Time Series Representation Learning

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10 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 61

Jun 10, 2026cs.LG

Representing Time Series as Structured Programs for LLM Reasoning

Large language models (LLMs) have demonstrated strong reasoning and instruction-following capabilities, making them potentially powerful tools for time-series analysis. However, time series lie outside their native textual modality, raising a fundamental question: how should time series be represented so that LLMs can reason about them effectively? Existing work typically serializes raw numerical sequences or fine-tunes pre-trained LLMs on time-series data. These approaches place the burden of extracting temporal structure directly on the LLM, creating a modality mismatch that often degrades performance on long sequences and introduces substantial computational overhead. In this work, we introduce Time-Series-to-Structured-Program representation (T2SP), a deterministic, training-free method that represents a time series as a structured symbolic program. T2SP decomposes time series into trends, periods, and salient events, expressing them in a program-friendly format aligned with the textual and code-like modalities on which LLMs are natively trained. By shifting temporal-structure extraction from the model to the representation itself, T2SP enables off-the-shelf LLMs to leverage their existing reasoning capabilities for time-series understanding. We evaluate T2SP on three reasoning tasks -- editing, captioning, and question answering -- where it consistently improves performance, reduces reasoning time, and lowers failure rates compared with raw-string representations. Our results demonstrate that T2SP provides an effective interface between time series and LLMs.

Jaeho Kim, Changhun Oh, Seokhyun Lee +2

Korea University · Mila, University of Montreal

Time Series Reasoning Time Series QA Time Series Representation Learning LLM Reasoning

Jun 9, 2026cs.LG

One Step Closer to Ground Truth: A Multi-Scale Residual-Aware Representation Learning Pipeline for Predicting Time Series Data

Transformer-based models have emerged as leading paradigms in time-series forecasting in recent years, employing self-attention mechanisms to capture long-range dependencies. Despite their success, these single-stage forecasting architectures exhibit persistent systematic residual biases arising from structural discrepancies, unmodeled stochastic components, or inadequate multi-scale temporal representations. This limitation persists when residuals are treated as irreducible noise, precluding adaptive correction of structured error patterns. To address this limitation, we introduce a two-stage, model-agnostic framework that explicitly decouples forecasting and residual learning into distinct stages of representation learning. A base transformer first generates the initial predictions. Subsequently, a dedicated meta-corrector dynamically models structured error patterns across multivariate channels, preserves cross-variable dependencies, and iteratively refines the residual bias of the base transformer. By formalizing this pipeline as a hypothesis space expansion, our framework addresses approximation limitations inherent in single-stage architectures, removes reliance on restrictive assumptions, and enables end-to-end learning of complex error dynamics. Evaluated on eight popular benchmark datasets using established protocols, our approach achieves state-of-the-art performance, with significant improvements in standard metrics (MSE, MAE). The results demonstrate the framework's ability to mitigate systematic biases and enhance robustness to complex temporal dynamics, advancing the practical applicability of transformer-based forecasting models.

Amrijit Biswas, Mustafa Kamal, Robin Krambroeckers +4

Artificial Intelligence Department, RobotBulls Labs Geneva, Switzerland · Department of Electrical and Computer Engineering, North South University Dhaka, Bangladesh

Multivariate Time Series Forecasting Residual Learning Time Series Forecasting Time Series Representation Learning Time Series Transformers Multiscale Time-Series Modeling

Jun 9, 2026cs.LG

LakeFM: Toward a Foundation Model for Aquatic Ecosystems Using Irregular Multivariate Multi-depth Time Series Data

Understanding and forecasting lake dynamics is critical for monitoring water quality and ecosystem health across lakes and reservoirs. While machine learning methods have been recently applied to ecological time-series data, existing works assume regular sampling in time and depth, and struggle to generalize across lakes with heterogeneous variables, depths, and observation patterns. To address these limitations, we introduce \textsc{LakeFM}, a foundation model for aquatic systems, pre-trained on large-scale ecological datasets comprising both simulated and observed lakes. Through extensive empirical evaluation, we show that \textsc{LakeFM} learns meaningful representations spanning broader lake-level characteristics, and achieves competitive or often superior-forecasting performance compared to existing time-series foundation and non-foundation models, while producing physically plausible predictions consistent with real-world lake dynamics.

Abhilash Neog, Sepideh Fatemi, Medha Sawhney +9

Virginia Tech Blacksburg, VA, USA · Grand Valley State University Muskegon, MI, USA · University of Wisconsin - Madison Madison, WI, USA +2

Irregular Time-Series Modeling Multivariate Time Series Forecasting Time Series Representation Learning Time-Series Foundation Models

Jun 8, 2026cs.LG

PAI: Preserving Amplitude Information in Representation-Based Time-Series Anomaly Detection

Representation-based time-series anomaly detection algorithms significantly outperform other methods on diverse anomaly detection tasks. However, we notice that they suffer from a major limitation in our evaluation - their learned embeddings are often amplitude-agnostic. Losing amplitude information can degrade performance on amplitude related anomalies, and this failure is prevalent across all existing representation-based methods. To address aforementioned issues, we propose a new anomaly scoring scheme named PAI. PAI consists of two complementary modules, a diagnostic module and a final score augmentation function. The diagnostic module compares cosine and Euclidean scoring on the same representation bank to test whether amplitude information is already captured in the learned representation. Then in final score augmentation function, PAI computes a point-wise median and MAD deviation score and a local mean-shift score-which are fused with the representation score to produce the final anomaly score. On the TSB-AD-U-Eva and TAB UV datasets, PAI improves all four evaluated representation-based methods across every reported metric, achieving average VUS-PR gains of 98.4% and 36.8%, respectively. Among all evaluated combinations, PaAno + PAI achieves the best performance, outperforming the state-of-the-art method by 15%. Further evaluation on bootstrap confidence intervals, anomaly-type breakdowns, and a TS2Vec input-normalization ablation further support the proposed scheme. These results suggest that explicitly retaining amplitude information is important for representation-based time-series anomaly detection, which has been underemphasized in existing scoring schemes. Code is available at: https://github.com/pantheon5100/PAI

Kang Zhang, Wei Jian Lau, Shoushou Ren +3

1HUAWEI · 2KAIST

Time Series Representation Learning Time-Series Anomaly Detection

Jun 3, 2026cs.LG

Generating Financial Time Series by Matching Random Convolutional Features

Generating realistic financial time series is challenging as training data is often limited to a single historical path. With such scarce data, overfitting is hard to avoid, especially under adversarial training where a trained discriminator can memorize the training samples. To mitigate this, recent approaches train generators to minimize the discrepancy between untrained feature representations of real and generated time series. In these works, the feature maps are based on path signatures, which can fail to capture relevant time series properties at tractable truncation depths. In this work, we instead train generators by matching random convolutional features of real and generated time series. Existing random convolutional feature maps, such as Rocket and Hydra, have been shown to provide informative representations of real-world time series, but cannot supervise generative models because they are non-differentiable. We introduce SOCK (SOft Competing Kernels), a fully differentiable random convolutional feature map, suited to train generative time series models. We show that generators trained by matching random SOCK features consistently outperform signature and diffusion baselines across a wide range of small-sample financial datasets. We further demonstrate SOCK's expressiveness on two-sample hypothesis testing and time series classification tasks, where SOCK matches or outperforms existing unsupervised feature maps.

Konrad J. Mueller, Nikita Zozoulenko, Ben Wood +2

Imperial College London · JPMorgan Chase & Co.‡

Time Series Generation Random Feature Methods Financial Time Series Time Series Representation Learning Finance

May 30, 2026cs.CV

An explainable hierarchical self attention-based approach for tremor detection in the time domain

Tremor is a common movement disorder associated with conditions like Parkinson's disease and Essential tremor, traditionally diagnosed through expert clinician assessment. Current automated detection methods rely on frequency-domain features informed by clinical expertise. In this work, we present an explainable, two-stage hierarchical framework for tremor detection in the time domain that learns tremor patterns directly from 3D kinematic marker time-series data across entire tremor-provoking trials. Our framework combined a deep convolutional and long short-term memory network to learn tremor representations from short, discrete, non-overlapping time segments of kinematic time series data from trials, which are then processed by a vision transformer that models their long-term temporal dynamics of time segment features for trial (session) level classification. Evaluated across nine body parts, the framework achieved F1-scores of 0.594 - 0.947 depending on body parts (average: 0.765), falling short of the frequency-domain state-of-the-art performance (0.909) while requiring minimal preprocessing. Attention weights and gradient-based class activation maps (Grad-CAM) identified time-domain features of tremor across body parts. This proof of concept demonstrated the feasibility of data-driven time-domain modeling for tremor detection across anatomically diverse body parts, while reducing reliance on expert-engineered spectral features and providing posthoc interpretability of temporal and anatomical patterns of tremor.

Timothy Odonga, Jeanne M. Powell, Mark Saad +5

Department of Biomedical Informatics, School of Medicine, Emory University, Atlanta, GA, USA · Jean and Paul Amos Parkinson’s Disease and Movement Disorders Program, Department of Neurology, School of Medicine, Emory University, Atlanta, GA, USA · Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

Time Series Classification Time Series Representation Learning

May 29, 2026cs.LG

Giving Sensors a Voice: Multimodal JEPA for Semantic Time-Series Embeddings

Transformer-based architectures have advanced sequence modeling in language and vision, yet general-purpose representation learning for heterogeneous multivariate time series remains underexplored. We introduce CHARM (Channel-Aware Representation Model), which incorporates channel-level textual descriptions into a Transformer encoder equivariant to channel order. CHARM is trained with a Joint Embedding Predictive Architecture (JEPA) and a novel loss promoting informative, temporally stable embeddings; latent-space prediction encourages robustness to sensor noise while description-aware gating provides interpretability through learned inter-channel relationships. Across anomaly detection, classification, and short- and long-term forecasting, the learned embeddings achieve strong performance using only a linear probe. Performance is driven primarily by the JEPA objective and conditioning architecture, with text descriptions serving as channel identifiers for cross-dataset generalization.

Utsav Dutta, Gerardo Pastrana, Sina Khoshfetrat Pakazad +1

C3 AI, Redwood City, CA, USA

Multivariate Time Series Forecasting Joint-Embedding Predictive Architecture Multimodal Embedding Time Series Representation Learning Time-Series Anomaly Detection

May 29, 2026cs.LG

Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection

Out-of-distribution (OOD) detection for time-series data remains comparatively underexplored compared to vision and language, with a limited principled understanding of how supervised time-series representations can be leveraged for reliable detection under distributional shifts. This work formulates time-series OOD detection as representation learning with hyperspherical embeddings, where class-conditional structure is induced by a von Mises-Fisher (vMF) likelihood-based objective on the unit sphere. The learned representation combines time- and frequency-domain views of the input signal via domain-specific encoders, integrating them into a joint embedding space for OOD detection. Detection uses distance-based scores over the learned embeddings, including k-nearest neighbors (k-NN) and Mahalanobis scores. We evaluate the approach at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results show consistent improvements under both k-NN and Mahalanobis scoring over strong contrastive learning and post-hoc baselines in the same setting. Code is available at https://github.com/tiiuae/hypertf-time-series-ood.

Willian T. Lunardi, Samridha Shrestha, Martin Andreoni

Technology Innovation Institute, Abu Dhabi, United Arab Emirates · Khalifa University, Abu Dhabi, United Arab Emirates

Hyperspherical Representation Learning Distribution Shift Detection Geometric Representation Learning OOD Detection Time Series Representation Learning

May 28, 2026cs.LG

Learning Transferable Predictability Representations

We study the problem of assigning a scalar score to a short trajectory window that reflects its position on an ordered continuum of predictability regimes, spanning structured deterministic dynamics to unstructured stochastic noise. Existing methods address deterministic-versus-stochastic discrimination within a single system and do not produce scores with a consistent numerical interpretation across systems. We formalize this as ordinal estimation over a five-level predictability ladder and identify a structural source of cross-system ambiguity: ranking supervision alone leaves the score coordinate unfixed up to a monotone reparameterization, which we term the gauge freedom of ordinal scoring. We propose the Gauge-Fixed Ordinal Network (GON), a temporal convolutional model trained with an anchor-and-variance objective that pins level-wise score means to shared target coordinates. GON operates on 2-jet features that expose local trajectory geometry, preserved by smooth flows and disrupted by stochastic surrogate procedures. On five held-out dynamical systems, initializing from a pretrained GON checkpoint consistently outperforms training from scratch across all window budgets, with adaptation depth reflecting geometric proximity to the training family. Zero-shot scores retain ordinal structure at the stochastic boundary, where surrogate procedures most strongly disrupt nonlinear geometry, and pretrained initialization consistently beats scratch across all window budgets. Pairwise discrimination and globally coherent ordinal scoring are distinct properties requiring a stable score coordinate for cross-system transfer, with direct implications for predictability assessment, model selection, and early-warning diagnostics across natural and engineered dynamical systems.

Diyali Goswami, Auroop R. Ganguly

Sustainability and Data Sciences Laboratory (SDS Lab), Northeastern University, Boston, MA, USA · AI4CaS: AI for Climate and Sustainability, Institute for Experiential AI, Northeastern University, Boston, MA, USA · Pacific Northwest National Laboratory (PNNL), Richland, WA, USA

Dynamical Systems Ordinal Regression Transfer Learning Time Series Representation Learning

May 28, 2026cs.LG

Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs

Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of reconstruction. We show that this reconstruction step is unnecessary; under mild conditions, compact-set universality on the model input space transfers to the data space whenever the embedding from data to input is continuous and injective. Guided by this result, and building on the rectilinear control path for Neural Controlled Differential Equations (NCDEs), we introduce a continuous and injective embedding for Log-NCDEs, a universal class of continuous-time models. Our approach records observations as increments and composes them over arbitrary query intervals to directly form log-signatures. This provides interval-level summaries without first interpolating the observed variables, while supporting online computation. Experiments on synthetic controlled dynamics and real-world time-series datasets show that the representation is accurate, efficient, and robust to irregular, asynchronous, and sparse observations.

Benjamin Walker, Alexandre Bloch, Lingyi Yang +2

Mathematical Institute University of Oxford · School of Mathematical Sciences University of Nottingham · Department of Mathematics, Imperial College London

Irregular Time-Series Modeling Neural Controlled Differential Equations Neural ODEs Time Series Representation Learning

May 27, 2026cs.LG

QuITE: Query-Based Irregular Time Series Embedding

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to

54.7\%

in forecasting and

15.8\%

in classification across diverse datasets and backbone architectures. Code is available at: https://github.com/Meaningfull9502/QuITE.

Junghoon Lim

SK Shieldus, Seongnam, Republic of Korea

Irregular Time-Series Modeling Multivariate Time Series Forecasting Time Series Classification Time Series Representation Learning

May 25, 2026cs.LG

STaT: Resolving Shape Distortion in Non-Stationary Time Series via Tri-Modal Synergy

Recent research in time series forecasting frequently investigates the integration of textual and visual modalities with numerical models to better navigate non-stationary environments. Despite delivering solid numerical results, existing multi-modal approaches usually encounter a dilemma: prioritizing the minimization of average errors can result in excessively smooth forecasts that overlook essential fluctuations. To resolve this limitation, we introduce STaT, an innovative multimodal architecture for Symbolic-Temporal-Textual Alignment, which seamlessly unites three synergistic modalities. Specifically, the symbolic modality converts continuous time series into discrete tokens, facilitating the accurate identification of structural patterns and turning points; the temporal modality extracts inherent sequential dependencies; and the textual modality leverages domain semantics to steer the macroscopic forecasting trends. Comprehensive evaluations on eight real-world benchmarks indicate that STaT delivers exceptional performance, enhancing conventional magnitude indicators by up to 8.9% while simultaneously decreasing shape distortion by up to 8.5%.

Hui Cheng, Jinsheng Guo, Zhenhao Weng +2

Hefei University of Technology Hefei, China

Non-Stationary Time Series Forecasting Multimodal Fusion Time Series Representation Learning

May 22, 2026cs.LG

Continuity and Ordinality Matter: Constraining Time Series Tokens for Effective Time Series Analysis with Large Language Models

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

Musheng Li, Ziying Zhang, Cheng jin +1

Department of Electronic Engineering Tsinghua University

Time Series Forecasting Time Series Representation Learning Time-Series Foundation Models

May 21, 2026cs.CE

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

Marco Gregnanin, Johannes De Smedt, Giorgio Gnecco +1

IMT School for Advanced Studies Lucca · KU Leuven · University of Chieti-Pescara

Multivariate Time Series Forecasting Graph Structure Learning Hypergraph Neural Networks Time Series Representation Learning Hypergraph Learning

May 21, 2026cs.LG

CASE-NET: Deep Spatio-Temporal Representation Learning via Causal Attention and Channel Recalibration for Multivariate Time Series Classification

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

Fan Zhang, Yating Cui, Hua Wang

Shandong Technology and Business University · Ludong University

Multivariate Time Series Classification Time Series Classification Temporal Attention Time Series Representation Learning

May 19, 2026cs.LG

LLM Pretraining Shapes a Generalizable Manifold: Insights into Cross-Modal Transfer to Time Series

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

Alexis Roger, Prateek Humane, Zhenghan Tai +4

Université de Montréal Mila - Quebec AI Institute

Cross-Modal Learning Language Model Pretraining Representation Geometry LLM-Based Time Series Forecasting Transfer Learning Time Series Representation Learning

May 8, 2026cs.LG

PIMSM: Physics-Informed Multi-Scale Mamba for Stable Neural Representations under Distribution Shift

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

Sangyoon Bae, Shinjae Yoo, Jiook Cha

Interdisciplinary Program in Artificial Intelligence Seoul National University Seoul, South Korea, 08826 · Department of Psychology Seoul National University Seoul, South Korea, 08826

Domain Generalization Physics-Informed ML Time Series Representation Learning Time-Series Foundation Models Multiscale Time-Series Modeling Temporal Distribution Shift+1

May 7, 2026cs.LG

Preliminary Insights in Chronos Frequency Data Understanding and Reconstruction

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

Alessandro Pagani, Marco Cominelli, Liying Han +11

DII, University of Brescia, Italy. · DEIB, Politecnico di Milano, Italy. · ECE Department, University of California, Los Angeles, USA. +6

Frequency-Domain Feature Learning Time Series Representation Learning Time-Series Foundation Models

May 6, 2026cs.LG

The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence

We report a systematic failure mode in predictive representation learning. Across 2695 neural network configurations trained to predict linear-Gaussian dynamics, the optimal encoder tracks the environment rather than the system it is meant to model. The mean causal fidelity -- the fraction of encoder sensitivity allocated to system degrees of freedom -- is 0.49, and only 2.5% of configurations exceed 0.70. The failure intensifies with dimension: at N=100, the optimal encoder becomes causally blind (fidelity ~10^{-8}) while achieving 92% lower prediction error than the causal representation. We prove this is not an optimization artifact but a structural property of the predictive objective: when environment modes are slower or less noisy than system modes, every minimizer of the population risk encodes the former. The set of dynamics exhibiting this predictive-causal gap is open and of positive measure in parameter space. In a nonlinear Duffing-GRU sweep, unconstrained predictors learn environment-dominant representations in 55% of tasks (95% CI 41--68%) versus 24% under operational grounding (p=2.3e-3); the median out-of-distribution MSE inflation under environment shift is 1.82x versus 1.00x. Operational grounding -- restricting the loss to system observables -- partially suppresses the gap, but causal fidelity is never recovered without an explicit system-environment boundary. The results identify the predictive-causal gap as a structural limit of learning, with implications for self-supervised representation learning, world models, and the scaling paradigm.

Kejun Liu

State Key Laboratory of Bioinspired Interface Material Science, Institute of Nano & Functional Materials, Soochow University, Suzhou 215123, China

Causal Representation Learning Predictive Representation Learning Time Series Representation Learning

May 2, 2026cs.LG

From Packets to Patterns: Interpreting Encrypted Network Traffic as Longitudinal Behavioral Signals

Human behavior is difficult to observe continuously at scale, yet it leaves measurable traces in everyday device use. We test whether encrypted smartphone network traffic---a ubiquitous, always-on, passive sensing modality---can passively capture behavioral patterns related to sleep, stress, and loneliness. We model shared behavioral structure using a transformer backbone with per-user adapters, allowing the model to represent both typical individual behavior and deviations from it. To make these representations interpretable, we apply a sparse autoencoder to extract behavioral features corresponding to distinct patterns of activity. We relate these features to sleep disturbance, stress, and loneliness using generalized estimating equations with Mundlak decomposition, separating between-person differences from within-person changes over time. We find that the three outcomes reflect distinct temporal structures: stress is primarily associated with stable between-person differences, loneliness with within-person variation, and sleep disturbance with a combination of both. Notably, these within-person dynamics are not captured by predefined network-traffic features, demonstrating the value of learned representations for longitudinal behavioral sensing. These results establish encrypted network traffic as a viable passive sensing modality, revealing interpretable behavioral dynamics---particularly deviations from an individual's baseline---that are not visible in raw traffic features.

Rameen Mahmood, Omar El Shahawy, Souptik Barua +5

New York University, New York, New York, USA · NYU Langone Health, New York, New York, USA · NYU Grossman School of Medicine, New York, New York, USA +3

Encrypted Network Traffic Analysis Time Series Representation Learning

May 2, 2026cs.LG

Continuous Temporal Representations of Event-Based Signals via Interference-Based Wave Modeling

Spatio-temporal signals arising from event-driven biological processes, such as surface electromyography (sEMG), exhibit asynchronous and highly structured activation patterns that are challenging to model using conventional discrete or purely real-valued representations. In this work, we propose a continuous temporal modeling framework based on interference-based wave representations. The approach maps event-like input signals into a complex-valued latent wave field, where temporal structure is encoded through phase modulation and interactions between latent components. By projecting the resulting wave field onto an energy domain, the model induces structured activation patterns that capture both temporal localization and relational dependencies within finite observation windows, without relying on explicit recurrence or causal state propagation. The proposed formulation is particularly suited for event-driven biosignals, where continuous representations enable efficient gradient-based optimization and robust feature extraction. In particular, the method is designed to support learning from sEMG data for downstream control tasks in biomechanical systems, such as prosthetic devices and exoskeletons. Experimental results demonstrate that the proposed interference-based wave model provides improved representation quality compared to purely real-valued representations, while maintaining computational efficiency suitable for practical deployment.

Magnus Bengtsson

Department of Engineering, University of Borås, Borås, Sweden

Representation Learning Time Series Representation Learning

May 1, 2026cs.LG

CGM-JEPA: Learning Consistent Continuous Glucose Monitor Representations via Predictive Self-Supervised Pretraining

Continuous Glucose Monitoring (CGM) can detect early metabolic subphenotypes (insulin resistance, IR;

β

-cell dysfunction), but population-scale deployment faces two coupled problems. First, the same physiological state appears through multiple views (CGM time series, venous OGTT, Glucodensity summaries), so single-view representations fail to transfer when deployment shifts the modality or setting. Second, baselines perform inconsistently across these shifts. Both problems point to one remedy: representations that abstract away from any single view to capture higher-level temporal and distributional structure. We propose CGM-JEPA, a self-supervised pretraining framework which predicts masked latent representations rather than raw values, yielding abstraction that transfers across modalities. X-CGM-JEPA adds a masked Glucodensity cross-view objective for complementary distributional information. We pretrain on

\sim

389k unlabeled CGM readings from 228 subjects and evaluate on two clinical cohorts (

N=27

and

N=17

public-release subsets) across three regimes (cohort generalization, venous-to-CGM transfer, home CGM) under 20-iteration

\times

2-fold cross-validation. X-CGM-JEPA ranks first or second on AUROC for both endpoints across all three regimes while no baseline does, exceeding the strongest baseline by up to

+6.5

pp in cohort generalization and

+3.6

pp in venous-to-CGM transfer (paired Wilcoxon,

p<0.001

). Under modality shift, it matches mean AUROC while redistributing toward weaker subgroups (ethnicity AUROC gap shrinks 25-54%); on sparse in-domain venous data, the distributional view lifts label-aware clustering (ARI

+39\%

, NMI

+40\%

). Code and weights: https://github.com/cruiseresearchgroup/CGM-JEPA

Hada Melino Muhammad, Zechen Li, Flora Salim +1

University of New South Wales · Google Research

Cross-Modal Representation Learning Self-Supervised Time Series Representation Learning Joint-Embedding Predictive Architecture Predictive Representation Learning Time Series Representation Learning

Apr 30, 2026cs.LG

Learning Fingerprints for Medical Time Series with Redundancy-Constrained Information Maximization

Learning meaningful representations from medical time series (MedTS) such as ECG or EEG signals is a critical challenge. These signals are often high-dimensional, variable-length and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs) are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact and semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of

k

latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are \textit{sufficient statistics} for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically \textit{disentangled} representations. We present the theoretical justification for our method, framing it as a novel \textbf{Disentangled Rate-Distortion} problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.

Huayu Li, ZhengXiao He, Xiwen Chen +4

University of Arizona, AZ, USA · Morgan Stanley, NY, USA · Clemson University, SC, USA +2

Disentangled Representation Learning Rate-Distortion Theory Self-Supervised Time Series Representation Learning Time Series Representation Learning

Apr 29, 2026cs.CV

VTBench: A Multimodal Framework for Time-Series Classification with Chart-Based Representations

Time-series classification (TSC) has advanced significantly with deep learning, yet most models rely solely on raw numerical inputs, overlooking alternative representations. While texture-based encodings such as Gramian Angular Fields (GAF) and Recurrence Plots (RP) convert time series into 2D images, they often require heavy preprocessing and yield less intuitive representations. In contrast, chart-based visualizations offer more interpretable alternatives and show promise in specific domains; however, their effectiveness remains underexplored, with limited systematic evaluation across chart types, visual encoding choices, and datasets. In this work, we introduce VTBench, a systematic and extensible framework that re-examines TSC through multimodal fusion of raw sequences and chart-based visualizations. VTBench generates lightweight, human-interpretable plots -- line, area, bar, and scatter, providing complementary views of the same signal. We develop a modular architecture supporting multiple fusion strategies, including single-chart visual-numerical fusion, multi-chart visual fusion, and full multimodal fusion with raw inputs. Through experiments across 31 UCR datasets, we show that: (1) chart-only models are competitive in selected settings, particularly on smaller datasets; (2) combining multiple chart types can improve accuracy by capturing complementary visual cues; and (3) multimodal models improve or maintain performance when visual features provide non-redundant information, but may degrade accuracy when they introduce redundancy. We further distill practical guidelines for selecting chart types, fusion strategies, and configurations. VTBench establishes a unified foundation for interpretable and effective multimodal time-series classification.

Madhumitha Venkatesan, Xuyang Chen, Dongyu Liu

University of California, Davis Davis, United States

Data Visualization Time Series Classification Multimodal Classification Multimodal Fusion Time Series Representation Learning

Apr 29, 2026cs.CV

Leveraging Imperfect Medical Data: A Manifold-Consistent Spatio-Temporal Network for Sensor-based Human Activity Recognition

Sensor-based Human Activity Recognition (HAR) has attracted increasing attention in medical and healthcare monitoring, particularly with the growth of Internet of Medical Things (IoMT). However, in real-world wearable sensing scenarios, IoMT signals are often corrupted by missing measurements, sensor failures, and environmental noise, which significantly degrade the performance of conventional deep learning models that assume clean and complete inputs. To address this challenge, we propose a Manifold-Consistent Spatio-Temporal Network (MCSTN) for robust HAR under imperfect sensing conditions. The proposed framework introduces a dual-level corruption modeling mechanism that simulates realistic sensor imperfections through both physical-level corruption and diffusion-driven continuous corruption. By enforcing representation consistency across multiple corrupted views, the model learns stable and corruption-invariant semantic representations. Furthermore, we design a dual-stream spatio-temporal architecture that explicitly decouples temporal dynamics modeling and spatial correlation learning. The temporal stream captures long-term activity dynamics, while the spatial stream models inter-sensor relationships, enabling more effective spatio-temporal representation learning. Extensive experiments on three widely used HAR benchmark datasets, PAMAP2, Opportunity, and WISDM, demonstrate that the proposed MCSTN achieves competitive performance compared with existing state-of-the-art methods, particularly under imperfect sensing conditions. These results validate the effectiveness and robustness of the proposed framework for real-world wearable IoMT sensing applications.

Jiangtao Fan, Anish Jindal, Amir Atapour-Abarghouei

Department of Computer Science, Durham University, Durham, DH1 3LE, UK

Human Activity Recognition Wearable Sensing Invariant Representation Learning Time Series Representation Learning

Apr 28, 2026cs.LG

EvoTSC: Evolving Feature Learning Models for Time Series Classification via Genetic Programming

Time series classification is an important analytical task across diverse domains. However, its practical application is often hindered by the scarcity of labeled data and the requirement for substantial computational resources. To address these challenges, this paper proposes EvoTSC, a novel genetic programming approach designed to automatically evolve lightweight feature learning models for time series classification. The core of EvoTSC is a carefully designed multi-layer program structure that strategically embeds diverse forms of prior expert knowledge into the evolutionary process, effectively guiding the search toward operations known to be highly effective for time series analysis. To mitigate the common overfitting problem in time series classification, a tailored Pareto tournament selection strategy is proposed to favor models that perform consistently well across varying training data subsets, promoting the discovery of highly generalizable models. Extensive experiments conducted on univariate time series classification datasets demonstrate that EvoTSC significantly outperforms eleven benchmark methods in most comparisons. Further analyses verify the contribution of each component and the resource efficiency of the evolved models.

Xuanhao Yang, Bing Xue, Mengjie Zhang

Centre for Data Science and Artificial Intelligence & School of Engineering and Computer Science, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand

Time Series Classification Genetic Programming Time Series Representation Learning

Apr 17, 2026cs.LG

Continuous ageing trajectory representations for knee-aware lifetime prediction of lithium-ion batteries across heterogeneous dataset

Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of degradation transitions, such as the knee point, and reliable early-life prediction of remaining useful life (RUL) remain open problems. This study proposes a unified framework for battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). The continuous formulation enables consistent extraction of degradation descriptors, including curvature, plateau length and knee-related metrics, while reducing sensitivity to dataset-specific discretisation. Across more than 250 cells, statistically significant correlations between knee onset and end-of-life (Pearson 0.75-0.84) are observed. Additional early-life analysis confirms that knee-related features retain predictive value when estimated from partial trajectories. Early-life models provide increasingly stable RUL predictions as the number of observed cycles increases, with meaningful predictive performance emerging within the first 5-20 cycles and remain robust under cross-dataset domain shift. The framework integrates continuous modelling, feature extraction and uncertainty-aware prediction, providing an interpretable and dataset-consistent approach demonstrating robustness across heterogeneous dataset types. Compared with conventional discrete or feature-based methods, the proposed representation reduces sensitivity to sampling resolution and improves cross-dataset consistency. The study is limited to laboratory-scale datasets and capacity-based end-of-life definitions.

Agnieszka Pregowska, Stefan Marynowicz

RUL Estimation Domain Generalization Time Series Representation Learning Lithium-Ion Batteries

Mar 26, 2026cs.CV

Hyperspectral Trajectory Image for Multi-Month Trajectory Anomaly Detection

Trajectory anomaly detection underpins applications from fraud detection to urban mobility analysis. Dense GPS preserves fine-grained evidence such as abnormal speeds and short-duration events, but its quadratic cost makes multi-month analysis intractable; sparse stay-point methods scale by discarding that evidence and require a separate modeling regime. We argue that this bottleneck is unnecessary: dense and sparse trajectories share a natural two-dimensional cyclic structure along within-day and across-day axes. TITAnD (Trajectory Image Transformer for Anomaly Detection) is the first framework to cast both in a single representation, a Hyperspectral Trajectory Image (HTI), a day

\times

time-of-day grid whose channels encode spatial, semantic, temporal, and kinematic information. Under this formulation, agent-level detection reduces to image classification and temporal localization to semantic segmentation. The Cyclic Factorized Transformer (CFT) models the two temporal axes directly, reducing attention cost by up to two orders of magnitude. With the HTI, multi-month dense anomaly detection becomes feasible for the first time, and CFT keeps it accurate and fast. Empirically, TITAnD matches or beats every evaluated baseline in AUC-PR on all four benchmarks. It surpasses vision models such as U-Net while using as few as 6.5M parameters, and it runs 11--75

\times

faster than a capacity-matched flat Transformer on the same trajectory images.

Md Awsafur Rahman, Chandrakanth Gudavalli, Hardik Prajapati +1

UC Santa Barbara, USA

Anomaly Localization Transformer Attention Time Series Representation Learning Time-Series Anomaly Detection

Feb 1, 2026cs.LG

PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection

Although recent studies on time-series anomaly detection have increasingly adopted ever-larger neural network architectures such as transformers and foundation models, they incur high computational costs and memory usage, making them impractical for real-time and resource-constrained scenarios. Moreover, they often fail to demonstrate significant performance gains over simpler methods under rigorous evaluation protocols. In this study, we propose Patch-based representation learning for time-series Anomaly detection (PaAno), a lightweight yet effective method for fast and efficient time-series anomaly detection. PaAno extracts short temporal patches from time-series training data and uses a 1D convolutional neural network to embed each patch into a vector representation. The model is trained using a combination of triplet loss and pretext loss to ensure the embeddings capture informative temporal patterns from input patches. During inference, the anomaly score at each time step is computed by comparing the embeddings of its surrounding patches to those of normal patches extracted from the training time-series. Evaluated on the TSB-AD benchmark, PaAno achieved state-of-the-art performance, significantly outperforming existing methods, including those based on heavy architectures, on both univariate and multivariate time-series anomaly detection across various range-wise and point-wise performance measures.

Jinju Park, Seokho Kang

Department of Industrial Engineering, Sungkyunkwan University

Self-Supervised Time Series Representation Learning Time Series Representation Learning Time-Series Anomaly Detection

Jun 10, 2025cs.LG

Unlocking Pretrained Vision Transformers for Time Series Classification

Adapting vision models for time series analysis is compelling, yet all existing approaches are falling short of dedicated time series foundation models (TSFMs) in classification. In this work, we propose Time Vision Transformer (TiViT), the first framework that successfully unlocks the representational power of frozen Vision Transformers (ViTs) pretrained on large-scale image datasets for time series classification. TiViT achieves state-of-the-art performance without any finetuning by utilizing the hidden representations of OpenCLIP models. We explore the structure of TiViT representations and find that intermediate ViT layers with high intrinsic dimension are the most effective for time series classification. Furthermore, we assess the alignment between TiViT and TSFM representation spaces and identify a strong complementarity, with additional performance gains achieved through feature concatenation. Finally, we unfreeze the ViT backbone of TiViT for continual pretraining and contrastive alignment with TSFMs on time series, enhancing the performance of lightweight TiViT variants. Our findings reveal a new direction for the domain and task adaptation of vision foundation models. Code is available at https://github.com/ExplainableML/TiViT.

Simon Roschmann, Quentin Bouniot, Vasilii Feofanov +2

Helmholtz Munich · Technical University of Munich · Munich Center for Machine Learning +2

Time Series Classification Vision Transformer Vision Foundation Model Adaptation Time Series Representation Learning