central property of natural dynamical systems: neural and atmospheric time series are organized by interacting processes across multiple physical timescales, and failure to preserve this multiscale structure contributes to brittleness under distribution shift. We formalize this failure mode as temporal kernel mismatch, where a model fits in-distribution dynamics with an effective memory policy that is not anchored to the signal's physical timescales, leading to representation drift and degraded transfer. We propose Physics-Informed Multi-Scale Mamba (PIMSM), a state-space architecture that maps spectrum-estimated transition points between frequency regimes (knee frequencies) to scale-specific discretization parameters and anchors them to acquisition time units. On Human Connectome Project fMRI, PIMSM improves robustness and representation stability under severe temporal-context truncation, extreme low-resource transfer, and resting-state-to-task-state generalization. Without modality-specific adaptation, the same architecture also attains the lowest variable-wise MAE across all reported horizons and variables on Weather-5K held-out-station spatial out-of-distribution forecasting. These results support temporal-scale alignment as a practical inductive bias for scientific foundation models that must preserve structure, not only fit correlations, under deployment shift.

How few parameters do we really need to forecast a periodic time series? An hourly electricity series, reshaped as a 24-row matrix with one column per day, is approximately rank-1: a daily shape modulated by a daily level (median centered rank-1 energy 0.82 on GIFT-Eval). Should we learn the shape? Smoothing, shrinkage, and low-rank fits all seem like obvious upgrades over the simple average of the last K=2 cycles. On all 97 GIFT-Eval configurations, we tested 8 such alternatives (e.g., Fourier, EWMA, James-Stein, rank-r SVD): none significantly beats the frozen baseline under Holm correction; two are significantly worse. The resulting method, FLAIR, is (a) Effective: matches PatchTST on aggregate GIFT-Eval (relMASE 0.838 vs 0.849); (b) Compact: 28 scalars for hourly, 57 for weekly; (c) Fast: 22 minutes on one CPU core of a MacBook Pro; (d) Closed-form & Hands-Off: one SVD per period candidate, GCV-averaged Ridge, no GPU, no pre-training, no per-task tuning. In the high-rank-1, many-cycle regime, extra flexibility is estimation noise.

In time-series domains where both predictive performance and interpretability are essential, deep neural networks achieve strong results but provide limited insight into how their predictions are made. Projection-based prototype networks address this limitation by grounding predictions in similarity to representative training examples, enabling case-based explanations and global prototype inspection. However, existing approaches rely on label supervision, tying prototypes to a specific task and requiring large labeled datasets. We introduce ProtoSSL, a novel framework for learning interpretable, projection-based prototypes from unlabeled time-series data and adapting them to downstream tasks. Our key idea is to separate motif discovery from label alignment. ProtoSSL first learns a reusable prototype bank using a self-supervised objective applied directly to prototype activations, and then aligns these prototypes to downstream tasks through an efficient assignment procedure. Across six electrocardiography (ECG) datasets, ProtoSSL improves label efficiency, outperforming supervised prototype baselines in low-data regimes with as few as 256 labeled examples; with fine-tuning, ProtoSSL outperforms supervised prototype baselines at full dataset scale. In a human evaluation study, ProtoSSL produces prototypes and prototype-based explanations that are judged more favorably than those learned with direct label supervision. We further show that the framework extends to audio classification. Thus, ProtoSSL enables both learning generalizable prototypes from unlabeled data before the downstream label space is known, and subsequent assignment of interpretable, projection-grounded prototypes to new time-series tasks.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol, a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7% relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. Moreover, MELO requires only lightweight per-step recursive updates without model retraining.

This paper presents a preliminary analysis of the ability of Chronos foundation model to process and internally represent frequency domain information. Foundation models that process time-series data offer practitioners a unified architecture capable of learning generic temporal representations across diverse tasks and domains, reducing the need for task-specific feature engineering and enabling transfer across signal modalities. Despite their growing adoption, the extent to which such models encode fundamental signal properties remains insufficiently characterised. We address this gap by analysing Chronos under controlled conditions, starting from the simplest class of signals: discrete sinusoids generated at fixed frequencies. Using lightweight online minimum description length probes applied to the decoder architecture, we test for the presence and separability of frequency information in the model's internal representations. The results provide insight into how frequential content is captured across the frequency spectrum and highlight regimes in which representation quality may degrade or require particular care. These findings offer practical guidance for users of Chronos in signal processing and information fusion contexts, and contribute to ongoing efforts to improve the interpretability and evaluation of foundation models for temporal data.

Synthetic data has transformed language model training, yet its role in time series forecasting remains poorly understood. We present a large-scale empirical study: nine experiment groups, 4,218 runs systematically evaluating synthetic time series augmentation across five architectures, four synthetic signals and seven datasets. The effect is sharply architecture-conditional: channel-mixing models (TimesNet, iTransformer) benefit in the majority of trials, while channel-independent models (DLinear, PatchTST) are consistently degraded. In selected low-resource settings the gains are striking: TimesNet trained on only 10% of Weather data with synthetic augmentation surpasses the full-data baseline (4 of 16 sparsity-dataset combinations). Averaged across all architectures, augmentation hurts in 67% of trials. We further find that only the Seasonal-Trend generator reliably helps across the tested benchmarks, and that hard curriculum switching is actively harmful (+24% MSE degradation). These results provide concrete, actionable guidelines on how to use synthetic data: use synthetic augmentation with channel-mixing architectures, use gradual annealing schedules, and treat low-resource augmentation as architecture- and dataset-dependent. Code is available at \href{https://github.com/hugoiscracked/synthetic-ts/tree/main}

Recent studies have explored large language models for time-series anomaly detection, yet existing approaches often rely on a single general-purpose model to directly infer anomaly indices or intervals, limiting controllability, interpretability, and reliability for complex anomaly patterns. We propose SAGE (Specialized Analyzer Group for Expert-like Detection), a multi-agent framework for structured anomaly diagnosis in univariate time series. It decomposes anomaly analysis into four specialized Analyzers for point, structural, seasonal, and pattern anomalies. Each Analyzer applies family-specific numerical tools and diagnostic visualizations to generate evidence, while an evidence-grounded Detector consolidates the evidence into confidence-scored anomaly records with intervals and candidate types. A Supervisor then converts these structured records into analyst-facing diagnostic reports. SAGE further constructs synthetic in-context examples from normal-reference training segments, without using real anomalous segments or anomaly-type labels as in-context examples. Across three benchmarks, SAGE achieves the best average performance among strong ML/DL and language-model-based baselines. Ablation studies and human evaluation further show that the proposed framework improves detection reliability and the practical usefulness of diagnostic outputs.

Structured state space models (SSMs) have recently emerged as a promising foundation for sequence modeling, with Mamba-based architectures demonstrating strong performance through input-dependent state transitions, albeit at considerable complexity. However, their application to time-series classification (TSC) has been largely limited to Mamba-style architectures, leaving the broader SSM design space underexplored. We present the first systematic study spanning diagonal SSMs (S4D) and input-dependent SSMs (Mamba family) on large-scale TSC benchmarks, asking whether such complexity is necessary for top performance. Our results reveal a surprising finding: S4D consistently outperforms Mamba-based variants in both accuracy and efficiency, challenging the assumption that increased complexity translates to meaningful gains in TSC. Building on this, we introduce MS4, lightweight modifications to S4D via a linear input projection and channel-mixing mechanism, and MS4N, a normalized variant that stabilizes state dynamics with negligible overhead. Evaluated on 59 datasets across MONSTER (up to 60 million samples, 50K timesteps, 82 classes) and the UEA benchmark, against 15 baselines, MS4 and MS4N consistently outperform Mamba-based models while remaining more efficient, and MS4N matches or surpasses competing deep learning models that are roughly 2x and 10x larger in parameters. These results position lightweight structured SSMs as a compelling alternative to scaling complexity for TSC.

Causal representation learning (CRL) seeks to recover latent variables with identifiability guarantees, typically up to permutation and component-wise reparameterization under appropriate assumptions. However, identifiability does not imply interpretability: latent semantics are typically assigned post hoc by alignment with known ground-truth factors. This limitation is particularly acute in scientific time series, where underlying mechanisms are unknown and discovering interpretable structure is a primary goal. In contrast, scientific observations (such as residue-pair distances, climate indices, or process sensors) are inherently semantic, as they correspond to named physical quantities. This raises a key question: can the interpretability of observations be transferred to the identifiable latent space? We propose MOSAIC (Module discovery via Sparse Additive Identifiable Causal learning), a sparse temporal VAE that integrates temporal CRL identifiability with support recovery over observed variables. MOSAIC identifies latent variables via regime-conditioned temporal variation, and recovers for each latent a sparse set of associated observations through an additive decoder, yielding module-level interpretability. We show that ANOVA main-effect supports are identifiable under general smooth mixing functions, and provide finite-sample recovery guarantees for a tractable sparse-additive variant. Empirically, MOSAIC recovers domain-consistent variable groups across RNA molecular dynamics, solar wind, ENSO climate, the Tennessee Eastman process, and a synthetic tokamak benchmark, enabling interpretable discovery of latent mechanisms in scientific time series.

Safe L2/L3 driving automation requires anticipating human-in-the-loop reactions during shared-control transitions. While most driving world models forecast the external environment, in-cabin intelligence remains strictly recognition-oriented and lacks multi-step rollout capabilities for driver dynamics. We introduce Driver-WM, a driver-centric latent world model that rolls out in-cabin dynamics causally conditioned on out-cabin traffic context. This formulation unifies physical kinematics forecasting with auxiliary behavioral and emotional semantic recognition. Operating in a compact latent space constructed from frozen vision-language features, Driver-WM adopts a dual-stream architecture to separately encode external traffic and internal driver states. These streams are directionally coupled via a gated causal injection mechanism, which uses a learned vector gate to modulate external contextual perturbations while strictly enforcing temporal causality. Experiments on AIDE show robust long-horizon forecasting on reactive high-motion clips, improved driver/traffic semantic alignment, and controlled interventions that expose the external-to-internal mechanism.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named Spectral Graph Conditional Exchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose Spectral Conformal prediction via wAveLEt transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world traffic datasets show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.

Accurate trend forecasting in healthcare time series is essential for planning and resource allocation. This paper proposes a Bayesian framework for predicting oncology demand trends, modeling weekly appointments as a Poisson process with a Gamma prior to the demand rate. To enhance adaptability and capture persistent directional patterns, we incorporate a residual-based boosting mechanism grounded in a Gamma-Log-Normal conjugate structure. This boosting approach allows the model to track both short- and long-term trend shifts while maintaining the analytical tractability of conjugate Bayesian updating. The methodology was evaluated on real oncology service data from Cariri, Ceara, Brazil, and compared against established baselines, including linear regression, ARIMA, naive forecasting, LSTM neural networks, and XGBoost. Results showed that the proposed model outperforms competing methods in trend detection accuracy, with gains in terms of percentage of correct direction of 38.25% in relation to the second best approach in some cases.

Time Series Foundation Models (TSFMs) have borrowed the long context paradigm from natural language processing under the premise that feeding more history into the model improves forecast quality. But in stochastic domains, distant history is often just high-frequency noise, not signal. Hence, the proposed work tests whether this premise actually holds by running continuous context architectures (PatchTST included) through the ETTh1 benchmark. The obtained results contradict the premise: an inverse scaling law shows up clearly, with forecasting error rising as context gets longer. A 3,000-step window causes performance to drop by over 68%, evidence that attention mechanisms are poor at ignoring irrelevant historical volatility. Retrieval-Augmented Forecasting (RAFT) is evaluated as an alternative. RAFT achieves a mean squared error (MSE) of 0.379 with a fixed 720-step window and selective retrieval, outperforming both long-context configurations and zero-shot foundation models (Chronos, Moirai) despite requiring far less computation. In addition, the retrieval step injects only the most relevant historical segments as dynamic exogenous variables, which gives the model a context-informed inductive bias it cannot build on its own from raw sequences. Therefore, foundation models going forward need to shift architecturally toward selective retrieval.

Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit, theoretically grounded rules for system evolution, their empirical estimation collapses due to severe data sparsity when applied to high-resolution, high-noise environments. We explore this statistical barrier using financial time series as a canonical, real-world testbed. To overcome the degeneracy of empirical counting, we introduce a framework that utilizes neural networks strictly as parameterization engines to generate explicit, time-varying Markov transition matrices. By constraining the neural network to output its predictions as a formal stochastic operator, we maintain complete structural interpretability. We demonstrate that these learned operators successfully capture complex regime shifts: the state-conditioned model achieves mean row heterogeneity $\barρ = 0.0073$ while the state-free ablation collapses to exactly zero, and operator row entropy correlates with realized variance at $r = -0.62$ ($p \approx 10^{-251}$), revealing that high-volatility regimes homogenize transition dynamics rather than diversify them. Furthermore, rather than enforcing the Chapman-Kolmogorov equations as a rigid structural requirement, we repurpose them as a localized diagnostic tool to pinpoint specific temporal windows where first-order memory assumptions break down. Ultimately, this framework demonstrates how neural networks can be constrained to make rigorous, classical operator analysis viable for complex real-world time series.

Accurate early warning of vineyard disease risk from environmental observations is essential for timely intervention and more sustainable crop protection. However, many existing studies formulate disease prediction as daily presence classification, which can favor persistence-driven predictions and provide only limited support for actionable short-horizon warning. In this paper, we present an event-based approach for early warning of vineyard disease risk from environmental time series and evaluate it through a vineyard case study. Rather than predicting daily disease status, the task is reformulated to predict transitions into annotated disease-risk periods within a future window of 3-7 days. To reduce fragmentation caused by short interruptions in the binary labels, new events are defined only after a minimum disease-free gap. This formulation encourages models to capture environmental precursors associated with upcoming risk periods instead of merely reproducing temporal persistence. Using multi-year agro-meteorological data, we construct input representations that capture humidity dynamics, rainfall accumulation, temperature variability, and seasonal structure through cyclic temporal encoding. We evaluate representative methods from classical machine learning and deep learning, including XGBoost, Long Short-Term Memory (LSTM) networks, and Temporal Convolutional Networks (TCNs), using both standard classification metrics and an event-oriented early warning protocol. The results show that the event-based formulation supports practical short-horizon warning, while the compared models exhibit distinct trade-offs between event recall, lead time, and false-alert behavior. Overall, the study underscores the importance of problem formulation in environmental time-series learning and demonstrates the value of event-based prediction for vineyard disease warning systems.