Time Series

World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that must query the same dynamics at multiple timescales. Hamiltonian Generative Networks (HGN) offer a principled path forward, grounding predictions in a continuous-time energy function that is, in principle, independent of the observation frame rate. In practice, however, their temporal generalization breaks down in non-conservative settings. We show that in externally forced, dissipative environments, HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes, including latent magnitude growth driven by an unconstrained action-force map, and global truncation error accumulation from an under-resolved integrator. We identify a targeted fix for each mechanism and demonstrate stable dynamics prediction at temporal resolutions well outside the training distribution. In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.

Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.

In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.

We introduce a new context-enriched, multimodal time series forecasting benchmark, TimesX. TimesX contains a wide selection of high-quality real-world time series with diverse domains and textual contexts obtained from an automated data generation pipeline, which helps address three main issues of existing multimodal forecasting benchmarks: (1) poor generalization due to the small scale and synthetic nature of benchmark data, (2) very limited types of textual contexts in the benchmarks, and (3) an inability to mitigate data leakage in evaluation. We conduct a thorough empirical study of zero-shot multimodal forecasting approaches on TimesX. Our results suggest that many approaches that perform well on existing benchmarks may fail on TimesX. In contrast, simple ensemble methods that leverage rich textual context accompanying time-series can outperform strong baselines on TimesX.

Deep learning has achieved remarkable success in various domains including time series analysis, computer vision and natural language processing. However, high computational and memory demands of state-of-the-art architectures pose challenges for deployment in resource-limited environments. Knowledge Distillation (KD) addresses this by transferring knowledge from a large teacher model to a smaller, more efficient student model while maintaining competitive performance. In this work, we investigate the effectiveness of KD for Time Series Classification (TSC) across three architectures: the classical Fully Convolutional Network (FCN), the convolutional Inception model and the transformer-based ConvTran model. We evaluate our approach on UCR Archive, the largest benchmark repository of time series datasets, by modifying architectural components such as convolutional filters, Inception modules and attention heads across the three architectures. Our results consistently show that KD most effectively benefits student models of intermediate complexity across all three architectures, with the distilled FCN student reducing parameters by a factor of 38, the distilled Inception student achieving nearly the same performance as the teacher with 42% fewer parameters and the distilled ConvTran student with 2 attention heads showing the most significant improvement through distillation. To encourage further research and reproducibility, we provide our implementation at https://github.com/MSD-IRIMAS/KD-4-TSC.

Finance, sensing, and demand streams violate the exchangeability that IID conformal prediction and the IID bootstrap assume, and existing libraries implement either a general resampling engine or conformal calibration without the other. tsbootstrap provides block, residual, sieve, and wild resampling, classical bootstrap confidence intervals, and adaptive conformal calibrators (EnbPI, ACI, NexCP, AgACI) through a single typed API in which a specification object selects each method. In a controlled coverage study the IID bootstrap undercovers sharply under dependence; dependence-aware methods reduce the coverage deficit, the sieve nearest to nominal under short-memory linear dependence. On the shared fixed-statistic path a compiled backend runs several times faster than arch, and a streaming reduce avoids materializing the $O(Bn)$ replicate tensor, limiting peak extra memory to $O(B)$ for the statistic array. The software is MIT licensed (v0.6.1).

Rough path signatures are a universal feature map for continuous paths and, via the expected signature, characterise path distributions. These guarantees do not directly extend to cadlag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore, neural TPP models, including recent generative approaches, optimise per-event objectives with no global sequence-level loss, while evaluation of variable-length event sequences lacks distributional discrepancy measures. This paper proposes a common pathwise framework for addressing these limitations. We introduce the interarrival embedding, a stable, injective lift from jump paths to continuous paths of bounded variation, extending signature methods to discrete event sequences. Our theoretical contributions give rise to sigTPP, the first signature-based generative model for TPPs, trained using a path-level loss on complete trajectories. We further analyse the space of counting paths and derive three distributional discrepancies, providing mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, sigTPP achieves the best average rank based on eight complementary metrics, outperforms or is within a standard error of the strongest baseline in 64% of the dataset-metric pairs, and according to a relative score, improves against every baseline by at least 19% on average.

Recent years have witnessed the emergence of multivariate modeling using time series foundation models (TSFMs), which achieve advanced zero-shot generalization. Modern multivariate TSFMs are predominantly pretrained on multivariate synthetic data, which is easier to scale but may fail to capture the complex temporal dynamics and cross-variable relationships present in real-world time series. This raises a key question: Whether and to what extent the leading TSFMs trained with the real-world corpus perform better than those trained with synthetic data? To answer this, we establish the RMISC corpus, a considerably large-scale, high-quality, openly accessible, real-world, and multivariate time series archive that contains around 200 datasets and 142 billion time points across diverse domains. Furthermore, we pretrain four advanced TSFMs on univariate, synthetic multivariate, and real-world multivariate data and evaluate their zero-shot generalization capabilities on standard in-distribution and out-of-distribution benchmarks. Experimental results show that incorporating real-world multivariate data predominantly improves the generalization performance for both univariate and multivariate TSFMs. These results provide a deeper understanding of how real-world multivariate data contributes to the development of stronger TSFMs.

Building sensors are embedded in physical topology, spatial hierarchy, and operational context, yet existing forecasters often treat them as isolated time series or rely on fixed covariate sets. We present TopoBrick, a training-free framework for zero-shot building IoT (Internet-of-Things) forecasting. TopoBrick uses building knowledge graphs to construct a compact structural skeleton and employs an agentic topology sampler to select target-specific exogenous variables. The selected variables are organized by deployment-time availability, separating past-known sensor states from future-known calendar, schedule, and meteorological exogenous variables. Across three real-world buildings, TopoBrick outperforms strong zero-shot foundation-model baselines and remains competitive with fully trained building-specific models. Ablations show that topology-aware sampling is more reliable than random, ontology-only, or fixed-hop selection, especially for physically coupled HVAC and weather-driven sensing variables.

Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series. While existing methods predominantly focus on local temporal shifts, they fail to explicitly model the global structural challenge where datasets are composites of distinct operational regimes. In this paper, we propose NEST, a specialized framework designed to model and recompose these evolving structures through a two-phase dense MoE architecture. NEST first facilitates structural specialization by partitioning the dataset into distinct operational regimes through unsupervised clustering in a principled moment-entropy space. We introduce a regime-oriented router mechanism that generates initial expert weights based on temporal content, subsequently refined through geometric modulation to regime centroids. Crucially, rather than acting as monolithic predictors, individual experts function as specialized kernels that capture regime-specific dynamics by evolving unique variate-attention patterns. Extensive evaluations on diverse benchmarks, including heterogeneous network traffic and physical phenomena, demonstrate that NEST consistently achieves state-of-the-art performance. Our code and datasets are available at https://github.com/Aaralshin/NEST

Rendering time series as chart images for CNN-based classification has become increasingly common in time-series classification (TSC). However, it remains unclear whether models learn underlying temporal patterns or rely on encoding-specific visual cues introduced by chart design. We present VEIL: a systematic study examining how chart encodings influence learned representations through complementary analyses of similarity, transferability, and attribution. Attention-guided training appears to mitigate this effect when encoding sensitivity is consistently identified across diagnostics, but provides limited or negative benefit when such signals are absent. These findings position VEIL within the broader question of how machines perceive visualizations -- extending graphical perception from human readers to vision models -- and show that visualization design choices shape learned representations in ways that warrant treating chart-based TSC as a representation and measurement problem rather than a simple modeling decision.

Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences. Continuous-time approaches instead treat time series as samples from an underlying input path, a formulation that naturally accommodates irregularly sampled or oversampled data. Among these, Neural Controlled Differential Equations (NCDEs) are a maximally expressive class of models that parametrise a vector field using a neural network and evolve their hidden state by solving a dynamical system driven by the input path. NCDEs typically use a non-linear vector field, so their expressive power and continuous-time flexibility come at the cost of a forward pass that is both computationally expensive and inherently sequential, limiting their scalability and practical applicability. This thesis advances the training and scalability of NCDEs through three complementary contributions. First, building on neural rough differential equations, Log-NCDEs apply the Log-ODE method to efficiently approximate an NCDE's solution during training, improving both computational speed and empirical performance. Second, Linear NCDEs replace the non-linear vector field with a linear one, enabling closed-form solutions and parallel-in-time computation without sacrificing theoretical expressivity. Third, Structured Linear NCDEs use structured linear vector fields to further enhance efficiency while maintaining theoretical expressiveness and empirical performance. Collectively, these methods reduce the time per training step for an NCDE by up to three orders of magnitude while achieving state-of-the-art performance across diverse time series benchmarks.

Deploying a time series foundation model requires GPU infrastructure, engineering overhead, and carries no guarantee of improvement over XGBoost. We provide the first systematic break-even analysis answering when this investment pays off. Across 30 benchmark datasets, we compare zero-shot and LoRA fine-tuned foundation models (Chronos, Moirai, Lag-Llama) against classical baselines (Naive, ETS, ARIMA, XGBoost) at six training set sizes from 2% to 100% of available data. Foundation models outperform classical methods at every evaluated training fraction on 15 of 30 datasets -- GPU deployment is unconditionally justified on these regardless of data volume. On 6 datasets, classical methods surpass zero-shot foundation models with as little as 2% of training data (21-2,768 samples); on the remaining 9, break-even ranges from 24 to 8,361 samples. One robust deployment rule requires no model training: if n_train < 700 and seasonality is non-negligible, use FM zero-shot and skip fine-tuning -- this resolves 10 of 30 deployment decisions immediately. Contrary to common practice, LoRA fine-tuning can actively degrade performance on short series. We operationalise these findings as a two-step decision framework -- compute dataset length and seasonality strength, run a brief 5-10% pilot only if needed -- enabling practitioners to make the FM-versus-classical decision before committing to full infrastructure. Four dataset features motivate mechanistic hypotheses for the remaining cases, though reliable automated prediction at this benchmark scale remains an open problem. Code, benchmark, and decision tools are available at https://github.com/nicolaisi/fm-breakeven.

Camera-radar (CR) fusion is a practical sensing configuration for autonomous driving, but existing models are typically trained with task-specific supervision, limiting reusable representation learning. We present CRISP, a spatiotemporal CR backbone pretrained through forecasting-based representation learning. Given historical multi-view images and radar sweeps, CRISP learns a unified bird's-eye-view (BEV) representation by predicting future LiDAR point clouds. LiDAR is used only as privileged supervision during pretraining; the deployed model requires only camera and radar. To make forecasting-based pretraining effective for CR fusion, CRISP introduces an enhanced radar encoder, radar-enhanced temporal self-attention, and multimodal feature rendering with modality innovation gating. These components inject radar range and Doppler cues into BEV temporal propagation and allow BEV tokens to selectively incorporate camera and radar evidence. Experiments on nuScenes show that CRISP improves long-horizon point cloud forecasting and transfers effectively to downstream tasks, including 3D detection, tracking, online mapping, motion forecasting, future occupancy prediction, and planning, suggesting that predictive CR pretraining is a promising path toward scalable driving representations under practical sensor configurations. The project website is https://umfieldrobotics.github.io/CRISP.

Time series forecasters that use exogenous covariates are fragile in deployment: when those covariates are noised, temporally misaligned, or missing, strong exogenous-fusion and exogenous-adapted models can degrade far above the endogenous-only floor. We study whether such robustness requires specialized architectures, or whether it can be obtained through a simple training intervention. We propose exogenous dropout, a model-agnostic method that randomly zeros whole exogenous channels during training. Across electricity-price forecasting, reservoir hydrology, and meteorology, exogenous dropout substantially improves robustness under Gaussian noise, temporal misalignment, and fully missing channels, while preserving clean accuracy. Applied to a dual-correlation network, it yields the most robust model in our experiments, outperforming a deliberately strong bounded architectural foil, BoundEx, which combines a learnable gate, a fallback residual to the endogenous backbone, and per-channel exogenous FiLM modulation. Architecture-by-dropout ablations, gate-behavior diagnostics, and a representation-level bound show that explicit architectural boundedness is not necessary for this robustness: an unbounded model trained with exogenous dropout is more robust than the bounded model in every domain. We release a corruption-robustness benchmark and recommend exogenous dropout as a simple, strong baseline for future work on time series forecasting with covariates.

Generative models have changed how machine learning represents complex data distributions, especially in language and vision, yet many real-world systems are observed instead as continuous, high-dimensional, and noisy sensor time series. Existing generative modeling of sensor data, however, remains fragmented across modalities, datasets, and task formulations, limiting a systematic understanding of when, how, and why generative models succeed or fail in real-world settings. To address this gap, we introduce SensorGen, a large-scale study of sensor-signal generation spanning 14 settings across 4 domains, 7 datasets, and 12 signal modalities. Leveraging SensorGen, we systematically evaluate generative models from five major families and uncover three key findings: (1) flow-matching models provide strong overall performance across most settings; (2) signal properties matter, with demographic covariates improving longitudinal generation and time-frequency modeling improving high-frequency signal generation; and (3) generated signals have practical utility beyond visual realism, with scaling improving generation quality and synthetic data improving downstream performance. Together, SensorGen establishes a broader understanding of design choices, evaluation protocols, and failure modes in real-world sensor data generation.

Engineering Digital Twins and Prognostics and Health Management (PHM) systems rely on robust perception modules to extract actionable information from heterogeneous and non-stationary time-series data. However, most existing approaches remain task-specific, data-hungry, and difficult to integrate into scalable monitoring and decision-making pipelines. Moreover, purely data-driven models often lack robustness and transferability across varying operating conditions. To address these challenges, this paper proposes a modular foundation model for time-series perception based on a collection of pretrained representation encoders. The framework leverages self-supervised learning on heterogeneous datasets to learn transferable and task-agnostic representations, which can be reused across multiple PHM tasks. A gating mechanism is introduced to dynamically select relevant encoders for a given target dataset, enabling conditional computation and adaptive model composition. The selected representations are projected into a shared latent space and aggregated using a Transformer-based self-attention module that explicitly models cross-encoder interactions. The resulting architecture supports multiple downstream tasks, including imputation, long-term forecasting, and few-shot learning, through lightweight task-specific heads, while keeping pretrained encoders frozen during adaptation. Extensive ablation studies demonstrate the complementary roles of self-supervised pretraining, encoder selection, representation alignment, and adaptive aggregation. Experimental results on the ETT benchmark show competitive performance across tasks, while a real-world industrial case study on virtual sensing for hydro-generator rotor temperature highlights the practical relevance of the approach.

Clinical time series prediction in intensive care units remains challenging due to heterogeneous physiological variables and informative missingness. The presence or absence of a measurement can reflect clinical decisions and patient severity, and thus missingness can serve as a predictive signal rather than a simple data artifact. This work presents CISM, a Channel-Independent Spectrogram framework with a Missingness stream for clinical multivariate time series prediction. CISM converts each clinical variable into a variable-wise time-frequency spectrogram, preserves variable identity through variable-aligned encoding, and aligns an explicit missingness stream with the spectrogram representation. Experiments on an in-hospital mortality task derived from MIMIC-IV show that CISM achieves the highest mean AUROC (0.7225), AUPRC (0.3308), and F1 (0.3808) among the compared time series, missingness-aware, vision, and time-frequency baselines. Ablation studies further show that observation patterns provide a meaningful informative signal. Pixel-level mask injection improves performance over plain spectrogram inputs and recovers much of this predictive value. The aligned missingness stream contributes a further, complementary gain in both AUROC and AUPRC. These results highlight the importance of modeling observation patterns as structured signals in clinical time series prediction.

Long-horizon behavior prediction aims to infer a user's next action based on a lengthy historical sequence, playing a crucial role in artificial intelligence field. The rise of large language models (LLMs) offers a promising direction for sequential behavior prediction, yet LLMs struggle with latent behavioral pattern induction and model-intrinsic cognitive biases when tackling long-horizon behavior prediction. Prior memory management methods follow a context-compression paradigm that attempts to address this task by alleviating the historical sequence burden, yet fail to resolve the core challenges. In this paper, we advocate a paradigm shift that reframes the lengthy historical sequence from a burden into a valuable resource to be exploited, and accordingly propose PraMem, which conducts beforehand practice over the lengthy historical sequence to build an experiential memory, thereby serving as the assisted input for accurate long-horizon behavior prediction. Extensive experiments across diverse tasks demonstrate that PraMem achieves superior performance than prior methods, and more in-depth analyses provide valuable insights into the mechanism and evolution of the experiential memory. Code: https://github.com/icip-cas/PraMem.

Time series forecasting remains challenging when the underlying data contain rare but critical extreme events. This issue is particularly important in hydrologic forecasting, where streamflow distributions are often highly skewed and extreme peaks can have substantial impacts on flood monitoring, water resource management, and early warning systems. Although Transformer-based forecasting models have achieved strong performance by modeling long-range temporal dependencies, they typically treat all time points uniformly and may therefore underrepresent rare extreme patterns. In this paper, we propose the Extreme-Adaptive Transformer (Exformer), a forecasting framework designed to explicitly model temporal dependencies involving both normal and extreme events. Exformer introduces an extreme-adaptive attention mechanism composed of three sparse components: Local, Stride, and Extreme. The Local and Stride components capture short-term and periodic temporal dependencies, respectively, while the Extreme component selectively models event-aware dependencies between normal and extreme streamflow patterns. Experiments on four real-world hydrologic streamflow datasets show that Exformer achieves superior 3-day forecasting performance compared with state-of-the-art baselines. Our findings demonstrate that explicitly incorporating extreme-aware attention improves the forecasting capacity of Transformer models on imbalanced time series with rare but consequential events.

Transformer architectures have shown strong potential in time series forecasting, where multi-head self-attention is widely used to capture temporal dependencies across historical timestamps. However, standard self-attention has quadratic time and memory complexity with respect to the look-back length. This cost may limit its use in resource-constrained or high-throughput forecasting systems, where fast and memory-efficient inference is important. Through qualitative and quantitative analyses, we observe that self-attention maps in time series forecasting often contain redundant patterns across different timestamps. This phenomenon can be related to the repeated temporal patterns and relatively stable temporal correlations in many real-world time series. Motivated by this observation, we propose Self-Gating Attention (SGA), a plug-and-play attention mechanism that represents the attention score with a shared learnable matrix and an input-dependent residual component. The shared matrix captures common attention patterns, while the residual component captures input-dependent variations. In this way, SGA avoids the query and key projections used in standard attention score computation, leading to linear time and score-matrix memory complexity with respect to the look-back length. We integrate SGA into several forecasting backbones and compare it with standard self-attention and lightweight attention variants on nine publicly available real-world datasets covering electricity, finance, weather, medical monitoring, human activity, and climate records. The results show that SGA improves inference efficiency on public benchmarks while maintaining competitive forecasting performance against state-of-the-art attention mechanisms. These benchmark results provide deployment-oriented evidence.

Time-series forecasting supports decisions in finance, en-ergy, transportation, public health, and industrial monitoring. Recent foundation models improve transfer across forecast-ing tasks, but many depend on centralized data and Trans-former attention, which restricts their use for long, high-di-mensional, and privacy-sensitive signals. This paper presents QuantFlow, a probabilistic forecasting framework that com-bines inverted sequence embedding, bidirectional Mamba state-space decoders, quantile regression, and federated learning. Each variable is embedded over the complete ob-servation window, processed in forward and reverse direc-tions, and projected to five conditional quantiles. TSMixup expands temporal diversity through Dirichlet-weighted inter-polation while preserving sequence structure. Experiments cover cryptocurrency, traffic, electricity, Electricity Trans-former Temperature, influenza, and weather data. QuantFlow obtains mean squared errors of 0.2834 on ETTm1 and 0.2218 on Weather, and a 20-client non-IID deployment retains use-ful accuracy after three communication rounds without cen-tralizing raw records. The results indicate that selective state-space modelling is a promising basis for scalable, uncer-tainty-aware, and privacy-conscious time-series prediction, while also revealing limitations on irregular epidemiological signals and long-horizon generalization.

Hierarchical state-space models (HSSMs) offer a promising approach to long-horizon prediction by segmenting sequences into temporal chunks. However, their performance hinges on how chunk boundaries are determined. While prior HSSMs typically rely on fixed-length chunking or similarity-based boundary detection, these methods often misalign with the intrinsic temporal structure of the data. We argue that chunking should instead be driven by prediction errors, which more directly indicate when longer-range context becomes necessary. Nevertheless, integrating surprise-based chunking into HSSMs introduces critical challenges, including hierarchical collapse during end-to-end training and the absence of surprise signals during open-loop prediction. To address these issues, we propose Surprise-based Nested Temporal Abstraction (SUNTA), a method that employs a decoupled training strategy to preserve surprise signals and uses internal inconsistency as a top-down surprise metric to determine chunk boundaries within imagined rollouts. Experiments on video prediction tasks in 2D and 3D environments demonstrate that SUNTA outperforms baselines, uniquely maintaining accurate predictions over 250 timesteps, whereas all baselines degrade within the first 10 timesteps.

Time series foundation models (TSFMs) have shown strong zero-shot forecasting performance, but their generalization in covariate-driven, non-stationary settings is underexplored. Electricity price forecasting (EPF) presents a challenging testbed due to complex temporal dependencies, distributional shifts, and strong reliance on structural and contextual information. We propose a two-dataset-benchmarking framework for EPF to mitigate contamination risk and enable fair evaluation of TSFMs. We examine key aspects of EPF including point and probabilistic forecasting performance, tail behavior, price spikes, and comparisons against domain-specific methods. We find that TSFMs are highly competitive and often outperform general-purpose baselines. Yet, their performance depends critically on covariate support, and they do not consistently surpass domain-specific methods tailored to EPF. Interestingly, simple ensembles of TSFMs and domain-specific methods appear to have significant potential, suggesting that the two approaches capture complementary predictive information.

Anomaly detection is a critical and evolving field in Machine Learning, with applications targeting different domains such as cybersecurity, finance, healthcare, manufacturing and IoT (Internet of Things) systems. Traditionally, anomaly detection algorithms have been designed using both supervised and unsupervised learning paradigms. The fundamental challenge in real-world anomaly detection scenarios is related to the inherent class imbalance (anomalies are typically rare) and, for supervised methods, to the scarcity of labelled anomalous data. Indeed, labelling is both expensive and time-consuming. Conversely unsupervised methods do not require labelling, but may suffer from high false positive rates when deployed in safety-critical applications. In this work we introduce a novel unsupervised algorithm for anomaly detection in time series based on the Haar discrete wavelet and a suitably designed $t$-test. We establish the theoretical foundation of the proposed $t$-test and, through extensive experimentation across 343 datasets, demonstrate that our algorithm outperforms state-of-the-art unsupervised and self-supervised benchmarks.

Low-voltage load forecasting is an important component in current and future energy systems with a high degree of electrification and decentralized generation. However, current forecasting methods require significant manual effort, often lack uncertainty estimation and proper peak prediction, and they are often not adequately evaluated in terms of grid requirements. In the present study, we provide an extensive evaluation of short-term net load forecasts of 200 real-world low-voltage feeders with a focus on the rapidly evolving time series foundation models. Our study compares Chronos-Bolt, Chronos-2 and TabPFN-TS to six baseline models and demonstrates superior performance, in particular for Chronos-2. An ablation study, in which weather covariates are omitted, shows that time series foundation models adapt to increased uncertainty, despite the importance of weather information. A novel application-oriented metric links the model's forecasting capabilities in peak prediction to the trade-off in grid asset planning and operation between cost reduction and minimizing the risk of failure.

We propose a model agnostic methodology to measure lag relevance in machine learning forecasting models applied to univariate time series. Particularly, we are working in the context of time series using the frameworks of Ghost variables and Shapley values, together with additive importance measures, to introduce the auto-relevance and partial auto-relevance functions as the lag importance values. Additionally, we propose a novel method to replace absent features in coalition based methods with a one step forecast from the same model. We evaluate these proposals under different simulations and real data cases. This combined framework perspective is particularly suitable for time series. In addition, to show our discoveries we use a pull of models from the seasonal ARMA family and recurrent neural networks. We found that the calculated relevance measures successfully demonstrate the expected lag structure in almost all cases.

We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.

Large language models are increasingly used as open-ended search operators in evolutionary optimization. We introduce Evolutionary Feature Engineering (EFE), a framework for using LLM-based evolution to discover preprocessing transformations for structured data. EFE represents transformations as Python programs with a standardized fit/transform interface, allowing them to be inserted directly into existing machine learning pipelines. During evolution, candidate programs are refined using dataset context, summary statistics, and downstream performance feedback on validation set. We instantiate EFE in two settings. For time-series forecasting, EFE-Time learns invertible, dataset-specific normalizations that improve off-the-shelf time-series foundation models. It reduces forecasting errors (MASE, WQL, MAE) 3% or more when averaged across datasets and improvements are as much as 19% on the COVID-Deaths dataset. Notably, these improvements occur with recent TSFMs such as Chronos-2. For tabular prediction, EFE-Tab evolves compact feature programs that add useful interpretable features and remove redundant ones, improving or matching existing LLM-based feature-engineering methods. We found EFE-Tab to be particularly effective on classical decision trees, where small sets of evolved features yield competitive accuracy while preserving interpretability. Overall, EFE demonstrates that LLM-based evolution can improve both accuracy and interpretability when automatically tackling structured data.

We introduce TiRex-2, a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates. Real-world forecasting is inherently sequential: observations arrive continuously, variables evolve jointly, and a subset of covariates is known ahead of time. Existing Transformer-based time series foundation models capture cross-variate dependencies but incur quadratic complexity in context length and require full-history recomputation as new observations arrive. TiRex-2 addresses these limitations through a memory-centric recurrent design that operates at constant per-patch cost under streaming. The model combines a bidirectional time mixer with an asymmetric grouped-attention variate mixer, enabling the integration of future-known covariates while preserving strict causality over target variables. To our knowledge, this is the first time series foundation model that achieves this combination of properties. To support scalable multivariate pretraining, we propose a synthetic coupling pipeline that composes diverse multivariate samples on the fly from large univariate corpora. Empirically, TiRex-2 achieves state-of-the-art zero-shot performance on GIFT-Eval and fev-bench, remains stable when streamed to arbitrary context lengths, and maintains constant inference cost per patch. The model uses 38.4M active parameters in univariate mode, with an additional 44.1M parameters activated for multivariate forecasting.

Different stages of manipulation tasks exhibit varying levels of difficulty, suggesting stage-dependent motion speeds and temporal prediction horizons. However, existing IL-based visuomotor policies typically imitate the execution speed of expert demonstrations and operate with a fixed temporal prediction horizon, limiting flexibility and overall task throughput. In this paper, we introduce AutoSpeed, a model-agnostic learning framework that enables existing visuomotor policies to predict trajectories with stage-adaptive motion speeds, without requiring speed or stage annotations. We treat future trajectories at different speeds as candidate optimization targets, evaluate each candidate using a composite cost that trades off prediction error against prediction horizon, and optimize the policy toward the minimum-cost candidate. With a fixed-length action sequence, speed modulation adjusts the effective temporal prediction horizon: simple stages are executed faster with a longer prediction horizon, whereas complex stages are executed more slowly with a shorter prediction horizon. Specifically, we implement speed modulation in the frequency domain via the discrete cosine transform (DCT), which enables smooth, non-integer speed scaling and thus preserves motion continuity. Extensive evaluations show that AutoSpeed substantially reduces task execution time while also improving success rates. Under the AutoSpeed framework, the inferred motion speeds exhibit a strong correspondence with task stages.

Time series are central to modern data mining applications, from industrial telemetry and server metrics to finance and physiology, yet time-series self-supervised learning often depends on view and augmentation choices that encode domain-specific invariances. We study how an SSL recipe behaves when its method-specific configuration is reused unchanged after the pretraining signal family changes, framing this as a fixed-recipe stress test rather than a comparison against optimally tuned methods. We introduce Latent Euclidean Next-Embedding Prediction Architecture (LeNEPA), a no-augmentation next-latent-token objective with a causal backbone. LeNEPA replaces the stop-gradient/EMA stabilization used by vanilla NEPA with SIGReg-based isotropy regularization and computes the predictive loss in a lightweight projected space that is discarded for evaluation. We compare LeNEPA with an ECG-tuned JEPA recipe under a fixed-horizon frozen-probe protocol on PTB-XL and Diag, a synthetic diagnostic corpus generated with Aionoscope. Both methods are retrained independently on each dataset while keeping their method-specific recipes unchanged. In this protocol, the ECG-tuned JEPA recipe is strong in-domain on PTB-XL but weaker when reused unchanged on Diag, whereas LeNEPA preserves useful frozen-probe gains on both datasets. Learning curves suggest faster early representation acquisition: LeNEPA reaches 80% of its final AUROC/AUPRC gain after 2--5k updates, compared with 5--10k updates for the faster JEPA readout. As a separate external frozen-encoder check, a CauKer-pretrained LeNEPA variant reaches 77.65% mean UCR-128 Random-Forest accuracy in a single-seed, best-checkpoint run, within 1.16 points of Mantis and within 0.24 points of MOMENT (77.89%). Overall, the results support no-augmentation latent prediction as a useful candidate recipe for low-retuning time-series SSL.

Time-series models are often evaluated by what they can forecast or classify, but those scores do not show whether their representations preserve the process state a user may want to inspect: event timing, phase, amplitude, frequency, or regime variables. We introduce Aionoscope, a generator-based diagnostic tool for debugging latent-state accessibility in frozen time-series representations. Aionoscope separates process generation from observation rendering, producing seeded synthetic streams with exact categorical and dense labels across mixture complexity and nuisance variation. We instantiate Aionoscope as Primitive Process Mixtures and evaluate 37 model-plus-adapter systems with a common pooled linear-probe protocol. The main result is a mismatch between coarse and fine-grained accessibility. Most systems make component presence easy to recover, but expose dense process state much less reliably: the highest observed dense-probe row reaches 0.689 mean masked $R^2$, while a dense-feature oracle reaches 0.999. This is the failure mode Aionoscope is designed to surface: a representation can look informative at the level of "what kind of signal is present" while hiding the timing, phase, amplitude, frequency, or regime variables needed for debugging.

Despite the increasing sophistication of industrial AI systems, the ability to reliably detect subtle and noisy anomalies in complex time series data remains a critical yet unresolved challenge. In large-scale industrial applications, labeling time series data is often prohibitively expensive and time-consuming, making unsupervised learning a practical and widely adopted approach. However, existing unsupervised methods frequently struggle to distinguish near-normal anomalies from normal patterns and are vulnerable to noise contamination within normal samples. To address these limitations, we propose a novel framework that leverages active learning to iteratively enhance the performance of unsupervised models. Our framework's core contributions are (1) a masked time-series reconstruction feedback strategy that forces the model to learn robust temporal dependencies, and (2) a minimax learning strategy that promotes robustness by differentially treating normal and abnormal samples. This process encourages the model to better capture the dynamics of subtle and noisy patterns. The proposed framework is evaluated across 28 test cases involving four multivariate time-series datasets and seven unsupervised backbone models. Experimental results demonstrate a 12.39% improvement in AUC compared to the original models, confirming that our method can be readily integrated into existing unsupervised reconstruction-based anomaly detection systems to significantly enhance their performance.

We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.

Forecasting models for health-signal digital twins must preserve the oscillatory, frequency, phase, and state-transition dynamics of physiological signals, yet the pointwise metrics used to benchmark them cannot detect when these fundamental properties are lost. We show that this blind spot misranks models: across 11 architectures, models with comparable pointwise error diverge by up to 53° in phase accuracy, equivalent to roughly 123 ms for a 1.2 Hz cardiac rhythm and invisible to standard metrics. To enable development of models that escape such failures, we introduce TimeSynth, a controlled benchmarking framework with two reusable components: a physiologically grounded generator producing signals with analytically known ground-truth dynamics from parametric models fitted to real electroencephalography, electrocardiography and photoplethysmogram signals, along with diagnostics quantifying amplitude, frequency, phase, and state-transition fidelity. Linear and full-sequence attention models systematically lose frequency and phase information despite acceptable amplitude error, whereas architectures with localized temporal structure better preserve dynamical fidelity and adapt to observable state transitions; none, however, reliably preserves stochastic switching. Because the dominant determinant of fidelity is architectural, model choice becomes a principled, use-case-driven decision rather than a search for a single winner. TimeSynth thus supplies the controlled preclinical stress test missing before models are coupled to patient data, with a reusable generator and diagnostics for fidelity-aware development.

Long-horizon multivariate time series forecasting (LTSF) remains challenging due to non-stationarity, regime shifts, and error accumulation. The Variability-Aware Recursive Neural Network (VARNN) is designed to track such variability by maintaining a residual-memory state driven by one-step prediction errors. However, its original formulation is limited to one-step sequence regression and does not directly support multi-step forecasting. In this work, we extend VARNN to long-horizon forecasting and introduce StateFlow, a recurrent forecasting framework that uses VARNN as a dual-state recurrent backbone to capture two complementary signals from the lookback sequence: a hidden-state trajectory representing primary temporal dynamics, including trend, seasonality, level changes, and recurring patterns, and a residual-memory trajectory representing structured local prediction deviations, driven from a nonlinear recurrent transformation of errors between one-step base predictions and observed values. A chunk-based decoder separately summarizes these trajectories and maps them to the future horizon for direct multi-step forecasting. We further employ a two-stage optimization strategy that first trains the VARNN encoder through a one-step base prediction objective to optimize the internal representations over the lookback sequence, and then trains a horizon-specific decoder for direct multi-step forecasting. Experiments on standard LTSF benchmarks show that StateFlow achieves competitive performance against strong linear, recurrent, convolutional, and Transformer-based baselines while preserving linear recurrent encoding and a compact model design.

Evolutionary neural architecture design for multivariate time-series forecasting remains underexplored, with most approaches relying on fixed Transformer architectures despite substantial variation across tasks and forecasting settings. This paper introduces an evolutionary neural architecture search framework for discovering task-adaptive Transformer-like models for time-series forecasting (EVOTS). Architectures are encoded using a modular genome representation that enables flexible composition of attention, feed-forward, and projection components, while a repair mechanism enforces structural validity throughout the evolutionary process. This formulation allows effective exploration of a diverse architecture space without relying on hand-crafted design rules. The proposed approach is evaluated on four benchmark datasets from the ETT family (ETTh1, ETTh2, ETTm1, and ETTm2) under multiple forecasting settings, including univariate-to-univariate, multivariate-to-univariate, and multivariate-to-multivariate prediction, with horizons of 96, 192, 336, and 720. In the multivariate-to-multivariate setting, the evolved architectures achieve competitive and, in several cases, improved mean squared error relative to a strong Transformer-based baseline. Additional analyses examine performance differences across forecasting settings and report wall-clock training time to provide a coarse indication of computational cost. Overall, the results demonstrate that evolutionary search can effectively discover flexible and high-performing Transformer-like architectures for multivariate time-series forecasting within practical runtime constraints.

The generation of synthetic relational databases often involves modeling complex temporal dynamics, such as transaction logs or event sequences. A significant challenge in this domain is the handling of categorical time series (e.g., status codes), where standard encoding methods like one-hot encoding fail to capture intrinsic frequency-domain features such as seasonality and cyclicity. In this paper, we introduce Sequential RC-TGAN (Seq. RC-TGAN), a temporal extension of the RC-TGAN framework, equipped with a novel integrated loss function based on the \textit{Spectral Envelope Theory}. This differentiable loss allows the generator to directly optimize the preservation of latent periodic structures via backpropagation. While spectral envelope theory is inherently designed for categorical sequences, we extend this frequency-domain regularization to continuous time series by employing a Variational Gaussian Mixture Model (VGM) discretization strategy. To establish a mathematically rigorous evaluation standard, we simulate categorical time series governed by a parameter $α$, with exactly known theoretical spectral envelopes. Integrating these dynamic sequences into the child tables of a relational database yields a robust ground-truth benchmark for evaluating the frequency-domain fidelity of our generative framework. Furthermore, we address the lack of robust evaluation standards for relational time series by proposing two new metrics: Spectral Density Divergence and Spectral Envelope Divergence. Experimental results on real-world datasets, as well as our simulated benchmarks, demonstrate that our end-to-end approach significantly outperforms state-of-the-art systems in reproducing cyclic patterns and long-term seasonality across both categorical and continuous features.

Staff absenteeism imposes substantial operational costs in high-demand work environments such as healthcare, emergency services, meat processing, construction, and courier and delivery services, where proactive workforce planning depends on reliable individual-level absence prediction. Existing regression and classification approaches share a structural limitation; they map features observed at time t to labels at the same time t, reproducing already-realised outcomes rather than predicting future events, and discard the sequential behavioural structure inherent in individual attendance histories. We propose a Time Series Classification (TSC) framework that separates historical attendance sequences from future absence labels, enabling genuinely proactive prediction. Due to the lack of public longitudinal attendance data, we construct a reproducible simulated dataset calibrated to the UCI dataset. We analyse Binary Focal Loss (BFL) and Geometric Mean (G-Mean) loss under severe class imbalance using only the imbalance ratio $ρ$. For BFL, the initial gradient ratio is $ρα/(1-α)$, implying the balanced weight $α= 1/(1+ρ) \approx 0.023$. Experiments show that performance is governed mainly by $α$, with BFL achieving specificity 0.813 and balanced accuracy 0.888, comparable to G-Mean. Unlike BFL, G-Mean adapts automatically without parameter calibration. Among three deep learning architectures evaluated, Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and the hybrid LSTM-Fully Convolutional Network (LSTM-FCN), the LSTM-FCN delivers strong precision and specificity. Stable performance is obtained with batch sizes >= 64 and window sizes between 40-80 days, yielding balanced accuracy of approximately 80% on held-out test data.

Cloud virtual machines are often overprovisioned, creating avoidable cost and operational inefficiency. We present CLOUDADV, an interactive engineer-facing advisory system for cloud instance sizing under workload drift. The system combines zero-shot time-series forecasting with bounded recommendation generation across day-, week-, and month-scale planning horizons. For each query, CLOUDADV constructs a structured decision context from historical utilization, forecast summaries, current VM metadata, candidate instance options, pricing, and explicit sizing heuristics. A higher-capacity LLM is used offline to generate reference recommendations, while a smaller production model is evaluated on the same prompts to assess deployment-time alignment under latency and cost constraints. Evaluation prioritizes downstream recommendation quality using simulated Azure cost savings and ex-post exceedance, with rolling-origin forecast accuracy reported as a secondary diagnostic against classical and supervised baselines. In a case study of seven production VMs, the reference recommendations reduce simulated monthly cost from about $1,503 to $708, yielding $795/month in savings (52.9%) under conservative heuristic constraints, while the highest observed exceedance rate among downgraded cases is 1.5%. Although Chronos-2 does not minimize every forecasting metric, it often induces recommendation patterns similar to those of a supervised per-VM baseline. These results suggest that zero-shot foundation models can support decision-aligned provisioning in non-stationary cloud environments while reducing the operational burden of repeated per-tenant retraining, revalidation, and redeployment.

We present a three-phase deep reinforcement learning system for personalized portfolio management that addresses three limitations shared by all prior financial RL work: 1) ticker lock-in, 2) monolithic objectives , and 3) static user models. Phase 1 pretrains a ticker-identity-free cross asset encoder via self-supervised learning on a multi-asset corpus, augmented by a frozen parallel branch using Chronos, a T5-based time series foundation model, fused via a learned gating mechanism. To our knowledge, this is the first application of a time series foundation model to portfolio management RL. The encoder generalizes to any publicly traded asset via a 50-dimensional observable metadata vector that requires no retraining for new tickers. Phase 2 fine-tunes a MoE (Mixture of Experts) portfolio actor critic with PPO under an objective-conditioned reward that simultaneously serves six distinct investment goals sampled per episode: short-term alpha, short-term gain, long-term gain, capital preservation, tax-loss harvesting, and long-term-gains-only. A MoE architecture assigns each objective to a specialized expert head (momentum, growth, defensive, tax-aware), and a learned intent router blends experts based on the active objective and current market regime, which eliminates cross-objective gradient conflict. Phase 3 adds a lightweight personalization layer further adapted at inference time to each individual via a 76-parameter LoRA module fine-tuned on real brokerage transaction history, inferring investment objectives from revealed trading behavior rather than questionnaires. A natural language intent parser converts free-form goals directly into structured investment objective parameters.

Decision-makers routinely rely on expert judgments accompanied by written explanations, yet explanation quality is difficult to measure at scale. Forecasting tournaments offer a natural testing ground: probabilistic judgments are paired with natural-language rationales and scored against realized outcomes. We introduce Explanation Quality Markers (EQMs), a set of sixty theory-guided reasoning patterns scored by large language models (LLMs). In a pre-registered analysis of over 55,000 forecast-rationale pairs from a multiyear forecasting tournament, EQMs predict accuracy at both the forecast and forecaster levels, consistently outperforming pre-LLM text-analysis methods. More than 90% of statistically significant pattern-level EQM-accuracy correlations match our directional hypotheses. The signal is asymmetric: EQMs identify likely underperformers more reliably than they distinguish the very best forecasters. Benchmarked against traditional indicators of forecasting skill, EQMs are the strongest predictor at the forecast level and competitive at the forecaster level, though weaker than prior accuracy. Human ratings of rationale quality are less consistently correlated with accuracy and place disproportionate weight on rationale length. Results transfer to an independent forecasting study. EQMs provide a scalable, interpretable method for extracting judgment-relevant information from written explanations.

Accurately predicting the temporal evolution of clinical biomarkers is crucial for the early diagnosis and management of neurodegenerative diseases such as Alzheimer's disease. However, this relies on longitudinal data to capture biomarker changes over time, which is often sparse and irregular due to the high cost, labor-intensive nature, and patient burden. To address these challenges, we propose ENC-ODE, an Event-level Neurodegenerative modeling in Continuous time with neural Ordinary Differential Equations. ENC-ODE predicts future biomarker evolution by modeling clinical events through diagnosis-conditioned continuous dynamics. A target-conditioned attention mechanism weights and aggregates event-level predictions for the target time and modality without history compression. Extensive experiments on Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that ENC-ODE outperforms representative sequence models while offering a scalable and neuroscientifically grounded solution for clinical support. The code is available at https://github.com/JardinDelSol/enc-ode.

Electroencephalography (EEG) foundation models aim to learn generalizable representations from large-scale brain recordings. However, the role of temporal feature extractors and whether pretrained time-series foundation models (TSFMs) can be effectively transferred to this setting remains underexplored. We conduct a controlled comparison of three temporal feature extraction strategies, including a linear baseline, a convolutional encoder, and a frozen pretrained TSFM (MOMENT), within a unified EEG foundation model. We evaluate their impact on representation quality using two downstream tasks: motor imagery and emotion recognition. Results reveal different trends across the evaluated benchmarks. On the motor imagery dataset, simple temporal representations perform competitively, whereas the emotion dataset benefits from richer temporal modeling. Although not specifically adapted to EEG, the pretrained TSFM serves as an effective temporal feature extractor, suggesting that general-purpose time-series representations can be transferred as frozen temporal feature extractors within EEG foundation models.

Top AI forecasting systems are approaching superforecaster-level accuracy on future world events, but still rely primarily on off-the-shelf LLMs combined with forecasting-specific context gathering and scaffolding. We study how to improve this recipe through ensembling: given a fixed number of samples, which off-the-shelf model forecasts should be combined to maximize accuracy? On binary questions from the Metaculus AI Benchmark, we find that individual accuracy is not enough: many frontier LLMs make highly correlated predictions, limiting the value of additional forecasts from the same or similar models. Instead, the strongest ensembles combine accurate but diverse forecasters, with models such as \model{Grok 4} contributing disproportionately because their predictions are less correlated with other frontier LLMs. These results suggest that the strength of the AI crowd comes not from sampling more forecasts indiscriminately, but from combining forecasts across models with complementary errors, motivating forecasting systems that explicitly optimize for both model quality and diversity.

We propose a path-space formulation of prediction in AI world models. Rather than sequences of one-step conditional distributions, we argue that a world model implicitly defines a probability measure over future trajectories. In the local regime where latent dynamics admit an effective Markovian description, this path measure takes the Onsager-Machlup form. Within this framework, prediction (most probable trajectory), planning (constrained optimization), and uncertainty (fluctuations) emerge as operations on a single action functional. We decompose the latent dynamics into reversible and irreversible components and introduce operational measures of entropy production from model rollouts. In controlled small-scale attention-based models, we find that attention asymmetry is acquired during training in proportion to the irreversibility of the data. Symmetrizing the learned attention suppresses entropy production and selectively degrades long-horizon prediction of irreversible dynamics while preserving relaxational prediction. These results suggest that irreversibility may serve as a computational resource for predictive world models. More generally, the fundamental predictive object is a distribution over future paths rather than states.

We introduce MACROCAST, a lightweight Time Series Foundation Model (TSFM) for real-time macroeconomic forecasting. Existing TSFMs suffer from data leakage in two forms: temporal contamination, as the model may have seen the realized values of the series it forecasts, and revision bias, as training on fully revised data diverges from the preliminary, vintage-specific releases available to real-time forecasters. MACROCAST is, to our knowledge, the first TSFM that rules out both forms of leakage entirely: at no stage of training is the model exposed to information that would not have been available to a forecaster in real time. We train MACROCAST first on purely synthetic time series in approximately one GPU-day and then fine-tune it on synthetic time series drawn from Bayesian VARs, dynamic factor models, and ARIMA specifications estimated on vintage-specific ALFRED data. Because pretraining uses only simulated data and fine-tuning uses only real-time vintages, no observed future or revised value ever enters the model; each fine-tuning run takes nine minutes. Evaluated on the FRED-MD database in a genuine real-time out-of-sample exercise, MACROCAST improves on the AR(1) benchmark for roughly 80% of series-horizon pairs, matches or surpasses Chronos-2 -- the strongest currently available TSFM -- and outperforms the Bayesian VAR and dynamic factor model benchmarks, all in a data-leakage-free manner.

Effective sub-typing (also known as grouping or clustering) of patients using their electronic health record (EHR) data can greatly inform precision medicine efforts. However, subtyping temporal EHR datasets is known to be challenging due to inherent EHR issues, including complexity and irregularity. In this study, we propose a self-supervised Mamba-based model that learns effective EHR representations and enables enhanced patient subtyping. We evaluate the proposed model on public and private real-world EHR datasets to classify the data based on the available labels and subtype patients based on the representations learned from the model. Through an extensive set of experiments, we demonstrate that our model's design choices lead to better performance compared to competitive baseline models for prediction. Moreover, we evaluate several clustering techniques to demonstrate that our findings offer valuable insights into subtyping patients based on temporal records from EHR models\footnote{Our implementations are available at https://github.com/healthylaife/triplet_mamba.

In many real-world applications, such as retail sales, energy usage, and supply chain planning, forecasting is performed across hierarchical structures. These structures often represent aggregations (e.g., products to categories to regions), where forecasts must not only be accurate but also coherent, meaning that lower-level predictions sum correctly to higher-level forecasts. Traditional statistical methods, such as Bottom-Up and MinT, enforce coherence through post-processing but fail to model complex nonlinear temporal dependencies and covariate interactions. We propose Hierarchical Temporal Fusion (HTF), a novel extension of the Temporal Fusion Transformer (TFT) that integrates structured hierarchical embeddings with a coherence-aware loss function to ensure consistent forecasts across all levels of a hierarchy. Rather than applying reconciliation after forecasting, HTF embeds coherence directly into the training objective. The coherence loss penalizes the difference between aggregated child forecasts and their corresponding parent forecasts during training, enabling the model to learn both temporal dynamics and structural consistency simultaneously. We evaluate HTF on two publicly available benchmark datasets: the M5 Walmart forecasting dataset and a publicly available hierarchical energy consumption dataset. Results demonstrate that HTF substantially reduces forecast incoherence while improving forecasting accuracy compared with classical reconciliation methods and deep learning baselines. In addition, attention visualization and embedding analysis provide insight into how temporal and structural information contribute to hierarchical forecasting performance.

Demand forecasting at the bottom of a retail hierarchy requires predicting tens of thousands of correlated long-horizon series across products, stores, and regions. Modern systems must scale across massive catalogs, capture shared demand dynamics, and remain interpretable enough to be trusted. Classical statistical methods need a separate model per series and are hard to manage at scale; deep autoregressive models struggle as the joint state grows to tens of thousands of dimensions; and recent graph-based forecasters, while capturing cross-entity dependencies, often produce opaque long-horizon forecasts. We propose GNBAN (Graph Neural Basis Attention Network), an end-to-end architecture combining heterogeneous graph representation learning with an interpretable basis-decomposition head. Retail data are represented directly as a heterogeneous graph derived from the relational schema, so a single model serves the entire catalog. Rather than predicting the horizon directly, GNBAN decomposes each forecast into trend, seasonal, and generic components. Its key innovation is a per-basis attention mechanism: each basis function keeps its own learnable query and retrieves information independently from the entity's historical neighborhood, letting different bases specialize to distinct temporal patterns while preserving interpretability. On two large-scale benchmarks, M5 Walmart and Favorita Grocery Sales, evaluated under matched protocols, GNBAN improves volume-weighted WRMSSE by roughly 4-5% over a matched graph baseline. Qualitative analysis shows the learned decomposition exposes trend, seasonal, and residual demand drivers without post-hoc explanation methods. These results demonstrate that scalable relational forecasting and interpretable forecast decomposition can be achieved together in a unified graph-based framework.

Light curves describe temporal variations in the brightness of celestial objects. Learning robust representations of light curves is essential for large-scale automatic discovery in the dynamic universe, but existing time-series foundation models often struggle with the uneven sampling, complex noise, and wide range of physical timescales that characterize astronomical observations. We propose a domain-informed representation learning framework for irregular astronomical time series with Joint-Embedding predictive architecture (JEPA), combining semantics-preserving views, uncertainty-aware tokenization, and multi-view self-distillation. The encoders are trained with multi-view self-distillation using LeJEPA regularization on the LEAVES dataset and evaluated on the StarEmbed classification benchmark. On StarEmbed, our model outperforms hand-crafted features on 15 of 16 classification metrics. In few-shot linear probing, it achieves macro-F1 scores of 42.56 $\pm$ 7.21 with one sample per class and 63.58 $\pm$ 1.20 with 100 samples per class, consistently improving over hand-crafted features. Beyond variable-star classification, the learned representation supports similarity search, parameter estimation, and photometric zero-point drift detection. We further evaluate cross-domain adaptation on 12 heterogeneous irregular time-series datasets from PYRREGULAR, where the adapted variant matches or exceeds previous state-of-the-art performance on 5 datasets, compared with at most 3 wins by any single prior baseline. These results demonstrate that domain-informed multi-view self-distillation is an effective strategy for learning representations of irregular time series, while also highlighting that successful time-series representation learning requires domain-specific inductive biases rather than a universally optimal architecture.

Traffic matrices (TMs) capture network-wide origin-destination demand and are central to traffic engineering, yet accurate whole-matrix forecasting remains challenging when prediction must be performed under the memory, update, and training-budget constraints of online network control. This paper investigates whether compact quantum-inspired recurrent models can provide effective TM forecasts without relying on dedicated graph, transformer, or diffusion modules. We adapt gated quantum-inspired Kolmogorov-Arnold network fast-weight programmers (QKAN-FWPs) to direct multi-step Abilene TM forecasting, where each model predicts the next 20 five-minute frames of a 144-channel origin-destination (OD) matrix from a two-hour history. We benchmark three QKAN placement variants against a matched-size long short-term memory (LSTM) network, a larger LSTM, and a classical gated fast-weight programmer under a shared fixed-budget training protocol. Among the evaluated recurrent models, G-QKANFWP achieves the best pooled root-mean-square error (RMSE), while using only 22.4% of the larger LSTM. It also outperforms both the matched-size LSTM and the classical G-FWP baseline, indicating that the gain is not due to gated fast-weight framework alone. Convergence and channel-wise analyses further show that the quantum-inspired variants obtain lower validation-loss area under the learning curve (AULC) than matched-size recurrent baselines, while G-QKANFWP and GQKAN-FWP achieve substantially more OD-channel wins. These results identify a classical slow programmer with a quantum-inspired fast programmer as a promising accuracy-efficiency design for resource-conscious network traffic-matrix forecasting.

Dynamic Time Warping (DTW) is a cornerstone for time series classification, but its reliance on Euclidean distances fails to capture latent cross-channel correlations in complex multivariate data. We propose a hybrid Quantum Dynamic Time Warping (qDTW) architecture, replacing the classical distance metric with the parameterized geometry of a quantum Hilbert space. Through structural ablation on benchmarks up to $C=8$ spatial dimensions, we establish fundamental topological rules for quantum sequence alignment. We introduce a Unified Pre-Embedding Adjoint Ansatz that decouples trainable entanglement from classical data, eliminating the severe phase-scrambling and information bottlenecks inherent to traditional measurements. We demonstrate this decoupled architecture allows untrained quantum kernels to act as highly expressive baselines, while parameterized training effectively untangles deeply overlapping hyper-dimensional data. Furthermore, we identify a strict spatial-temporal expressivity tradeoff: temporal depth (data re-uploading) is necessary for dimensionally restricted univariate circuits, but applying it to wide multi-qubit registers triggers chaotic frequency-spectrum explosions and representation collapse. By navigating these topological hazards, our multivariate quantum architecture outperforms classical baselines, setting a new standard for integrating parameterized quantum circuits with dynamic programming

World models are increasingly used for planning, yet most analyses of rollout error assume vector-valued states and scalar error amplification. Many planning environments, however, are naturally graph-structured: agents, tools, skills, routes, and dependencies interact through evolving relations. In this work, we study how prediction errors accumulate in Graph World Models (GWMs). We formulate fixed-edge and dynamic-edge GWM rollouts under a unified state-action transition framework and derive topology-aware error bounds. For fixed-edge rollouts, we show that long-horizon node error separates into a topology factor, governed by the graph spectral radius, and a model factor, governed by layer spectral norms. For dynamic-edge rollouts, we introduce a joint node-edge error operator that captures feedback between feature prediction and structure prediction, revealing when edge errors amplify future message passing. Motivated by these bounds, we propose Error-Aware GWM, a training objective that combines spectral regularization, rollout consistency, and critical-node weighting. Across synthetic graph topologies and heterogeneous agent-graph testbeds, we find that rollout error and planning regret grow with horizon, that dynamic-edge training is necessary when structure evolves, and that Error-Aware GWM improves long-horizon stability without sacrificing one-step accuracy. Our results characterize when graph world models remain reliable under autoregressive planning and when topology makes them fail.

We introduce a neural network-based framework for learning time series estimators through a process we term decision-theoretic pretraining. Analysts specify a generative world, a distribution over data-generating processes, and a target decision objective. A neural network trained on stratified simulations from this world approximates the corresponding optimal decision rule, yielding a neural estimator that provides forecasts, parameter estimates, predictive intervals, or model-selection for zero-shot inference on previously unseen time series. The joint specification of the generative world and objective enables the estimators to directly approximate process-level, finite-sample properties: near-optimal risk, bias control, minimax performance, and uniform calibration. Our experiments demonstrate that these neural estimators can outperform traditional baselines such as maximum likelihood estimation and model selection via AICc, for the same model structural model classes. Furthermore, even when trained purely on simulations of structural models, they achieve competitive or state-of-the-art forecasting accuracy on major real-world benchmarks, compared with statistical, neural or large pre-trained models. We illustrate the framework by addressing two longstanding challenges: finite-sample bias and miscalibration in AR(p) models, and the forecast combination puzzle. These applications highlight the approach's main advantage: its ability to approximate solutions to analytically intractable or computationally prohibitive time series problems, including complex structural equations or optimality criteria. Ultimately, by enabling explicit control over decision-theoretic trade-offs, the framework equips analysts with highly efficient estimation tools tailored to their specific analytical needs.

Inspired by advances in natural language processing and computer vision, "time-series foundation models" (TSFMs) have recently been introduced with the promise of strong generalization across diverse time-series tasks, including forecasting, classification, and anomaly detection, as well as across domains such as healthcare, climate science, and manufacturing. However, their utility for gas-sensing data remains largely unexplored. To address this gap, this paper systematically evaluates recent TSFMs on electronic nose (E-Nose) data. In particular, we investigate whether embeddings produced by representative TSFMs, including Chronos-2 and MOMENT, provide effective representations for gas identification and concentration prediction. Specifically, we show that fine-tuning is necessary to achieve satisfactory performance on E-Nose data, and fusing TSFM embeddings with representations learned by specialized predictive models can further improve the performance, suggesting both the potential and limitations of current TSFMs for gas-sensing applications.

While many explainable AI (XAI) methods have been proposed, most are not designed for time-series forecasting models and often rely on the implicit assumption that timestamp features are independent. This assumption ignores the fundamental property of temporal dependence and can lead to explanations that violate the sequential and causal structure of the data. We introduce \textsc{KARMA}, a method for explaining time-series predictors by constructing a Markov surrogate model that captures the temporal dependencies learned by the predictor. Our approach revolves around three main aspects: identifying the minimal history length $K$ that is predictively sufficient for the model, estimating the best-fitting $K$-order Markov transition kernel from the discretized history space, and a five-level global explanation hierarchy that can be derived from the Markov transition kernel, which we illustrate using real-world weather data (Beijing PM 2.5). We also certify using complex synthetic data with known true causal edges that KARMA (i) recovers the data causal structure as learned by the model via a controlled experiment and (ii) identifies temporal dependencies better than established attribution methods such as TimeSHAP.

Generative models have achieved remarkable success in data synthesis, though recent advances driven by increasing model scale have introduced challenges in computational cost and efficiency. Quantum machine learning offers a promising alternative, representing complex data distributions using compact, highly expressive models. Here, we propose QDiffusion-TS, the first quantum generative diffusion model for time series synthesis, and validate it on the IQM quantum processor. The framework extends a classical diffusion architecture by replacing feed-forward components within the denoising transformer with quantum neural networks, yielding a hybrid quantum transformer that reduces the number of trainable parameters in each replaced component by nearly three orders of magnitude. Evaluated on financial time series from Apple and Amazon, the model generates synthetic data that more accurately reproduces the real distributions, reducing Wasserstein distance by approximately 44% relative to its classical counterpart across both datasets. In a downstream forecasting task, augmentation with the generated data improves predictive performance by up to 71% in RMSE over a baseline trained solely on real data. These results show that quantum enhanced architectures can consistently match and frequently surpass classical performance with substantially fewer parameters, establishing a practical framework towards more efficient and scalable data-driven generative modelling.

Since its initial release in 2020, Darts has become a widely used open-source Python library for time series analysis. A series of foundation models have recently claimed accuracy improvements in zero-shot forecasting, promising a paradigm shift from training custom models to harnessing pre-trained general-purpose forecasters. Foundation models, however, are often released as isolated packages with fragmented interfaces and limited interoperability with common tooling, making joint evaluation and integration within complete pipelines difficult. In Darts, we developed a unified $\texttt{FoundationModel}$ class collection (Chronos-2, TimesFM 2.5, TiRex, PatchTST-FM) that provides standardized, full-cycle forecasting interfaces with minimal external dependencies for integrating foundation models into the ecosystem. Existing Darts pipelines can now use foundation models with only a name change; new pipelines can use them for zero-shot or fine-tuned forecasting, uncertainty estimation, and backtesting, combined with data processing and evaluation tooling, all within a unified framework.