Time_Series
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CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Series
2026-09-30 10:47:01Maxx Richard Rahman, Mostafa Hammouda, Wolfgang MaassAbstract
Longitudinal clinical cohorts are multimodal, irregularly sampled and pervasively incomplete: in ADNI, positron emission tomography and cerebrospinal fluid assays are absent from roughly half of all visits. Linear state-space models handle irregular sampling gracefully but treat a missing modality by masking the input, leaving the transition operator untouched. We prove that this is a representational limitation: the latent state of any linear state-space layer whose transition operator does not depend on the availability pattern is an additive function of the availability indicators, so no such layer can represent an interaction between two modalities being jointly present or jointly absent. We propose CAMOS, which gives each modality a bank of second-order oscillators coupled through a matrix that sits inside the differential equation and is gated by availability, so the transition operator itself becomes a function of which measurements were taken. Coupling invalidates the analysis of uncoupled oscillatory models, and we restore it: a per-channel Gershgorin budget makes the effective stiffness positive definite uniformly over all $2^M$ availability patterns and all gaps, an energy argument charges amplification to availability transitions rather than sequence length, and a channel factorization preserves exact associative parallel scans. On ADNI, CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on same-visit staging, landmark prediction and longitudinal forecasting, and under zero-shot transfer to OASIS-3 it is the only model that avoids collapse to the majority class.
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URL
https://arxiv.org/abs/2609.39484
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Inferring Causal Relations between Two Sequences of Events with Language Models
2026-09-30 09:51:33Nishchal Prasad, Eric Gaussier, Emilie Devijver, Alexander Obeid Guzman, Armen Aghasaryan, Gregor G\"osslerAbstract
Causal AI is a branch of Artificial Intelligence which helps understand and reason about cause and effect relationships, not just patterns or correlations. Causal discovery aims to infer elements of the underlying causal structure--often represented as a directed graph--from observational and, when available, interventional data. While causal discovery is the fundamental step for moving beyond mere associations toward genuine understanding, and thus the basic building block of causal AI, it becomes intrinsically difficult when causal relations must be inferred from single observations. In such situations, standard causal discovery methods cannot be used and one has to identify causal relations from limited amount of information. This is typically the case for, e.g., sequences of events produced by different alarms which need to be analyzed on the fly to detect abnormal phenomena, which are usually rare. We show in this study that it is possible to leverage the predictive power of Large Language Models (LLMs) to infer causal relations between only two sequences of events. This approach, which is validated on both synthetic and real data, provides better results than standard causal discovery algorithms on several time series data, even though these data were converted into smaller, single observed sequences.
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URL
https://arxiv.org/abs/2609.39406
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Wavelet Flow Matching for Time Series
2026-09-30 09:25:21Lucas Poinsignon, Jorge da Silva Gon\c{c}alves, Samuel Ruip\'erez-Campillo, Julia E. VogtAbstract
Synthetic time series are increasingly used for data augmentation, privacy-preserving data sharing, and downstream model development, yet faithfully reproducing both multi-scale temporal structure and cross-channel dependencies remains challenging. We study multivariate time-series generation through flow matching in the wavelet domain. By operating on multilevel discrete wavelet coefficients rather than directly in the time domain, the model represents coarse structure and progressively finer details at separate scales. Their naturally different variances further induce an implicit coarse-to-fine generative process without requiring an explicit multi-scale schedule. Since the transform acts independently on each channel, we pair it with a channel-token transformer whose attention directly models cross-channel dependencies. Across seven benchmark datasets and four sequence lengths, our method is best or tied on a majority of dataset-metric combinations, with the largest and most consistent improvements in Context-FID and discriminative score.
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URL
https://arxiv.org/abs/2609.39374
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WinoTS: Wavelet-based Self-Distillation for Time Series Models
2026-09-30 09:06:05Noam Major, Kathy Razmadze, Yoli ShavitAbstract
Self-supervised pre-training of time series models is currently dominated by next-token prediction and reconstruction objectives. In continuous-valued domains, these paradigms often waste model capacity on high-frequency, point-wise noise at the expense of learning invariant structure. While invariance-based self-distillation has proven highly effective in computer vision, its application to temporal data remains largely underexplored. Effectively adapting such methods to time series requires carefully designed augmentations: spatial operations like cropping can shift the timing of repeating cycles or distort the signal, while basic jittering may provide limited variation. We introduce Wavelet-based self-distillation for time series (WinoTS), an invariance-based pre-training paradigm designed specifically for temporal signals. At its core, WinoTS leverages time-frequency augmentations to construct multi-scale structural views without distorting underlying signal dynamics. Across extensive evaluations, WinoTS outperforms state-of-the-art baselines in long-term forecasting, cross-domain zero-shot transfer, and unsupervised anomaly detection. Notably, linear probing on frozen WinoTS representations frequently surpasses fully supervised models trained from scratch. Systematic ablations demonstrate that WinoTS is a flexible, architecture-agnostic framework yielding gains across time series backbones, and establish that time-frequency transformations provide a principled alternative to vision-style spatial augmentations.
Abstract (translated)
URL
https://arxiv.org/abs/2609.39337
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A Time-Aware Bag-of-Receptive-Fields for Interpretable Irregular Time Series Classification
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Irregular time series, characterized by non-uniform sampling intervals, missing observations, and variable lengths, are ubiquitous in healthcare, mobility, and environmental monitoring, yet effective and interpretable classifiers for this setting are limited. Existing approaches often rely on imputation, which can obscure the temporal structure of the data, or require complex neural architectures that are opaque and difficult to explain. In this work, we extend the Bag-Of-Receptive-Fields (BORF), a fast, deterministic, and interpretable transform for time series, to the irregular setting. Our key contribution is a time-weighted normalization scheme in which each observation is weighted proportionally to its associated time delta, making pattern extraction sensitive to the actual temporal distribution of samples rather than only their index position. This requires deriving an efficient sliding-window recurrence for the time-weighted standard deviation, preserving the linear time complexity of BORF. We benchmark the resulting method against state-of-the-art irregular time series classifiers on datasets from the PYRREGULAR repository, demonstrating competitive classification performance with the added benefit of human-interpretable explanations.
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URL
https://arxiv.org/abs/2609.39268
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From Benchmarks to Production: Transferring Time Series Anomaly Detection Methods for Electricity Production Monitoring
2026-09-30 08:20:20Nicolas Vautier, Paul Caron, Nardi Xhepi, F\'elicie Bizeul, Manel Boumghar, Christophe Degouy, Paul BoniolAbstract
Accurate forecasting of electricity production is essential for maintaining the operational efficiency and strategic planning of energy utilities. In industrial settings, such forecasts are generated daily to ensure supply-demand balance and optimal management of production assets. However, the increasing complexity of modern power systems and data flows poses significant challenges for ensuring the reliability and consistency of these forecasts. This paper addresses the problem of anomaly detection in short-term production forecasts at EDF, formulated as identifying atypical intra-day patterns that may signal data quality issues or operational irregularities. We introduce TAMIS, a scalable and interpretable system that analyzes daily production time series to automatically detect anomalous days based on deviations from historical patterns learned from past data. Designed for human-in-the-loop workflows, TAMIS surfaces top-ranked anomalies through an automated daily newsletter, enabling efficient expert review and continuous monitoring. An extensive experimental evaluation on real-world industrial data demonstrates that TAMIS achieves the best accuracy-efficiency trade-off compared to baseline methods. To foster further research and reproducibility, we publicly release the anonymized application datasets used in our study.
Abstract (translated)
URL
https://arxiv.org/abs/2609.39257
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What Streaming Anomaly Detection Finds in Industrial Time Series
2026-09-30 08:04:26Magali Parrino, Antoine Ajenjo, Emmanuel Remy, Pierre Stephan, Paul BoniolAbstract
EDF relies on continuous monitoring of its power plants to detect anomalies as soon as they occur. Given the absence of a universally optimal streaming method in unsupervised settings, we compare streaming methods with state-of-the-art TSAD models deployed online on a real nuclear power plant dataset. This work also evaluates Automated Anomaly Detection in a streaming context. Results show higher consistency for online TSAD and strong robustness from ensembling strategies.
Abstract (translated)
URL
https://arxiv.org/abs/2609.39232
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In a Streaming World, Should You Stand Still? A Comprehensive Benchmark of Anomaly Detection in Streams
2026-09-30 07:56:52Magali Parrino, Antoine Ajenjo, Emmanuel Remy, Pierre Stephan, Pierre Senellart, Paul BoniolAbstract
Time series anomaly detection (TSAD) is increasingly deployed in streaming settings, where data arrive sequentially and may exhibit non-stationarity. As a result, several works from the recent literature propose streaming anomaly detection methods that rely on incremental updates to adapt over time. However, most of these approaches originate from the streaming outlier detection literature and largely ignore core characteristics of time series anomalies. Moreover, their empirical evaluation is typically conducted on synthetic or small-scale benchmarks with limited diversity, making it unclear whether streaming methods are truly advantageous in realistic TSAD scenarios. In this work, we carry out the first large-scale experimental study comparing streaming and static TSAD methods under a unified streaming evaluation benchmark. We consider a realistic setting in which an initial batch of data is available for model training, followed by online evaluation of both detection accuracy and computational efficiency. In addition, we propose a distribution-drift dataset of real time series, called TSB- drift, to isolate scenarios where streaming updates are theoretically justified. Our results show that, contrary to common assumptions, static TSAD methods significantly outperform streaming approaches in most streaming settings. Such finding highlights a critical gap between the design of existing streaming methods and the requirements of modern TSAD, and calls for a rethinking of how streaming capabilities should be integrated into TSAD.
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URL
https://arxiv.org/abs/2609.39215
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FlapKAD: A Simulation Dataset of Coupled Wing Kinematics and Aerodynamic Dynamics for Flapping-Wing Aerial Vehicles
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Experimental investigation and modeling of flapping-wing aerial vehicles are limited by the scarcity of large-scale records that temporally align wing kinematics, aerodynamic responses, and flight states. Existing datasets are often limited in scale and affected by measurement noise and temporal misalignment between rapidly varying wing motion and the associated dynamic response, particularly during high-frequency flapping. We introduce FlapKAD, an episode-structured simulation dataset comprising 2,000 rigid-wing flight episodes and 720,152 valid time steps, with bilateral wing kinematics, aerodynamic responses, and flight states recorded synchronously within a common clock. FlapKAD supports a unified bidirectional sequence-prediction benchmark constructed from the same temporally aligned episodes. The forward task predicts future vertical force coefficients and body vertical velocity from histories of realized flap and twist angles, whereas the inverse task reconstructs future flap- and twist-angle trajectories from the corresponding response histories. A benchmark of eight representative time-series architectures across multiple prediction horizons reveals direction- and horizon-dependent model behavior, systematically higher reconstruction errors for twist angle than for flap angle, and no consistent advantage from increased architectural complexity. FlapKAD provides a reproducible dataset and benchmark for studying coupled wing-kinematic, aerodynamic, and flight-state dynamics in flapping-wing aerial vehicles.
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URL
https://arxiv.org/abs/2609.38719
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Cropland PAtteRNS: Parallel Dimensional Attention Networks and Attention to Dataset Disparity for Crop Segmentation in Satellite Imagery Time Series Data
2026-09-29 17:59:29Joseph Metcalfe, Sara Sharifzadeh, Fabio CaraffiniAbstract
The landscape of satellite imagery time series datasets and boundary-pushing architectures for cropland segmentation has never been richer. However, in this gold rush, important truths are being missed on both fronts, as a drive for the most novel concepts or the largest datasets pushes finer details to the side. In this paper, we present our hybrid transformer-convolutional model, Cropland Parallel Attention and Refinement Network for Segmentation (PAtteRNS), the first model to use self-attention mechanisms separately for each of the temporal, spectral, and spatial aspects of Sentinel-2 multispectral SITS data. To achieve fully-factorised attention in our proposed model, we introduce a novel parallel transformer architecture which significantly reduces the computational complexity of triple-factorised self-attention. We validate our architecture with an in-depth ablation study, and analyse the performance of our model against state-of-the-art crop segmentation models on multiple tile-size variants of the popular PASTIS and MTLCC datasets. Our findings show our model to outperform all others in the task of crop class segmentation, verified across multiple important segmentation metrics, with especially strong performance against compared models seen in the often under-reported parcel delineation quality, for which we use the Boundary IoU metric. We also find that flawed class groupings within datasets can have a significant negative impact on model performance, and report that alternate tile-size variants of crop segmentation datasets produce results incomparable to one-another, invalidating fair comparison between model performance when trained on different tile-sizes. Based on these findings, we suggest further work is required to standardise best practices when constructing SITS crop segmentation datasets, and to enable future dynamic-tile-sizing for ideal model performance.
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URL
https://arxiv.org/abs/2609.38165
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No Scale Left Behind: Multi-Scale Autoencoder with Bi-directional Attention for Time Series Anomaly Detection
2026-09-29 16:55:32Jiaheng Guo, Haochen Zhang, Yu-Chao Huang, Jinhao Duan, Nicholas Konz, Tianlong ChenAbstract
Time series anomaly detection (TSAD) plays a crucial role in healthcare, finance, industrial monitoring, and other sectors. Within and between these settings, anomalies span vastly different temporal scales, from sub-second point spikes to multi-hour drift patterns. However, most existing TSAD methods commit to a single temporal granularity, and multi-scale designs either analyze different scales in isolation or are constrained to a predefined coarse-to-fine hierarchy, both failing to sufficiently capture multi-scale interactions. To resolve this limitation, we propose Multi-Scale Autoencoder with Cross-Scale Attention for TSAD (MSCAD), a simple yet powerful semi-supervised TSAD framework founded on parallel autoencoder branches corresponding to different patch sizes. A stack of symmetric bidirectional cross-scale attention blocks enables every pair of scales to exchange information before reconstruction without allowing any single scale to be privileged. On the comprehensive TSB-AD benchmark (40 datasets, 530 series), MSCAD achieves large performance gains against 50 baselines across multiple metrics, with VUS-PR of 0.57(+9.6%) on the univariate split and 0.47(+9.3%) on the multivariate split compared to the state-of-the-art.
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URL
https://arxiv.org/abs/2609.38004
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GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting
2026-09-29 14:36:16Rui Han, Min Yang, Xu Zhang, Xinghao Yang, Wei Liu, Yongshun GongAbstract
Diffusion models have recently shown strong potential for probabilistic multivariate time-series forecasting by modeling complex conditional distributions. Recent decoupled diffusion frameworks further separate forecasting into deterministic prediction and stochastic residual generation, making it natural to derive dependency graphs from deterministic representations and use them to guide residual diffusion. However, we show that this direct structural transfer is unreliable. Although deterministic-derived graphs encode useful global dependency priors, they exhibit substantial edge-level misalignment with residual dependency structures, introducing inaccurate or redundant conditions during residual generation. This reveals a previously overlooked deterministic-to-residual structural alignment problem in decoupled diffusion forecasting. To address this problem, we propose GARDiff, a Graph-Aligned Residual Diffusion framework for probabilistic multivariate time-series forecasting. Instead of treating deterministic-derived graphs as fixed diffusion conditions, GARDiff progressively adapts them to residual generation. Specifically, GARDiff estimates residual uncertainty to distinguish high- and low-uncertainty regions, enabling uncertainty-aware structural refinement, and further performs timestep-aware edge sparsification during reverse diffusion to evolve graph conditions from broad dependency aggregation to localized residual refinement. Extensive experiments on six real-world benchmarks demonstrate that GARDiff consistently improves probabilistic forecasting performance and uncertainty calibration over strong baselines.
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URL
https://arxiv.org/abs/2609.37694
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ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation
2026-09-29 14:04:03Fariza Rashid, Duc Van Le, Rahat Masood, Gustavo Batista, Aruna Seneviratne, Suranga SeneviratneAbstract
Time series imputation has progressed from statistical and deep learning approaches to diffusion-based models, which have shown strong recent performance. Existing diffusion-based methods typically condition the reverse process using local contextual information from the current or neighbouring windows. Meanwhile, global dataset-level structure often remains implicit, limiting performance when local observations are sparse, noisy, or unrepresentative. To address this issue, we propose ProCTI, a diffusion-imputation framework that augments local conditioning with retrieved global dataset-level priors through learned prototypes. A hybrid conditioning mechanism integrates this global context with local signals during reverse diffusion, enabling more accurate reconstruction under varying missingness scenarios. Experiments across multiple benchmark datasets show that ProCTI outperforms strong baselines overall under random missingness, while remaining competitive under attribute-wise missingness. Furthermore, we use a latent-regime data model to characterise the precise conditions under which prototype-derived global conditioning provably improves imputation. We support this with a general theoretical analysis of local-global conditioning.
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URL
https://arxiv.org/abs/2609.37632
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Loss-Guided Pretraining Data Selection for Time-Series Foundation Models
2026-09-29 11:08:45Yike Li, Shaoxu Song, Jianmin WangAbstract
Time series foundation models (TSFMs) are pretrained on heterogeneous collections containing billions of observations, yet their training windows are typically sampled without estimating whether they provide useful learning signal. We introduce a static data-selection framework that scores each window with a reference forecaster and retains an intermediate interval within every source dataset. Specifically, we connect forecasting loss to optimization difficulty by showing that normalized squared loss controls the per-sample gradient norm under a local Jacobian condition. We then define a reference loss score and apply dataset-stratified selection to preserve the diversity of samples. Across various TSFM architectures, our method outperforms random selection by an absolute margin and even improves both relative MASE and CRPS over full-data pretraining by retaining fewer candidate pretraining windows. Further analyses show strong cross-scale and cross-architecture score correlations, indicating that a small reference model can often select data for larger targets, provided that the reference and target share compatible difficulty orderings.
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URL
https://arxiv.org/abs/2609.37255
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Accelerated surrogate dynamics for dynamical, stochastic system evolution
2026-09-29 10:07:29Marco Jochum, Ioannis Kouroudis, Gohar Ali Siddiqui, Taher Amine Hamzaoui, Manuel G\"o{\ss}wein, Alessio GagliardiAbstract
Dynamic simulations are an entrenched way of gaining insight into the evolution of system dynamics. Their computational cost however is often prohibitively high, especially in cases of stochastic frameworks. Machine learning algorithms are especially suited as simulation surrogates. Nevertheless, they face some very distinct limitations. Firstly, the sheer dimensionality of these systems, however, precludes the use of traditional time series models who struggle with high dimensional feature spaces. Additionally, traditional time series focus exclusively on either long or short range effects, causing local or global drift given enough time. In this paper, we propose a framework that addresses those limitations. Our framework combines a Variational Autoencoder, with a convolutional or graph basis that reduces the dimensionality of the system. This latent vector is propagated in time using a Temporal Fusion Transformer model, which includes both long range and short range effect encoding, as well as static covariate support. We test our framework on three distinct cases, to prove its robustness and in all three we have achieved practically identical to the simulation results at a fraction of the time. Further, our framework is flexible enough to be adapted to any new system and provides an inbuilt uncertainty quantification for targeted experiment design.
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URL
https://arxiv.org/abs/2609.37184
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A Dual-Track Curation-and-Classification Framework for Resolving Ground-Truth Label Noise in Operational Sentinel-2 Wheat Area Estimation
2026-09-29 08:12:04Kasimali Agharia, Ujjwal Kumar GuptaAbstract
Operational estimation of wheat-cultivated area is persistently constrained by discordance between administrative record-keeping and remotely sensed classification products. We address this administrative reference discordance for the 2022 Rabi season in Patiala district, Punjab, India, using a thirteen-timestep Sentinel-2 NDVI time series. A curated 849-sample reference dataset, developed through an iterative rule-based bootstrapping procedure, underpins both a feature sensitivity analysis and an operational classifier. Feature sensitivity independently assessed via Cohen's d and gradient-boosted information gain converges on the February-to-March grain-fill window as most discriminative. Four classifiers (1D-CNN, LSTM, hybrid CNN-LSTM, and XGBoost) were benchmarked on an identical 679/170 sample split. XGBoost achieved the highest overall accuracy (78.82%) against deep-learning baselines (64-66%), consistent with tree-based ensembles' favourable parameter-to-sample ratio in low-sample regimes. At full-population deployment across 36.25 million valid district pixels, the operational classifier attained 86.31% precision and 71.05% recall. The predicted wheat extent deviated by only +2.99% from the official tabular target, whereas the government's spatial reference mask exhibited a +25.11% positive area bias against the identical target. This asymmetry indicates that a classifier trained on an auditor-curated reference set reconciles more closely with the official tabular area than the spatial product conventionally used to validate it. We present this dual-track curation-and-classification framework as a methodological reference for crop-area reconciliation in label-noisy administrative settings.
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URL
https://arxiv.org/abs/2609.36975
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JudgeCast: Time Series Forecasting with Experience-Informed Covariate Judgements
Abstract
Covariate effects vary across contexts and shift over time, requiring forecasters to assess how to use them for each forecasting context. As forecasting proceeds, observations for earlier forecasts become available, providing feedback on past covariate use for subsequent forecasts. However, when multiple covariates act together, the forecast error reveals the numerical discrepancy from the observation but not how the covariates should have been used. We introduce JudgeCast, an experience-based framework for time series forecasting with covariates. Following the judgmental adjustment practice, a frozen TSFM provides the base forecast, while a frozen LLM uses the current context and relevant experience to adjust it. Within the adjustment, assessing covariate effects and determining the numerical adjustment serve distinct roles, so JudgeCast first forms explicit covariate-wise judgments and then determines the adjustment. After observation, JudgeCast uses the observed residual of the base forecast to reconstruct alternative judgments and evaluates the original and alternatives through their resulting adjustments. The best-performing decision is selected and retained as validated experience for subsequent forecasts. Across diverse real-world datasets, JudgeCast outperforms strong baselines. Ablations show that explicit covariate-wise judgment can improve forecast-time adjustment, while residual-guided experience construction yields more reliable forecasting gains than retaining raw decisions as experience.
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URL
https://arxiv.org/abs/2609.36966
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State Transport Routing for Short-horizon Adaptation in Multi-horizon Photovoltaic Forecasting
2026-09-29 07:42:31Xu Yuqing, Zhou Liguo, Sun Ze, Yu Lei, Jiang MingmingAbstract
Recent power measurements provide valuable information for photovoltaic(PV) power forecasting, but directly extrapolating short-term trends can introduce substantial errors over longer forecast horizons. To address this challenge, we propose state transport routing (STR), a lightweight adapter that refines the predictions of a frozen forecasting model. STR combines the original forecast with two complementary trajectories derived from the latest measured power level and its recent trend. A horizon-conditioned router adjusts their contributions over the first 120 min, while leaving subsequent predictions unchanged. Experiments on four public PV datasets show that STR consistently outperforms a parameter-matched residual adapter. On PVDAQ, the same approach improves five neural forecasting backbones, reducing all-horizon normalized mean absolute error by 0.0201-0.2364 percentage points, with paired 95% confidence intervals excluding zero. No reliable improvement is observed for LightGBM. These findings demonstrate the potential of structured state adaptation to improve short-term forecasting across different neural architectures without retraining the underlying models or altering their longer-horizon predictions.
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URL
https://arxiv.org/abs/2609.36926
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Cyclostationary Phase Conditioning for Medical Time Series Diffusion
2026-09-29 07:12:03Samuel Ruiperez-Campillo, Michele Copetti, Jorge da Silva Goncalves, Sonia Laguna, Thomas Hofmann, Julia E. VogtAbstract
Many physiological time series, such as cardiac and brain recordings, exhibit cyclostationarity: their statistics vary periodically with an underlying cycle phase. Corruption from motion, poor contact, and physiological interference obscures morphology needed for diagnosis, making signal restoration essential. Existing diffusion approaches condition on corrupted observations alone and must learn cyclic structure implicitly. We instead propose two inductive biases which encode cyclostationarity: a shift-covariant wavelet representation and dense per-sample phase conditioning inferred from the corrupted input. We further introduce a training-free cyclostationarity index that quantifies phase structure and predicts when phase conditioning will help. Finally, we propose antithetic coupling of reverse trajectories to reduce sampling variance while achieving comparable performance with fivefold fewer network evaluations. Across modalities, our results show that explicitly encoding measurable cyclic structure improves physiological time-series restoration.
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URL
https://arxiv.org/abs/2609.34965
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Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval
2026-09-29 06:23:02Cassandra Yang, Yufan TangAbstract
Embedding-based retrieval is attractive for long sequence collections because each item can be encoded once and searched by nearest-neighbor ranking. The difficulty is that the objects being indexed are often observed under a noncanonical clock: cardiac cycles stretch with rate, speech changes with tempo, and sensor traces reach comparable states at different speeds. This paper studies a specific source of instability in patch-based encoders for this regime. If patch boundaries are chosen from signal geometry, then the tokenization can change under the same temporal deformation that the representation is expected to tolerate. We propose GeoPatch, a fixed-scaffold patch encoder that keeps token support independent of geometry and uses slope, curvature, acceleration, affine-residual, and confidence descriptors only as continuous conditioning variables. The design turns boundary variation into feature modulation: geometry can change the embedding through a controlled pathway, but it cannot change the number, order, or support of local tokens. We formalize this distinction through a mechanism-level stability analysis that separates boundary drift, affine timing variation, confidence-weighted geometry perturbation, and retrieval-margin effects. The same local tokens support global embedding retrieval and late-interaction scoring, so the scoring rule can be matched to the evaluation protocol. Across ECG, speech, and multivariate time-series retrieval tasks, GeoPatch improves early-rank retrieval under timing variation while exposing a clear trade-off between local surface matching and strict non-overlap retrieval.
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URL
https://arxiv.org/abs/2609.36809
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