Irregular multivariate time series (IMTS) are prevalent in critical domains like healthcare and finance, where accurate forecasting is vital for proactive decision-making. However, the asynchronous sampling and irregular intervals inherent to IMTS pose two core challenges for existing methods: (1) how to accurately represent the raw information of irregular time series without introducing data distortion, and (2) how to effectively capture the complex dynamic dependencies between observation points. To address these challenges, we propose the Adaptive Spatio-Temporal Graph Interaction (ASTGI) framework. Specifically, the framework first employs a Spatio-Temporal Point Representation module to encode each discrete observation as a point within a learnable spatio-temporal embedding space. Second, a Neighborhood-Adaptive Graph Construction module adaptively builds a causal graph for each point in the embedding space via nearest neighbor search. Subsequently, a Spatio-Temporal Dynamic Propagation module iteratively updates information on these adaptive causal graphs by generating messages and computing interaction weights based on the relative spatio-temporal positions between points. Finally, a Query Point-based Prediction module generates the final forecast by aggregating neighborhood information for a new query point and performing regression. Extensive experiments on multiple benchmark datasets demonstrate that ASTGI outperforms various state-of-the-art methods.
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SwiftTS: A Swift Selection Framework for Time Series Pre-trained Models via Multi-task Meta-Learning
Applications · Time Series
Pre-trained models exhibit strong generalization to various downstream tasks. However, given the numerous models available in the model hub, identifying the most suitable one by individually fine-tuning is time-consuming. In this paper, we propose \textbf{SwiftTS}, a swift selection framework for time series pre-trained models. To avoid expensive forward propagation through all candidates, SwiftTS adopts a learning-guided approach that leverages historical dataset-model performance pairs across diverse horizons to predict model performance on unseen datasets. It employs a lightweight dual-encoder architecture that embeds time series and candidate models with rich characteristics, computing patchwise compatibility scores between data and model embeddings for efficient selection. To further enhance the generalization across datasets and horizons, we introduce a horizon-adaptive expert composition module that dynamically adjusts expert weights, and the transferable cross-task learning with cross-dataset and cross-horizon task sampling to enhance out-of-distribution (OOD) robustness. Extensive experiments on 14 downstream datasets and 8 pre-trained models demonstrate that SwiftTS achieves state-of-the-art performance in time series pre-trained model selection. The code and datasets are available at \href{}{https://github.com/decisionintelligence/SwiftTS}.
Applications · Time Series
While many advances in time series models focus exclusively on numerical data, research on multimodal time series, particularly those involving contextual textual information, remains in its infancy. With recent progress in large language models and time series learning, we revisit the integration of paired texts with time series through the Platonic Representation Hypothesis, which posits that representations of different modalities converge to shared spaces. In this context, we identify that time-series-paired texts may naturally exhibit periodic properties that closely mirror those of the original time series. Building on this insight, we propose a novel framework, Texts as Time Series (TaTS), which considers the time-series-paired texts to be auxiliary variables of the time series. TaTS can be plugged into any existing numerical-only time series models and effectively enable them to handle time series data with paired texts. Through extensive experiments on both multimodal time series forecasting and imputation tasks across benchmark datasets with various existing time series models, we demonstrate that TaTS can enhance multimodal predictive performance without modifying model architectures. Our Code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/TaTS
Applications · Time Series
Explaining predictions of black-box time-series models remains a challenging problem due to the dynamically evolving patterns within individual sequences and their complex temporal dependencies. Unfortunately, existing explanation methods largely focus on point-wise explanations, which fail to capture broader temporal context, while methods that attempt to highlight interpretable temporal patterns (e.g., achieved by incorporating a regularizer or fixed-length patches) often lack principled definitions of meaningful segments. This limitation frequently leads to fragmented and confusing explanations for end users. As such, the notion of segment-wise explanations has remained underexplored, with little consensus on what constitutes an *interpretable* segment or how such segments should be identified. To bridge this gap, we define segment-wise explanation for black-box time-series models as the task of selecting contiguous subsequences that maximize their joint mutual information with the target prediction. Building on this formulation, we propose TimeSeg, a novel information-theoretic framework that employs reinforcement learning to sequentially identify predictive temporal segments at a per-instance level. By doing so, TimeSeg produces segment-wise explanations that capture holistic temporal patterns rather than fragmented points, providing class-predictive patterns in a human-interpretable manner. Extensive experiments on both synthetic and real‑world datasets demonstrate that TimeSeg produces more coherent and human-understandable explanations, while achieving performance that matches or surpasses existing methods on downstream tasks using the identified segments.
Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias—the natural tendency to prioritize certain events or stimuli—we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules with attentional bias. We define and formalize the concept of attentional bias as the internal memory objective deep learning architectures. We show that existing deep learning architectures leverage the same attentional bias based on $L_2$ loss function. Going beyond $L_2$ loss function, we present a set of alternative attentional bias configurations along with their effective approximations. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on the choice of attentional bias objective, retention gate, associative memory architecture, and memory learning algorithm. Our experiments show different designs yield models with varying strengths. Furthermore, our special instances of Miras achieve exceptional performance in language modeling, commonsense reasoning, recall intensive, and time series tasks, outperforming Transformers and other modern linear recurrent models.
We give a comprehensive theoretical analysis of transformers as time series pre- diction models, with a focus on MOIRAI (Woo et al., 2024). We study its ap- proximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, one of the state-of-the-art multivariate time series prediction models capable of modeling arbitrary number of covariates. We prove that MOIRAI is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and em- pirical success. For generalization, we establish learning bounds for pretraining when the data satisfies Dobrushin’s condition. Experiments support our theoretical findings, highlighting the efficacy of using transformers for time series forecasting.
Applications · Health
Wearable sensors provide abundant physiological time series observations, yet the resolution at which we should extract features for downstream tasks remain unclear. We hypothesize that temporal resolution is a fundamental axis of representation learning, with different clinical and behavioral outcomes relying on features at distinct scales. To test this resolution hypothesis, we introduce HiMAE (Hierarchical Masked Autoencoder), a self-supervised framework that combines masked autoencoding with a hierarchical convolutional encoder–decoder. HiMAE produces multi-resolution embeddings across its intermediate layers that enable systematic evaluation of which temporal scales carry predictive signal, transforming resolution from a hyperparameter into a probe for interpretability. Across classification and generative benchmarks, HiMAE consistently outperforms state-of-the-art foundation models that collapse scale, while being orders of magnitude smaller. Due to the convolution based design choices behind HiMAE, the model is also compact enough to run entirely on-device, achieving sub-millisecond inference on smartwatch-class CPUs for true edge inference. Together, these contributions position HiMAE as both an efficient self supervised learning method and a discovery tool for understanding how time resolution contributes to downstream task alignment.
Applications · Time Series
Fluid-solid interaction (FSI) problems are fundamental in many scientific and engineering applications, yet effectively capturing the highly nonlinear two-way interactions remains a significant challenge. Most existing deep learning methods are limited to simplified one-way FSI scenarios, often assuming rigid and static solid to reduce complexity. Even in two-way setups, prevailing approaches struggle to capture dynamic, heterogeneous interactions due to the lack of cross-domain awareness. In this paper, we introduce **Fisale**, a data-driven framework for handling complex two-way **FSI** problems. It is inspired by classical numerical methods, namely the Arbitrary Lagrangian–Eulerian (**ALE**) method and the partitioned coupling algorithm. Fisale explicitly models the coupling interface as a distinct component and leverages multiscale latent ALE grids to provide unified, geometry-aware embeddings across domains. A partitioned coupling module (PCM) further decomposes the problem into structured substeps, enabling progressive modeling of nonlinear interdependencies. Compared to existing models, Fisale introduces a more flexible framework that iteratively handles complex dynamics of solid, fluid and their coupling interface on a unified representation, and enables scalable learning of complex two-way FSI behaviors. Experimentally, Fisale excels in three reality-related challenging FSI scenarios, covering 2D, 3D and various tasks. The code is available at https://github.com/therontau0054/Fisale.
Deep Learning · Generative Models and Autoencoders
Score-based generative modeling through differential equations has driven breakthroughs in high-fidelity image synthesis, offering modular model design and efficient sampling. However, this success has not been widely translated to timeseries forecasting yet. This gap stems from the sequential nature of time series, in contrast to the unordered structure of images. Here, we extend the theoretical formulation used for images to explicitly address sequential structures. We propose a diffusion-based forecasting framework (TEDM) that adapts score estimation to temporal settings and elucidates its design space. Such a design allows empirical computation of noise and signal scaling directly from data, avoiding external schedules. Notably, this reduces sampling complexity to linear in the forecast horizon. Without elaborate preprocessing, TEDM sets new state-of-the-art results on multiple forecasting benchmarks. These results illustrate the growing potential of diffusion models beyond vision. TEDM generates low-latency forecasts using a lightweight architecture, making it ideal for real-time deployment.
Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and (2) *contrastive reasons*, which are subsets of input features that, when modified, alter a prediction. Prior studies have examined these explanations in different contexts, such as non-probabilistic versus probabilistic frameworks and local versus global settings. In this study, we introduce a unified framework for analyzing these explanations, demonstrating that they can all be characterized through the minimization of a unified probabilistic value function. We then prove that the complexity of these computations is influenced by three key properties of the value function: (1) *monotonicity*, (2) *submodularity*, and (3) *supermodularity* - which are three fundamental properties in *combinatorial optimization*. Our findings uncover some counterintuitive results regarding the nature of these properties within the explanation settings examined. For instance, although the *local* value functions do not exhibit monotonicity or submodularity/supermodularity whatsoever, we demonstrate that the *global* value functions do possess these properties. This distinction enables us to prove a series of novel polynomial-time results for computing various explanations with provable guarantees in the global explainability setting, across a range of ML models that span the interpretability spectrum, such as neural networks, decision trees, and tree ensembles. In contrast, we show that even highly simplified versions of these explanations become NP-hard to compute in the corresponding local explainability setting.
General Machine Learning · Causality
Learning instantaneous and time-lagged causal relationships from time-series data is essential for uncovering fine-grained, temporally-aware interactions. Although this problem has been formulated as a continuous optimization task amenable to modern machine learning methods, existing approaches largely neglect the use of coarse-grained, lag-agnostic causal priors, an important form of prior knowledge that is often available in practice. To address this gap, we propose a novel framework for structure learning from time series to integrate lag-agnostic priors, enabling the discovery of lag-specific causal links without requiring precise temporal annotations. We introduce formulations to precisely characterize the lag-agnostic prior, and demonstrate their consequential and process-equivalence to priors, maintaining consistency with the intended semantics of the priors throughout optimization. We further analyze the challenge for optimization due to the increased non-convexity by lag-agnostic prior constraints, and introduce a data-driven initialization to mitigate this issue. Experiments on both synthetic and real-world datasets show that our method effectively incorporates lag-agnostic prior knowledge to enhance the recovery of fine-grained, lag-aware structures.
Theory · Reinforcement Learning and Planning
We study decision making with structured observation (DMSO). The complexity for DMSO has been characterized by a series of work [ FKQR21 , CMB22 , FGH23 ]. Still, there is a gap between known regret upper and lower bounds: current upper bounds incur a model estimation error that scales with the size of the model class. The work of [FGQ+23 ] made an initial attempt to reduce the estimation error to only scale with the size of the value function set, resulting in the complexity called optimistic decision-estimation coefficient (optimistic DEC). Yet, their approach relies on the optimism principle to drive exploration, which deviates from the general idea of DEC that drives exploration only through information gain. In this work, we introduce an improved model-free DEC, called Dig-DEC, that removes the optimism mechanism in [FGQ+23 ], making it more aligned with existing model-based DEC. Dig-DEC is always upper bounded by optimistic DEC, and could be significantly smaller in special cases. Importantly, the removal of optimism allows it to seamlessly handle adversarial environments, while it was unclear how to achieve it within the optimistic DEC framework. By applying Dig-DEC to hybrid MDPs where the transition is stochastic but the reward is adversarial, we provide the first model-free regret bounds in hybrid MDPs with bandit feedback in multiple settings: bilinear classes, Bellman-complete MDPs with bounded Bellman-eluder dimension or coverability, resolving the main open problem left by [LWZ25]. We also improve online function-estimation procedure used in model-free learning: For average estimation error minimization, we improve the estimator to achieve better concentration. This improves the $T^{\frac{3}{4}}$ and $T^{\frac{5}{6}}$ regret of [FGQ+23 ] to $T^{\frac{2}{3}}$and $T^{\frac{7}{9}}$ in the cases with on-policy and off-policy exploration. For squared estimation error minimization in Bellman-complete MDPs, we redesign the two-timescale procedure in [ AZ22 , FGQ+23], achieving $\sqrt{T}$ regret that improves over the $T^{\frac{2}{3}}$ regret by [ FGQ+23 ]. This is the first time the performance of a DEC-based approach for Bellman-complete MDPs matches that of optimism-based approaches [JLM21, XFB+23].
Applications · Time Series
Synthetic time series generation (TSG) is crucial for applications such as privacy preservation, data augmentation, and anomaly detection. A key challenge in TSG lies in modeling the multi-modal distributions of time series, which requires simultaneously capturing diverse high-level representation distributions and preserving local temporal fidelity. Most existing diffusion models, however, are constrained by their single-space focus: latent-space models capture representation distributions but often compromise local fidelity, while data-space models preserve local details in the data space but struggle to learn high-level representations essential for multi-modal time series. To address these limitations, we propose L2D-Diff, a dual-space diffusion framework for synthetic time series generation. Specifically, L2D-Diff first compresses input sequences into a latent space to efficiently model the distribution of time series representations. The distribution then guides a data-space diffusion model to refine local data details, enabling faithful generation of time series distribution without relying on external conditions. Experiments on both single-modal and multi-modal datasets demonstrate the effectiveness of L2D-Diff in tackling unconditional TSG tasks. Ablation studies further highlight the necessity and impact of its dual-space design, showcasing its capability to achieve representation coherence and local fidelity.
CPiRi: Channel Permutation-Invariant Relational Interaction for Multivariate Time Series Forecasting
Deep Learning · Everything Else
Current methods for multivariate time series forecasting can be classified into channel-dependent and channel-independent models. Channel-dependent models learn cross-channel features but often overfit the channel ordering, which hampers adaptation when channels are added or reordered. Channel-independent models treat each channel in isolation to increase flexibility, yet this neglects inter-channel dependencies and limits performance. To address these limitations, we propose CPiRi, a channel permutation invariant (CPI) framework that infers cross-channel structure from data rather than memorizing a fixed ordering, enabling deployment in settings with structural and distributional co-drift without retraining. CPiRi couples spatio-temporal decoupling architecture with permutation-invariant regularization training strategy: a frozen pretrained temporal encoder extracts high-quality temporal features, a lightweight spatial module learns content-driven inter-channel relations, while a channel shuffling strategy enforces CPI during training. We further ground CPiRi in theory by analyzing permutation equivariance in multivariate time series forecasting. Experiments on multiple benchmarks show state-of-the-art results. CPiRi remains stable when channel orders are shuffled and exhibits strong inductive generalization to unseen channels even when trained on only half of the channels, while maintaining practical efficiency on large-scale datasets. The source code is released at https://github.com/JasonStraka/CPiRi.
Applications · Time Series
Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.
Applications · Time Series
Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and engineering problems. As real-world physical environments like PDE system parameters are always capricious, how to generalize across unseen out-of-distribution (OOD) forecasting scenarios using limited training data is of great importance. To bridge this barrier, existing methods focus on discovering domain-generalizable representations across various PDE dynamics trajectories. However, their zero-shot OOD generalization capability remains deficient, since extra test-time samples for domain-specific adaptation are still required. This is because the fundamental physical invariance in PDE dynamical systems are yet to be investigated or integrated. To this end, we first explicitly define a two-fold PDE invariance principle, which points out that ingredient operators and their composition relationships remain invariant across different domains and PDE system evolution. Next, to capture this two-fold PDE invariance, we propose a physics-guided invariant learning method termed iMOOE, featuring an Invariance-aligned Mixture Of Operator Expert architecture and a frequency-enriched invariant learning objective. Extensive experiments across simulated benchmarks and real-world applications validate iMOOE's superior in-distribution performance and zero-shot generalization capabilities on diverse OOD forecasting scenarios.
Applications · Time Series
We address multivariate time–series imputation by learning the velocity field of a data-conditioned ordinary differential equation (ODE) via flow matching. Our method, Time-Gated Multi-Scale Flow Matching (TG-MSFM), conditions the flow on a structured endpoint comprising observed values, a per-time visibility mask, and short left/right context, processed by a time-aware Transformer whose self-attention is masked to aggregate only from observed timestamps. To recon- cile global trends with local details along the trajectory, we introduce time-gated multi-scale velocity heads on a fixed 1D pyramid and blend them through a time- dependent gate; a mild anti-aliasing filter stabilizes the finest branch. At inference, we use a second-order Heun integrator with a per-step data-consistency projection that keeps observed coordinates exactly on the straight path from the initial noise to the endpoint, reducing boundary artifacts and drift. Training adopts gap-only supervision of the velocity on missing data coordinates, with small optional regu- larizers for numerical stability. Across standard benchmarks, Time-Gated Multi- Scale Flow Matching attains competitive or improved MSE/MAE with favorable speed–quality trade-offs, and ablations isolate the contributions of the time-gated multi-scale heads, masked attention, and the data-consistent ODE integration
Applications · Time Series
Unknown unknowns (U2s) are deployment-time scenarios absent from development/testing. Unlike conventional anomalies, U2s are not out-of-distribution (OOD); they stem from changes in underlying system dynamics without a distribution shift from normal data. Thus, existing multi-variate time series anomaly detection (MTAD) methods—which rely on distribution-shift cues—are ill-suited for U2 detection. Specifically: (i) we show most anomaly datasets exhibit distribution shift between normal and anomalous data and therefore are not representative of U2s; (ii) we introduce eight U2 benchmarks where training data contain OOD anomalies but no U2s, while test sets contain both OOD anomalies and U2s; (iii) we demonstrate that state-of-the-art (SOTA) MTAD results often depend on impractical enhancements: point adjustment (PA) (uses ground truth to flip false negatives to true positives, inflating precision) and threshold learning with data leakage (TL) (tuning thresholds on test data and labels); (iv) with PA+TL, even untrained deterministic methods can match or surpass MTAD baselines; (v) without PA/TL, existing MTAD methods degrade sharply on U2 benchmarks. Finally, we present sparse model identification–enhanced anomaly detection (SPIE-AD), a model-recovery-and-conformance, zero-shot MTAD approach that outperforms baselines on all eight U2 benchmarks and on six additional real-world MTAD datasets—without PA or TL. Code and data available in https://github.com/ImpactLabASU/U2Recognition.
Deep Learning · Attention Mechanisms
Standard attention stores keys/values losslessly but reads them via a per-head convex average, blocking channel-wise selection. We propose the Free Energy Mixer (FEM): a free-energy (log-sum-exp) read that applies a value-driven, per-channel log-linear tilt to a fast prior (e.g., from queries/keys in standard attention) over indices. Unlike methods that attempt to improve and enrich the $(q,k)$ scoring distribution, FEM treats it as a prior and yields a value-aware posterior read at unchanged complexity, smoothly moving from averaging to per-channel selection as the learnable inverse temperature increases, while still preserving parallelism and the original asymptotic complexity ($O(T^2)$ for softmax; $O(T)$ for linearizable variants). We instantiate a two-level gated FEM that is plug-and-play with standard and linear attention, linear RNNs and SSMs. It consistently outperforms strong baselines on NLP, vision, and time-series at matched parameter budgets.
As large language models (LLMs) continue to revolutionize AI research, there is a growing interest in building large-scale brain foundation models to advance neuroscience. While most existing brain foundation models are pre-trained on time-series signals or connectome features, we propose a novel graph-based pre-training paradigm for constructing a brain graph foundation model. In this paper, we introduce the Brain Graph Foundation Model, termed BrainGFM, a unified framework that leverages graph contrastive learning and graph masked autoencoders for large-scale fMRI-based pre-training. BrainGFM is pre-trained on a diverse mixture of brain atlases with varying parcellations, significantly expanding the pre-training corpus and enhancing the model’s ability to generalize across heterogeneous fMRI-derived brain representations. To support efficient and versatile downstream transfer, we integrate both graph prompts and language prompts into the model design, enabling BrainGFM to flexibly adapt to a wide range of atlases, neurological and psychiatric disorders, and task settings. Furthermore, we employ meta-learning to optimize the graph prompts, facilitating strong generalization to previously unseen disorders under both few-shot and zero-shot learning conditions via language-guided prompting. BrainGFM is established on 27 neuroimaging datasets spanning 25 common neurological and psychiatric disorders, encompassing 2 types of brain atlases (functional and anatomical) across 8 widely used parcellations, and covering over 25,000 subjects, 60,000 fMRI scans, and a total of 400,000 graph samples aggregated across all atlases and parcellations. The code is available at https://github.com/weixinxu666/BrainGFM.