Temporal Learnability

Continuous-time (CT) machine learning has emerged as a principled framework for modeling temporal dynamics as a continuous process, particularly when observations are sampled at arbitrary time points or span long-range horizons. However, major branches of CT machine learning have matured in separate research communities, leaving their mathematical relationships and design trade-offs insufficiently characterized. In this survey, we develop a unified, concept-driven view of major CT machine learning branches through a taxonomy that organizes families according to their underlying base mathematical formulations. We present a canonical mathematical formulation that relates these families through different architectural choices of vector-field parameterization, stochasticity, memory mechanisms, and discretization. We compare training algorithms, optimization strategies, and failure modes, highlighting the trade-offs across families. We further provide a comparative analysis of theoretical computational complexity alongside an illustrative architecture-controlled benchmark analysis on representative architectures from each family. We also review software ecosystems supporting their implementation. Finally, we identify open challenges in approximation theory, training stability, hardware-efficient implementations, benchmarking, foundation models, and scientific machine learning, and discuss an agenda for future research.

Early detection of cognitive decline from speech offers a scalable and non-invasive alternative to conventional clinical assessment. Verbal fluency tasks are particularly informative, but most automated approaches aggregate features across an entire recording, overlooking temporal speech dynamics. We propose the Cognitive Instability-Aware Cross-Modal Attention Network (CCMAN), a transfer learning framework that learns task-agnostic cognitive speech representations from multiple memory-probing tasks before fine-tuning on a minute-long semantic and phonemic verbal fluency task. CCMAN integrates semantic, acoustic, and linguistic information through bidirectional cross-attention, gated multimodal fusion, and transformer-based temporal modelling to derive interpretable biomarkers of cognitive decline. Experiments were conducted on 165.44 hours of speech from 843 participants (498 healthy controls, 245 with mild cognitive impairment, and 100 with dementia). CCMAN achieved Macro-F1 scores of 0.81 and 0.59 for binary and multiclass semantic fluency classification, and 0.77 and 0.53 for phonemic fluency, consistently outperforming strong static and temporal baselines. Statistical analyses showed that semantic drift variance and pause variance, but not mean semantic drift, were significantly elevated in both MCI and dementia relative to healthy controls, while pause duration increased progressively over the task with the steepest slope in dementia, supporting global and progressive temporal speech instability as interpretable biomarkers. Evaluation on the independent PROCESS-2 benchmark further demonstrated the generalisability of the proposed framework, improving the baseline Macro-F1 by up to 9%. These findings support temporal speech instability as a dynamic speech biomarker for robust, interpretable, and generalisable early detection of cognitive decline.

Time-series foundation models are evaluated almost exclusively on public archives that predate them, so a strong score cannot be separated from having seen the test set during pretraining. The obvious remedy is a hold-out that postdates the models. We build one: thirteen forecasters -- four classical, three trained per dataset, six pretrained -- on seven groups drawn from five domains, every observation published after the last model was released, and every dataset rebuildable without an API key. Under this protocol pretrained models win 5 of 7 groups, lose one to a Theta baseline, and on daily exchange rates are indistinguishable from a seasonal naive forecast, along with every other method tested. We then ask what separates the wins from the losses, and report a negative result: the two intrinsic properties one would reach for -- seasonal strength and spectral entropy, measured on the input window -- do not account for the pattern, and seasonal strength is if anything negatively associated with the advantage. What does track it is corpus familiarity. Our largest gain (28% lower MASE than the best classical method, on weekly Wikipedia pageviews) falls on Wikipedia pageviews, the domain TimesFM's authors describe as the bulk of its pretraining corpus, at the same granularities and differing only in time window. Within the pretrained family, where every model forecasts identical series so that series difficulty cancels, the TimesFM family outranks the Chronos family by -0.53 ranks on Wikipedia against -0.09 everywhere else (1,500 vs. 754 series, Mann-Whitney p < 1e-5). We conclude that a temporal hold-out removes memorisation of a window but not familiarity with a domain, that benchmarks therefore need domain hold-outs stated relative to disclosed corpora, and that the practitioner's question is less which model is better than whether their domain is one the model was raised on.

Time series foundation models (TSFMs) are increasingly pre-trained on synthetically generated time series trajectories, where the data generating process is known. Current pre-training recipes are based on loss objectives which compare TSFM outputs to realized future values of each trajectory. We instead propose loss objectives which compare TSFM outputs to the conditional forecast distribution of each trajectory, a procedure we call synthetic data distillation (SDD). SDD corresponds to a Rao-Blackwellization of the training objective, in that it leaves the expectation of stochastic gradients unchanged while provably reducing the covariance of the stochastic gradient under the Loewner partial ordering. We empirically validate SDD on a TSFM model family of sizes from $4$M to $2.5$B parameters, and observe faster convergence of validation loss at every model size: on Gaussian Process data, SDD attains or improves upon the Status Quo loss whilst requiring $10\%-40\%$ less training iterations.

Recurrent models provide a natural path to long-context modeling, yet models trained with backpropagation through time (BPTT) often fail beyond their training horizon. Classical analyses emphasize gradients that vanish or explode along temporal paths. However, dense per-token losses can still train a shared recurrent rule despite severe decay, showing that decay alone does not determine whether learning fails. We instead study state credit: the signal through which future losses reach earlier recurrent states before contributing to parameter updates. Accordingly, we intervene directly on state credit and propose Credit Stabilization through Time (CST). During backward propagation, CST locally rescales the state-credit signal to stabilize its norm without rotating the component being corrected, while leaving the forward computation unchanged. Because controlled synthetic tasks and real data exhibit different credit dynamics, we specialize CST to each regime. In both settings, CST improves performance beyond the training horizon, with gains observed at up to 128x the training length.

In data-driven predictive maintenance (PdM), feature extraction is usually treated as fixed preprocessing: a descriptor set is chosen once and reused while the downstream model or forecasting horizon changes. This paper isolates the representation-learning stage and presents a quantile-led feature-extraction framework based on a dual-stage MLP-QRNN hierarchy. QRNN1 learns a broad ten-quantile conditional distribution for each sensor channel, while skip-connected QRNN2 refines a retained mid-tail quantile set into compact, channel-resolved, distribution-aware features. A fixed thirteen-pipeline ablation spans 1-hour, 70-hour, and 30-day regimes across 72 machines in 9 industrial facilities, with the downstream temporal classifier held fixed within each regime. Increasing the retained mid-tail set from two to four quantiles improves 30- and 60-minute F1-score, reaching 75.92% and 72.44% with attention enabled. The results also show that representations do not transfer reliably beyond their design horizon unless feature capacity, temporal embedding, activation strategy, and sensor breadth are scaled with the forecasting task. The unmodified short-horizon extractor falls to 42.90% F1 at 70 hours, whereas horizon-conditioned extractors reach 60.38% at 70 hours and 79.97% at 30 days. The framework therefore supports treating PdM feature extraction as a horizon-dependent representational stage rather than fixed preprocessing.

Retail banking attrition is usually represented as a terminal binary event, even though client relationships often weaken earlier through partial movements of deposits, investments, and recurring activity to external financial institutions. This paper defines that preceding state as financial fragmentation and presents an end-to-end temporal machine-learning system for predicting it before complete disengagement. Using anonymized multi-source data from a large retail bank, the framework predicts whether a valid external transfer or investment event will occur within 90 days. The study uses 595,220 client-month observations, with 346 engineered features combining monthly client profiles, balances, product relationships, prior flow-of-funds behavior, macroeconomic conditions, and competitor activity. A four-stage XGBoost cascade estimates (1) whether an external outflow will occur within 90 days, (2) the expected amount, (3) the originating product, and (4) the destination financial institution. The primary classifier achieved a test precision-recall area under the curve of 0.823. At the validation-selected threshold, it produced 86.4% precision, 75.1% recall, and an F1 score of 0.803. Ranking test observations in descending Stage 1 fragmentation score, the top 1% of clients yielded 95.3% precision, while the top 5% captured 78.7% of observed outflow cases. The amount model placed 94.9% of predictions within an adjacent amount bucket. Destination prediction reached a macro-F1 of 0.81 across 27 classes; source-product prediction achieved a weighted F1 of 0.92. By moving the analytical focus from terminal churn to earlier fund migration, the proposed approach provides a practical foundation for proactive, explainable, and economically informed client-retention decision support.

Foundation models (FMs) trained on large-scale accelerometer data have been proposed as general-purpose feature extractors for health monitoring, but systematic evidence of their advantages is lacking. We present the first comprehensive evaluation of four open-source accelerometer FMs against supervised baselines covering 19 tasks across the domains of activity recognition including activities of daily living, clinical monitoring, and physiological inference. We find task-dependent performance results: supervised models remain competitive with FMs on human action recognition (HAR), with no consistent advantage for either, while selected FMs lead on fall and stress detection and are the most robust to sensor-placement variation. As frozen feature extractors, FMs are strongest for demographic inference, whereas sleep staging performance remains near chance level for all models. The internal FM representations show strong similarity across layers, highlighting potential for future FM improvements. Linear and frozen probing reveals that UniMTS provides the strongest representations and is the only FM that surpasses the supervised baselines without finetuning. Concept discovery analysis shows all models capture high-intensity activities clearly but struggle with sedentary, complex or ambiguous activities. We provide scenario-based deployment recommendations. Furthermore, we identify FM-derived activity profile inference-moving beyond fixed category classification-as a promising research direction.

Due to the diversity of real-world time series, no single forecasting model consistently dominates across all samples. Ensemble learning addresses this by combining complementary model strengths, yet existing methods rely on fixed rules or black-box models based solely on numerical inputs, failing to leverage LLM reasoning for interpretable weighting decisions. We propose REATS, which leverages LLM reasoning capabilities as an intelligent ensemble router that jointly processes textual temporal pattern descriptions and numerical features to produce interpretable, sample-adaptive ensemble weights through chain-of-thought reasoning. To enable effective LLM-based ensembling, we study its key design choices and propose: (i) a structured input pipeline that transforms raw time series into hybrid textual--numerical representations with fixed token cost, enabling rule-based chain-of-thought construction without API dependency, augmented with retrieved similar-sample priors; (ii) a diverse multi-row weight supervision scheme coupled with a token-efficient percentage-table format that reduces numerical complexity and mitigates LLM hallucinations; and (iii) a two-stage fine-tuning framework combining SFT with GRPO, where a reciprocal reward mapping transforms the continuous unbounded MSE gap into bounded signals with amplified near-oracle sensitivity, addressing the uniform sensitivity and outlier-dominated advantage compression inherent in naive reward designs for regression-based GRPO. Experiments on eight benchmarks demonstrate that REATS outperforms competitive ensemble baselines while providing natural language explanations and demonstrating strong transfer learning and out-of-domain generalization to unseen candidate models.

Modern sequence models, from Transformers to State Space Models, have enabled powerful generative modeling across diverse domains, yet they are typically trained to predict what happens while treating when it happens as a secondary concern. In data-mining settings where events are associated with explicit timing information, this separation can limit temporal reasoning, anomaly detection, and faithful reconstruction of event chronology. A common strategy is to treat timing as an auxiliary signal, training a separate timing model using representations learned solely for event prediction. However, this two-stage approach implicitly assumes that representations optimized for event prediction already contain sufficient temporal structure. We introduce ChronoSSM, an autoregressive State Space Model (SSM) that jointly models events and timestamps with a shared backbone trained using combined token and temporal generation objectives. We compare the joint regime, where temporal supervision updates the backbone, with the two-stage regime, where timing is learned only using the frozen event representations. Across four domains spanning dense and partial timestamp supervision, joint training consistently makes inter-arrival information more recoverable from frozen representations without any systematic degradation in content-generation quality overall. Our results show that temporal supervision can produce more temporally informative representations without materially degrading autoregressive event modeling.

Temporal decisions in language-model systems often depend on both symbolic task state and elapsed wall-clock time, such as cache expiration, job completion, quota resets, deadlines, or stale sessions. We study whether elapsed time can be supplied as a non-token, system-side scalar and composed with visible symbolic state by a frozen-backbone language model. We introduce ChronoState, a compositional temporal-state benchmark in which symbolic state appears in the prompt, elapsed seconds tau are supplied through a hidden chronometric-injection channel, and the model selects a forced-choice temporal action. Here, "hidden" means hidden from the user-visible token sequence, not from model computation. Using Qwen2.5-3B-Instruct as a frozen bf16 backbone with a 31-dimensional sinusoidal-plus-log time encoding, gated FiLM residual modulation, and a rank-8 LoRA action surface, hidden-time CI reaches 0.9305 +/- 0.0134 accuracy and 0.9410 +/- 0.0103 balanced accuracy. No-time and shuffled-time controls fall to 0.5511 +/- 0.0042 and 0.3323 +/- 0.0097, respectively, with high shuffled-time wrong-state consistency supporting causal dependence on the injected scalar within the trained distribution. Generalization remains strong for held-out templates, durations, and multi-constraint compositions, but held-out quota-family transfer is weak at 0.5065 +/- 0.0559, while a fair prompt+LoRA timestamp baseline reaches 0.9893 +/- 0.0052. Thus, ChronoState supports a narrow conclusion: hidden elapsed time can be composed with symbolic task state under direct supervision, but does not establish autonomous time tracking, broad unseen-family abstraction, or superiority over prompt-injected timestamps.

Time series forecasting (TSF) plays an important role in a wide range of real-world applications. Recently, time series foundation models (TSFMs), pretrained on large-scale datasets, have demonstrated strong generalization capabilities and emerged as an important paradigm for TSF. Reinforcement learning (RL) post-training has consequently attracted growing attention as a means of further improving their performance on downstream tasks. However, we find that, in certain forecast regions, RL post-training may gradually shift the output distributions of TSFMs away from the ground truth, thereby limiting their performance. We refer to this phenomenon as \textbf{suboptimal collapse}. Our analysis suggests that difficulty in initially sampling high-quality trajectories near the ground truth is an important contributing factor to suboptimal collapse. To address this issue, we propose Ground-Truth Neighborhood Regularization (GTN-R) for RL post-training of TSFMs. GTN-R uses the ground truth as a reference for locating high-quality regions and guides the model's probability mass toward the ground-truth neighborhood. This increases the probability of sampling high-quality trajectories, mitigates suboptimal collapse, and improves performance. Moreover, GTN-R can be flexibly integrated into various RL methods for TSFMs. Extensive experiments show its effectiveness.

Probabilistic long-term time-series forecasting commonly relies on trained models. Training-free conformal methods typically construct intervals around a pre-existing point forecaster and do not natively represent a complete predictive distribution; sequential variants additionally suffer from increasingly delayed feedback at long horizons. We propose KReF, a training-free retrieval framework that treats retrieved historical futures as a querylocal empirical predictive distribution. After robust preprocessing, KReF embeds each lookback using handcrafted statistics or frozen random Fourier features and retrieves similar historical lookback-future pairs. Their similarity weights directly define predictive masses, quantiles, CRPS, and a weighted-mean point forecast. KReF further uses the observed query lookback to construct a probability-integral-transform map and applies validation-selected expansion and shrinkage rates to adapt interval boundaries. Across six LTSF benchmarks and four horizons, KReF obtains the lowest CRPS in all 12 dataset-embedding settings and the lowest IS90 in 9 settings. Without gradient-based fitting, its point forecasts also match or surpass trained baselines on two of six datasets. An archive-oracle analysis further reveals substantial headroom under finer horizon- and channel-wise routing. These results establish retrieval as a useful and underexplored inductive bias for LTSF.

Training multimodal models to align time series with language runs into a self-supervision trap. The usual recipe asks an LLM to read a series and write a description, so label quality is capped by the perceptual skill the model is supposed to learn. The data can never teach more than the labeler already knows. A second gap makes this worse: most datasets use a single variable, but the patterns that matter (cross-channel correlation, lead-lag structure, co-occurring anomalies) appear only with several variables, right where the labeling LLM's limits are most exposed. These two problems create a trilemma: existing methods are reliable, realistic, or scalable, but none achieves all three. We resolve this by decoupling perception from description. Deterministic code computes a set of statistics from real, open-source multivariate series; the LLM verbalizes those precomputed facts. Perception, which LLMs do poorly, is handled by computation, while the LLM handles expression. This produces CGTime, our 4B-parameter computation-grounded time-series-language model. CGTime outperforms far larger general-purpose models on multivariate understanding tasks: it attains the best multivariate fact score on our held-out benchmark (0.283 vs. 0.173 for GPT-4o-mini and 0.203 for GPT-5.4-nano), a gap that survives Holm-corrected paired significance tests against every baseline. It also states verifiable numerical facts in generated captions more accurately and covers a broader range of statistical properties.

Oscillatory signals, such as vibration, carry class-discriminative information in specific frequency bands; perturbing them in raw feature space for counterfactual analysis easily destroys their temporal structure and produces physically implausible results. In this work, we introduce IMFACT (IMF-based counterfACTuals), a model-agnostic framework for generating plausible counterfactual explanations for time series classifiers that operates in the decomposition space of Empirical Mode Decomposition. An input signal is split into Intrinsic Mode Functions (IMFs), and selected IMFs are progressively substituted with those of a Nearest Unlike Neighbour (NUN) until the classifier flips to the target class. We evaluate six IMF-selection strategies and a multi-NUN cycling extension on two UCR benchmarks (FaultDetectionA, FruitFlies). The variance-based strategy with three NUNs outperforms two prominent baseline techniques on reliability and plausibility metrics, while cycling across three NUNs yields the best proximity across both datasets.

Precise anomaly localization over long-context time series is a crucial task in monitoring applications across clinical care, industrial operations, financial services, and logistics, where brief evidence may hide inside long spans of high-frequency data. Time-Series Language Models (TSLMs) are able to ingest time series data and verbalize findings on anomalies in natural language; however, recent benchmarks report a decrease in retrieval performance at long contexts, mirroring failure modes in text, vision, and audio. In the text domain, Recursive Language Models (RLMs) can recover much of this lost performance by keeping context external to the large language model (LLM), allowing the model to query it through code. We present TimeRLM, an RLM formulation for time-series that sequentially manipulates the signal using code and vision capabilities. We further introduce AnomalyXL, a synthetic long-context anomaly localization benchmark with programmatically injected anomalies that require precise retrieval. We implement five different task categories and two variants: AnomalyXL-MCQ and AnomalyXL-Localize. TimeRLM outperforms every evaluated TSLM and single-pass baseline on four of the five AnomalyXL-Localize tasks, reaching 0.682 IoU on localization and 0.745 on classify-with-evidence, versus at most 0.329 and 0.072 across all baselines. We post-train TimeRLM using reinforcement learning. The resulting model further improves performance and requires approximately one-third as many agent interaction turns as its untrained base model to produce a final answer. On unseen real-world ECG, sleep and software observability recordings, the post-trained TimeRLM retains or improves performance, surpassing TSLMs despite being trained exclusively on synthetic data. Our findings suggest recursive interaction with time-series is an effective approach for long-horizon retrieval.

Time series forecasting is fundamental to decision-making in complex systems, where future dynamics are influenced not only by historical observations but also by evolving contextual features. Recent advances in large language models (LLMs) have extended forecasting beyond numerical extrapolation toward context-aware reasoning. However, existing approaches often lack explicit mechanisms to identify relevant contexts, reason about their impacts, and validate forecasts against temporal and domain constraints. In this work, we propose CastFSR, an agentic framework that formulates context-aware forecasting as a Fast--Slow--Reflect workflow. In fast thinking, CastFSR profiles observations and selects lightweight forecasters to construct a data-driven forecast prior. In slow deliberation, it retrieves contextual evidence, adaptively determines informative look-back windows, and reasons about how contexts reshape future dynamics. In reflection, it iteratively refines forecasts to ensure temporal, contextual, and domain consistency. CastFSR supports both training-free inference with off-the-shelf LLMs and efficient deployment through a two-stage SFT and reinforcement learning strategy that transfers its orchestration capability to compact LLMs. Extensive experiments on public datasets demonstrate that CastFSR consistently outperforms representative baselines. Our code is available at https://github.com/Xiaoyu-Tao/CastFSR.

Machine-learning benchmarks often pair a label that aggregates a long temporal horizon with input observed through one or a few short windows. Their apparent performance ceiling may therefore be an acquisition-protocol ceiling rather than a model-capacity ceiling. We study labels of the form $Θ_{g,T}=T^{-1}\int_0^T g\{Z(t)\}\,\mathrm{d}t$ when the latent Gaussian process contains both a stable individual trait and a correlated within-individual state. An exact protocol-conditioned Bayes-risk identity provides a common tool. First, we decompose label variance into an $O(1)$ trait component and an $O(T^{-1})$ state component, explaining why a snapshot can retain cross-sectional predictability while poorly tracking within-person change. Second, we derive task-dependent effective temporal spans: mean labels depend on the ordinary correlation time, whereas occupation-time labels depend on an entire spectrum of higher-order correlation times. Third, state-driven occupation-label variance is maximal when the stable trait lies at the threshold; window efficiency decays much more slowly away from that boundary. Under an equal segment budget, exact risks and Monte Carlo experiments show that repeated segments at one time rapidly saturate, whereas temporally dispersed observations continue to increase state explainability. The trait ceiling uses quantities available from ordinary test-retest data; only the state ceiling requires short-lag temporal calibration. The results distinguish architectural limits from protocol limits and show that the label, rather than duration or segment count alone, defines the relevant timescale.

Recent advances in sign language (SL) understanding (SLU) have led to remarkable progress in tasks such as continuous SL recognition and SL translation. However, these tasks are designed with predefined objectives, requiring models to learn a fixed mapping from sign videos to glosses or spoken-language sentences. As a result, they provide only a limited assessment of whether a model truly understands the semantic content of SL videos. To address this limitation, \textbf{we first propose a new task, Sign Language Question Answering (SLQA)}, which evaluates SL understanding by requiring models to answer arbitrary natural language questions about SL videos. Unlike previous SLU tasks, SLQA provides a more flexible and comprehensive evaluation framework that assesses multiple reasoning capabilities beyond recognition and translation. To facilitate this task, \textbf{we further construct two SignQA benchmarks} based on PHOENIX14T and CSL-Daily by automatically generating question-answer pairs from existing gloss and sentence annotations using carefully designed templates. The resulting datasets cover five complementary question categories, including position reasoning, structural reasoning, visual search, gloss recognition, and translation understanding. \textbf{Finally, we propose a simple yet effective baseline model} equipped with a Question-Conditioned Modulated Temporal Downsampling module and an in-domain knowledge transfer strategy, enabling effective knowledge transfer from existing SLU tasks while enhancing question-aware temporal feature modeling. Extensive experiments demonstrate that our baseline consistently outperforms representative vision-language models across all question categories, establishing a strong benchmark for future research on SLQA. Datasets are available at:{https://huggingface.co/datasets/hulala/SignQA-2026}.

A temporally drifting data stream may pass through discrete regimes rather than changing continuously. We ask whether such regimes are recoverable from the weights of models trained on the stream, using a hidden Markov model (HMM) fit to the chronologically ordered trajectory of those weights. We study this question in two domains known to drift over time: multimodal misinformation detection, using the Fakeddit dataset; and sentiment analysis, using the Yelp dataset. We train classifiers on consecutive temporal windows and fit an HMM to the trajectory of their aligned weights, recovering latent states that partition each timeline into coherent phases. On both datasets, classifiers generalize better to data from windows sharing the state of their training window than to windows across state boundaries. This within-state transfer advantage survives a control for temporal proximity and modestly exceeds the advantage recovered by a naive partition into contiguous states of equal size. Although the states are estimated solely from model weights, they correlate more strongly with shifts in the data's class distribution than with the weight-space geometry used to estimate them. After class divergence and lag are residualized out, the within-state advantage exceeds its permutation null on both tasks, indicating that the states recover structure relevant to transfer beyond the data distribution. Every effect replicates on both tasks but is attenuated on Yelp, whose label distribution is more temporally stable.

Objective. We tested whether frozen representations from five EEG foundation models support decoding of long-range temporal correlations, measured as the detrended-fluctuation-analysis (DFA) exponent of the alpha-band amplitude envelope. Approach. REVE, LaBraM, BENDR, CBraMod, and BIOT were evaluated in CAUEEG and BrainLat. A common 240 s estimator used 8-13 Hz filtering, DFA over 2-23.8 s, artifact masking, and quality control. One fixed nested-cross-validation readout predicted DFA and a fixed-mode aperiodic exponent. Controls tested pre-pool order sensitivity and aperiodic residualization. Results. CAUEEG included 764 recordings and BrainLat 79. BIOT decoded DFA in CAUEEG (R-squared = 0.232; conditional subject-bootstrap 95 percent interval, 0.121-0.310), and CBraMod was positive but imprecise (R-squared = 0.121; 0.003-0.214). Neither replicated in BrainLat, where all five point estimates were negative. In contrast, CBraMod and BIOT decoded the aperiodic exponent in both cohorts (R-squared = 0.459-0.757). BIOT remained positive after removal of the measured linear aperiodic association in matched CAUEEG data (R-squared = 0.240). The post-hoc order control was batch- and configuration-sensitive. Because chronological EEG epochs are not exchangeable, it was descriptive, not an LRTC-specific test. No revised DFA transfer direction passed source-label permutation testing. Cohort membership was near-ceiling decodable from all five embeddings, but this is not a pure site effect. Significance. CBraMod and BIOT show a replicated, model-specific spectral-temporal dissociation: aperiodic decoding is present in both cohorts, whereas alpha-envelope DFA decoding is cohort-dependent. These findings bound the evaluated readouts; they do not establish representational absence or an architectural cause. Transfer and clinical associations remain exploratory.

Self-supervised foundation models have recently shown strong potential for electroencephalogram (EEG)-based analysis. However, existing approaches struggle to capture the inherently multi-scale temporal structure of EEG signals, where local neural patterns and long-range dependencies jointly encode task-relevant information. This limitation hampers cross-scale representation learning and generalization across diverse downstream tasks. To address this challenge, we propose MSBraM, a Multi-Scale self-supervised Brain foundation Model designed to learn hierarchical EEG representations. MSBraM follows a two-stage pretraining framework. First, a multi-scale neural tokenizer discretizes raw EEG signals into semantic codes at different temporal resolutions via vector-quantized reconstruction. Second, the model is pretrained to predict masked codes using a curriculum multi-scale masking strategy, progressively integrating fine-grained local patterns with global temporal context. We pretrain MSBraM on over 2,400 hours of EEG data and evaluate it across 10 downstream tasks on 12 public datasets. Extensive experiments show that MSBraM achieves superior performance on other state-of-the-art pretrained models, demonstrating strong generalization and transferability. These results indicate that explicitly modeling multi-scale temporal dynamics is critical for effective EEG foundation models.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

Sequential recommendation (SR) models capture continuously observed behavior, but a returning user may have no interactions for months or years. We define this setting as Zero-Observation Reactivation: the user has a pre-gap history, while the platform observes no behavioral signals during a macro-gap Delta t. Under a chronologically aligned Gap-Synthesize Protocol on three Amazon datasets (Video Games, CDs & Vinyl, and Movies & TV), Hit@10 decreases monotonically across the evaluated gap buckets and reaches its lowest level beyond one year. The pattern appears across recurrent, unidirectional, and bidirectional SR backbones. We propose DeltaGate, a lightweight output-layer plugin that keeps the backbone frozen and routes each representation dimension between the personalized history and a learned, zero-initialized global prior. The gate is conditioned jointly on Delta t and the personalized representation. In a controlled diagnostic, we hold the personalized representation fixed and vary Delta t to isolate the trained gate's response to the gap input. In the >365d Video Games bucket, DG-SASRec reaches 0.047 Hit@10 versus 0.031 for SASRec, while DG-BERT4Rec reaches 0.046 versus 0.025 for BERT4Rec, with 66K trainable parameters (2--4% overhead). End-to-end retraining attains higher absolute accuracy but changes the backbone embeddings; the frozen plugin preserves zero backbone drift, uses about 40x fewer trainable parameters, and retains observable dimension-wise routing. The source code is available at https://github.com/jdding/DeltaGate.

Sparse autoencoders (SAEs) decompose language model activations into sparse features, yet these models traditionally encode each token independently, failing to expose information that persists across a sequence. We first show that temporal persistence can naturally emerge in standard SAE features: after a feature activates, the hidden state remains aligned with its direction, and past activations help reconstruct later hidden states. How long this lasts varies widely across features. We therefore introduce Persistent Sparse Autoencoders (Persistent SAEs), an extension of standard SAEs that learns a persistence coefficient for each feature, allowing the model to learn feature-specific timescales from reconstruction alone. Our experiments show that Persistent SAEs retain competitive reconstruction quality while learning a spectrum of timescales: short-timescale (fast) features stay locally interpretable, whereas long-timescale (slow) features accumulate information that identifies the current context. Moreover, we show in a prompt-injection monitoring case study that slow features preserve injection-related signals and remain causally effective over long contexts. These results suggest that Persistent SAEs offer new opportunities for interpreting and monitoring language models via persistent sparse features.

Robust 3D reconstruction is essential for robotics and embodied perception. Recent feed-forward approaches such as DUSt3R have demonstrated impressive progress in dense 3D reconstruction from RGB images, achieving global geometric consistency and strong generalization. However, extending such dense 3D reconstruction to event cameras remains challenging due to their asynchronous, sparse, and highly dynamic nature, as well as the lack of large-scale, well-labeled datasets. In this work, we introduce Event3R, a feed-forward framework that directly maps asynchronous event streams to globally consistent 3D point clouds. Event3R represents incoming events as spatial-temporal voxels, enabling time-aware feature integration through a temporal attention module that enhances the module's temporal feature learning. To further strengthen temporal representation learning and reduce reliance on labeled data, we propose a Masked Bin Modeling (MBM) strategy for self-supervised pre-training, enabling robust temporal representation learning with minimal labeled data, and retain it as an auxiliary fine-tuning objective. In addition, contrastive alignment and consistency regularization losses are incorporated during fine-tuning to reinforce structural correspondence and temporal coherence across views. Extensive experiments on both synthetic and real-world benchmarks demonstrate that Event3R achieves robust, temporally consistent, and globally aligned 3D reconstructions, significantly outperforming existing event-based methods.

Feature tracking plays a fundamental role in understanding scene motion and supports various downstream tasks. Event cameras, with their high temporal resolution and asynchronous sensing, enable low-latency and motion-robust perception, making them well-suited for feature tracking under fast and non-linear motion. However, existing event-based feature tracking methods rely on fixed heuristic rules based on hand-tuning for event accumulation. Such strategies fail to adapt to diverse motion dynamics, leading to degraded performance under abrupt motion changes or low-motion scenarios. In this paper, we model event accumulation as a sequential decision-making problem and introduce reinforcement learning (RL) framework to adaptively control the accumulation process for online event-based feature tracking. Our approach trains a RL agent that decides whether to continue accumulating events or to perform tracking inference based on motion cues. The proposed adaptive temporal agent enables dynamic adaptation to varying motion patterns without relying on hand-crafted rules. Furthermore, we introduce a Dynamic Event-based Tracking (DEFT) dataset with dynamic motion distributions to evaluate the robustness of the feature tracking. Extensive experiments demonstrate that integrating our plug-and-play framework to existing feature tracking methods consistently outperforms heuristic-based approaches, improving robustness under dynamic motion while offering a better balance between tracking accuracy and efficiency. Our project codes and datasets are available at https://github.com/kmax2001/GoSTOP

Industrial time series serve as the foundation for Prognostics and Health Management (PHM) to ensure the reliability and safety of industrial equipment such as aero-engines. However, existing approaches are typically limited to single-modality modeling, which restricts their generalization in complex scenarios. Although recent advances in large language models (LLMs) provide new opportunities for multimodal learning, bridging continuous time-series signals and discrete textual semantics remains an open challenge. To this end, we propose VLT, a multimodal foundation model that jointly models time-series, frequency-spectrum visual representations, and textual knowledge. A key insight is to utilize the frequency spectrum as a visual bridge to connect continuous temporal signals with discrete semantics. Specifically, a Time-aware Mixture-of-Experts (Time-MoE) is designed to capture heterogeneous temporal dynamics, while a Frequency-Text Augmented Learner enables joint modeling of spectral and semantic features within a shared representation space. Furthermore, a time-centric gradient alignment mechanism is introduced to mitigate cross-modal optimization conflicts via gradient normalization and reliability-aware dynamic reweighting. Extensive experiments on multiple industrial datasets demonstrate that VLT outperforms state-of-the-art methods, achieving superior robustness and generalization under few-shot, noisy, and incomplete-modality settings.

Multivariate Time Series Anomaly Detection (MTSAD) is essential for reliability and safety in domains such as industrial process monitoring and financial risk management, yet conventional approaches rely on application-specific models that are costly to train and hard to scale. Foundation Models (FMs), pre-trained on broad data with strong zero-shot generalization, have recently become available for univariate time series forecasting, raising the question of whether they can address MTSAD without task-specific training. We investigate the zero-shot application of a univariate forecasting FM, TimesFM, to industrial MTSAD on the Secure Water Treatment (SWaT) benchmark, evaluating two strategies: treating the FM as a per-feature forecaster with thresholded prediction errors, and as an embedder whose intermediate representations feed standard outlier detectors. Neither of our proposed setups is competitive with established baselines; embeddings reveal only partial separation between normal and anomalous segments, insufficient for reliable detection. The cause is that the FM is too effective at capturing temporal dynamics, yielding low error even within fully anomalous windows, so persistent anomalies become indistinguishable from normal behavior. However, these observations yield valuable insights: the error peaks at anomaly boundaries, indicating FMs reliably detect distribution changes. We conclude that the proposed naive zero-shot FMs are unsuitable for MTSAD but promising for change-point detection.

State Space Models (SSMs) have emerged as a powerful paradigm for efficient long-sequence modeling, offering parallel training and fast linear-time recurrent inference. However, like other recurrent architectures, SSMs must compress an unbounded history into a fixed-size state, which limits context retention and makes precise retrieval over long-range context inherently difficult. To overcome this limitation, we propose Delay State Space Models (DSSMs), a delay differential equation (DDE)-inspired extension of diagonal SSMs that augments discrete SSM recurrences with explicit delayed-state feedback. Making explicit delayed feedback practical requires new stability parameterization, history management, and FFT-training tools. We address these challenges with a practical discretization and parameterization grounded in a simple delay-independent stability condition. To bypass direct time-domain kernel construction, we derive the DSSM transfer function and compute kernels in the frequency domain, using a kernel contour shift to suppress aliasing and recover accurate FFT training. Empirically, DSSMs substantially improve targeted delayed-retrieval tasks while outperforming S4D on most standard sequence metrics and remaining close on the others.

Knowledge graph foundation models such as Ultra and Trix achieve strong inductive transfer by learning relation-graph representations that generalise to unseen entities and relations. Extending this transferability to temporal knowledge graphs (TKGs) remains challenging: existing temporal models tie their parameters to dataset-specific entities, relations, or timestamps and are not designed to transfer to TKGs with disjoint vocabularies. We propose GRATE (Gated Rotary Attention for Temporal Encoding), an entity-side message function that adds no learnable parameters and encodes time through relative time differences by rotating each edge message according to its time gap to the query and applying a query-conditioned gate to select temporally relevant signals. GRATE integrates into NBFNet-style KG foundation models while preserving structural transferability. Existing TKG benchmarks evaluate within shared train/test vocabularies and cannot directly test cross-dataset temporal transfer; we therefore construct GDELTIndT and WIKIIndT, inductive transfer benchmark suites with disjoint entities, relations, and timestamps spanning both interpolation and extrapolation. Across these benchmarks and held-out forecasting datasets, a single jointly pretrained GRATE checkpoint improves over the static base model in most settings.

Multi-Modal Knowledge Graphs (MMKGs) enrich entities with multiple modalities such as text and images, yet entities with highly similar multi-modal features remain difficult to distinguish. Temporal information of an entity can serve as an additional modality to disambiguate such entities, but existing approaches rarely treat time as a separate modality alongside text and images due to two major challenges: (1) sparse temporal semantics, which hinder alignment with richer modalities, and (2) multiple timestamps, which introduce noise or reduce robustness in representation learning. To address these challenges, we propose Time Imprint, a framework that treats time as an entity-level modality and jointly aligns temporal, textual, and visual representations via a three-view contrastive objective. Additionally, to mitigate multi-timestamp ambiguity, Time Imprint studies a compact timestamp subset selection design space and aggregates the selected timestamps into a discriminative temporal embedding with attention pooling, balancing temporal specificity and robustness. Experiments on three MMKG benchmarks demonstrate that Time Imprint achieves state-of-the-art link prediction performance, improving Hits@1 by up to 6.07% overall and yielding up to 58% gains on the subset of the top-1% ambiguity samples. We further examine different fusion strategies and the sensitivity to timestamp availability and quality, clarifying when and why time-as-modality is most beneficial, while adding only modest training overhead. We release our code at https://anonymous.4open.science/r/Time-Imprint.

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

Real-world data distributions evolve over time, inducing temporal distribution shift that can substantially degrade the reliability of deployed machine learning systems. However, the extent to which architectural choices and their associated inductive biases affect temporal robustness remains insufficiently understood. We present a systematic empirical comparison of temporal robustness across three heterogeneous, time-indexed domains encompassing image classification, multi-label text classification, and text regression tasks. Using a unified evaluation framework based on temporal drift matrices, we train models on cumulative historical data and evaluate their performance on both earlier and later time periods, thereby quantifying cross-temporal generalization. Our study spans model families ranging from simple multilayer perceptrons and convolutional networks to recurrent networks and pretrained Transformer-based encoders. Collectively, the results show that architectural inductive biases systematically shape temporal robustness: models whose inductive biases lead them to exploit localized, highly discriminative features attain the highest in-distribution accuracy, yet those features are often the ones that change most over time, so these models degrade fastest, while pretrained encoders that draw on coarser, more stable representations drift more gradually. These observations offer practical guidance for selecting architectures for real-world systems subject to temporal drift.

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

Lightweight neuromorphic computing offers a promising route to efficient AI, with particular benefits for resource-constrained edge deployments. However, its scalable deployment that can reliably transfer the expected performance has long been hindered by device-to-device variations, which necessitate costly and repeated re-training on new copies and undermine the practical advantages. To address this issue, we introduce a model-free temporal-switch (TS) framework to improve the direct transfer performance, without post-training calibration or adjustment. The TS framework provides a methodology to incorporate a broader spectrum of devices in the training process. In the validation using memristor-based reservoir computing, it enables high performance on unseen devices with a directly transferred readout. It achieves improved prediction in the representative Mackey--Glass benchmark, and the accuracy of 92.4% in spoken digit classification. Its efficacy is validated across different memristor families and RC configurations. Theoretical analysis not only reveals the general computational mechanism underlying its efficacy, but also underlines its potential applicability to other physical platforms.

In this paper, we present the solution developed by our team, XInsight Lab, which achieved first place in Track 3 of the 4th EI-MIGA-IJCAI Challenge with a test accuracy of 0.76923. To address the challenge of weak and sparse implicit emotion evidence in long videos, this paper extends the winning solution from the previous competition and proposes a compact multi-modal temporal modeling framework. The framework integrates and evaluates the effects of multi-source features, including 2D/3D skeletons, facial expression Blendshapes, DINOv2/v3 vision foundation models, X-CLIP video features, and Gemini semantic priors. Architecturally, we propose a cross-attention mechanism that utilizes static pose features, denoted as Base, as the Query and dynamic micro-motion differential features, denoted as Offset, as the Key and Value. By capturing local relative velocities, this mechanism eliminates static biases related to individual body shape and identity. Concurrently, an adaptive pooling method based on Multiple Instance Learning is employed to extract instantaneous emotions while suppressing background noise in long sequences. Finally, the paper reveals the representation collapse phenomenon of general vision foundation models in micro-dynamic tasks, and analyzes the underlying mechanisms where networks fall into public-leaderboard-driven pseudo-generalization due to shortcut learning and rote memorization.

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

This study demonstrates an alignment of per-word processing time in a popular state-space language model Mamba and human readers. In Mamba, the recurrent state transition at each layer conceptually takes some duration of time, the discretization timestep $Δ_t$, determined dynamically in response to the input. Using a naturalistic reading dataset, we show that the per-word timestep from Mamba is a significant predictor of human reading times, and remains significant even when known predictors such as GPT-2 surprisal are controlled for. We further suggest, through formal analysis of Mamba's architecture and internal dynamics, that Mamba can serve as a new, valuable lens to look at human real-time language processing with ever-updated memory, because it allows us to look at how each module (layer) weighs short- and long-term information retention, and how noise may interact with dynamic, continuous memory representation. Code is available online.

Real-world robot learning increasingly relies on heterogeneous data, but demonstrations and rollouts often mix useful progress with stalls, corrections, and suboptimal behavior. Effective policy learning therefore requires frame-level advantages that distinguish reliable local progress from failures and regressions. We propose Self-supervised Temporal Ensemble Advantage Modeling (STEAM), a label-free method that learns such advantages from expert demonstrations. STEAM trains an ensemble of temporal-offset predictors on frame pairs within expert trajectories, using the normalized temporal offset between two frames as a self-supervised signal. Each predictor maps a frame pair to a distribution over temporal offsets, which is converted into a scalar advantage. STEAM then takes the minimum advantage across the ensemble to score mixed-quality rollout data conservatively. Across real-world bimanual towel folding, chip checkout, cola restocking, and single-arm pick-and-place tasks, STEAM identifies stalls, failures, and recoveries. When combined with CFGRL, STEAM further improves policy success rate by 59%, 54.3%, 23% and 16.2% over baselines, respectively.

Temporal variation poses a unique challenge for named entity recognition (NER) in historical texts, where entities drift in surface form and salience across time. While language models (LMs) have made progress in various NLP tasks, their ability to reason about temporality, especially in diachronic contexts, remains limited or at least, questionable. In this paper, we systematically study how temporal metadata can be structurally embedded into NER models using a range of lightweight fusion strategies. We experiment with both absolute and relative temporal representations, injected into Transformer-based architectures via early or late fusion mechanisms such as cross-attention, adapters, and concatenation. Our evaluations on French and German historical datasets reveal that late fusion strategies yield more robust and temporally generalisable performance, particularly in early and noisy periods.

Learning representations that remain robust across centuries of variation in handwriting is a key challenge in diachronic representation learning. Taking one of the longest continuously used writing systems, ancient Greek, as a case study, we introduce three datasets for diachronic representation learning: Hell-Char, a curated training set spanning the 3rd-1st centuries BCE, and two evaluation sets, PaLit-Char (2nd-5th c. CE) and Med-Char (9th-14th c. CE). To address the challenges of symbolic variation, scarce data, and systematic degradation, we propose: a similarity-weighted supervised contrastive loss that biases embeddings using dynamically estimated inter-class similarities, and a lacuna-driven augmentation scheme that simulates realistic manuscript corruptions. Trained with these strategies, both a lightweight CNN and a pretrained ResNet achieve strong recognition performance and produce embeddings that more coherently separate character classes than PCA or generic pretrained models. These embeddings enable clustering, identification of stylistic subgroups, and construction of prototype images that visualize diachronic evolution and transitional letterforms. Our results demonstrate that respecting intrinsic inter-letter relationships and augmenting with domain-informed corruptions yield robust, interpretable representations, offering a transferable paradigm for representation learning under scarce, temporally evolving, and noisy conditions. Code and data available at: https://github.com/ipavlopoulos/diachronic-greek-letterforms.

Supervised learning demands large quantities of labeled data, a bottleneck that is expensive and reliant on domain-specific expertise. Self-supervised learning, particularly contrastive learning, has emerged as a compelling alternative, enabling rich representation learning directly from unlabeled data. Yet its success hinges critically on the design of positive and negative sample pairs. Existing approaches for time series rely on hand-crafted augmentations and masking heuristics that embed strong domain assumptions, often limiting generalization across diverse temporal patterns and potentially introducing spurious correlations. In this work, we challenge this paradigm by demonstrating that explicitly encoding temporal shift invariance through a simple, deterministic view construction is sufficient to learn strong representations for time series classification. By exploiting temporal structure, our method, Shift Invariant Feature Training (ShiFT), achieves state-of-the-art performance on six diverse real-world time series benchmark datasets, as well as the UCR and UEA archives, while reducing training time. Beyond empirical performance, we present a systematic analysis of contrastive learning dynamics in time series settings, examining the effects of batch size and the number of negatives on downstream performance. Our findings provide practical insights for designing efficient contrastive learning frameworks for time series representation learning. The source code is publicly available at https://github.com/sfi-norwai/ShiFT.

EEG foundation models can learn generalizable representations from large-scale EEG corpora to enable single-backbone transfer across diverse clinical and brain-computer interface tasks. Existing models typically discretize the continuous multi-channel EEG waveform into patches or codebook tokens and train a transformer with masked self-supervision. Recognizing that this discretization fragments continuous brain rhythms and obscures fine-grained temporal dynamics, we present B[FM]$^2$(Brain Foundation Model via Flow Matching), whose inductive bias aligns with the data by pretraining directly on the raw signal using continuous-time flow matching without patches, tokenization, or masking. However, multi-channel EEG signals pose an architectural challenge for flow matching: time is densely sampled and highly autocorrelated (thousands of timepoints), while the electrode axis is short (tens of channels) at distinct scalp positions. To address this time-electrode asymmetry, we introduce SplitUNet, a velocity network that factorizes each block into separate 1D temporal and 1D electrode convolutions and downsamples only along time, preserving electrode topology throughout the hierarchy. B[FM]$^2$ sets a new state of the art on 7 of 9 standard downstream EEG classification tasks, using a pretraining budget of only 36,895 segments ($\approx$ 307h), 1-2 orders of magnitude ($\approx$ 30x) less than required by existing EEG foundation models. Further, it generates synthetic EEGs that two board-certified neurologists cannot distinguish from brain data (Cohen's $κ=$ -0.096). https://jd730.github.io/projects/BFM2

Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

Accurate state of health (SOH) estimation is a critical diagnostic service for lithium-ion battery management. However, reliance on labor-intensive manual feature engineering and opaque black-box models hinders scalable industrial deployment. To address this, we introduce TC-SOH: a modular, plug-and-play service architecture for autonomous, end-to-end SOH prediction. TC-SOH employs a temporal-contrastive mechanism and a cross-window prediction pretext task to extract degradation-relevant representations directly from raw operational data. To improve transparency, we connect model efficacy with representation diagnostics: visualization, sensitivity analysis, redundancy analysis, bidirectional probing, future-SOH probing, and temporal shuffling show that learned features overlap with selected expert descriptors while retaining additional SOH-relevant variation, and that ordered temporal context improves subsequent-SOH prediction. Across four public datasets, TC-SOH outperforms the considered physics-informed and data-driven baselines, reducing MAPE by 1.91 times and RMSE by 2.13 times.

High-quality time series forecasting is pivotal for real-world decision-making. However, traditional point-wise metrics often fail to reveal complex temporal patterns and align poorly with human intuitive preferences. While the ''LLM-as-a-Judge'' paradigm has revolutionized text evaluation by providing flexible, human-aligned judgment, its application to time series remains largely unexplored. In this paper, we leverage Vision-Language Models (VLMs) as judges for time series forecasting, harnessing their ability to comprehend time series plots grounded in textual information. Specifically, we propose a novel framework integrating micro- and macro-level judgments informed by contextual information to evaluate time series forecasting. To this end, we introduce TimeVista, a comprehensive VLM-as-a-Judge benchmark comprising 5563 time series samples paired with detailed evaluation rubrics. Extensive meta-evaluations demonstrate that VLMs are highly reliable judges, achieving significantly higher consistency with human preferences than conventional metrics. Building upon our benchmark, we comprehensively assess recent Time Series Foundation Models (TSFMs) under the VLM-as-a-Judge paradigm. Our results demonstrate that VLMs serve as robust and interpretable judges, providing a comprehensive, human-aligned standard for evaluating time series models.

Temporal classification errors are often treated as representation failures, but they can also arise from how available evidence is converted into decisions. This paper proposes a representation--calibration decomposition for temporal classification. We keep a trained native classifier frozen and separate two inference-time interventions: a conservative residual multi-scale branch that adds auxiliary logits to the native prediction, and a post-hoc branch-aware calibrator that recombines native and residual evidence at decision time. This design distinguishes missing temporal evidence from underused decision-level evidence without retraining the backbone. Across FI-2010, PTB-XL, UCI-HAR, MHEALTH, and HARTH, we find that gains are strongly regime-dependent. Residual multi-scale evidence is most useful in noisy or representation-limited settings, especially short-horizon FI-2010 and weaker recurrent backbones, while branch-aware calibration helps when native and auxiliary logits contain complementary evidence not fully exploited by the raw decision rule. Near-saturated settings show limited gains from either intervention. These results suggest that temporal classification should be understood not only as representation learning, but also as the problem of trusting, combining, and calibrating evidence from multiple views.

Affective and cognitive disorders manifest as distributed, time-varying brain network dynamics across regions, channels, and time, challenging robust representation learning from EEG/sEEG for clinical diagnosis. We propose RECTOR (Masked Region-Channel-Temporal Modeling), an end-to-end self-supervised framework that unifies joint region-channel-temporal representation learning beyond fixed anatomical priors. At its core, RECTOR-SA is a hierarchical, block-sparse self-attention induced by Adaptive Functional Partitioning that evolves region structures from static anatomical definitions to adaptive functional regions. The self-supervision is driven by Masked Topology and Representation Learning, which jointly optimizes three complementary objectives: Masked Predictive Modeling, Topological Structure Modeling, and Cross-View Consistency. Across diverse benchmarks, RECTOR sets a new state-of-the-art in EEG emotion recognition and sEEG task-engagement classification. Crucially, its strong robustness to missing channels and cross-montage generalization underscores its potential for large-scale pre-training on heterogeneous EEG/sEEG, providing interpretable insights at both region and channel levels.

Fine-grained action recognition demands temporal reasoning that general-purpose architectures address through different cost-accuracy tradeoffs: 3D dense operators couple computation to the input volume, while difference-based methods approximate motion through rigid, hand-crafted subtraction of uncontextualized features - each reflecting a deliberate design choice with corresponding limitations in expressiveness or flexibility. We present MamBOA, a backbone-agnostic temporal framework built upon a novel interleaved scan structure that recasts the selective state-space recurrence (S6) as a native motion synthesizer. By interleaving consecutive feature representations extracted from a pretrained backbone into a single alternating sequence, the proposed scan structurally drives the recurrence to encode both temporal observations of each position within a shared hidden state, separated by only a single decay step - rendering the inter-frame transition an intrinsic component of the state dynamics rather than an externally computed quantity. A cascade of dedicated alignment and decoding operations then distills this joint encoding into an explicit motion representation, which a dual-path pooling mechanism adaptively aggregates by balancing attention-driven selection with uniform temporal coverage. The framework interfaces seamlessly with CNN, Transformer, and Mamba backbone families, adding only ~2.1 GFLOPs per feature pair. On Diving48, MamBOA achieves 85.02% Top-1 accuracy with an image-pretrained backbone and 86.24% with a video-pretrained backbone processing the entire video in a single forward pass - demonstrating that structurally induced state-space dynamics constitute a principled and general foundation for motion modeling.

Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(τ)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that $D(τ)$ separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static ($τ=0$) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching $88.5\pm4.5\%$ under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that $D(τ)$ is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

When working with real-world temporal data, it is common to encounter features whose distribution is changing over time. The naive employment of Machine Learning models on this unstable data might lead to rapidly degrading performance, especially if the new distribution is much different from what was previously seen during training. In order to cope with this problem, it is critical to automatically identify features that are changing over time. With these features detected, data scientists and other practitioners will be able to mitigate the issue (for instance, by applying data transformations), deploying more robust models that retain high performance for longer periods of time. In this paper, we describe which temporal changes a feature should not suffer from, and propose TEDD, a technique to a) identify when a dataset might lead to an unstable Machine Learning model and b) automatically detect which features cause such lack of robustness. In order to achieve it, we leverage a regression model to highlight which features contribute to a good prediction of an instance's timestamp. We compare our approach to other methods in real and synthetic data, testing their detection capability on all simple change patterns. We show that our method: detects all types of basic changes, both for numerical and categorical features; can detect multivariate drifts; returns a comparable value measuring the amount of change of each feature; requires no parameter tuning; and is scalable both on number of features and instances of the dataset.

We present AEM, an Action-Effect Memory pretraining framework for robot manipulation that learns compact temporal representations from vision-action history. Unlike prior robot representation pretraining methods that mainly focus on single-frame visual encoding, AEM targets the temporal nature of manipulation, where the current observation alone is often insufficient under partial observability. AEM models manipulation as an action-driven interaction process by interleaving visual and action features and applying masked modeling to recover missing content from incomplete histories, thereby learning action-conditioned state evolution. The Mamba-encoded output of the final vision token is used as a compact history representation, serving as the global context for decoding and downstream control. This design preserves a single-vector temporal bottleneck while keeping inference efficient. We evaluate AEM with Diffusion Policy and Flow Policy. AEM consistently improves manipulation performance in both simulation and real-world settings, outperforming baselines across clean scenes, cluttered and random scenes, and non-Markovian tasks. Ablation studies further show that history-aware pretraining surpasses single-frame pretraining and direct frame stacking, while reducing inference latency and computational cost.

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.

Unsupervised building change detection aims to learn building-change masks from unlabeled bi-temporal remote sensing images. Existing label-free methods often follow a discrepancy-to-mask paradigm, directly using temporal differences, frozen foundation-model responses, prompt-based outputs, or post-processing results as final change maps. Although these strategies provide annotation-free cues, they do not learn a task-specific building-change detector and remain vulnerable to the gap between generic temporal discrepancies and building-defined structural changes. In practice, such discrepancies are often noisy and task-irrelevant, as appearance shifts, registration errors, and non-building modifications can produce strong but misleading responses. To address this problem, we propose SST-CD, a spatially selective self-training framework that reformulates fully label-free building change detection as end-to-end detector learning under noisy pseudo supervision. SST-CD uses temporal discrepancies as candidate pseudo labels and trains the detector only on spatially reliable pixels, whose reliability is estimated by a local consistency criterion that filters inconsistent regions from supervision. To further stabilize noisy self-training, a lightweight feature adapter recalibrates bi-temporal features, while a prototype-based decoder produces compact change and no-change representations. Experiments on LEVIR-CD, WHU-CD, and DSIFN-CD show that SST-CD achieves F1 scores of 83.08%, 91.69%, and 86.60%, respectively, outperforming existing unsupervised and label-free baselines.

Time series foundation models (TS-FMs) aim to learn generalizable temporal representations that can be adapted to a wide range of downstream tasks. In real-world multimodal settings, time series are frequently affected by temporal misalignment and partial modality missingness, where different modalities are observed at heterogeneous time scales or are partially absent. Existing approaches typically rely on naive imputation or masking strategies, which fail to account for cross-modal dependencies and often lead to misaligned or degraded representations. We propose TRACE, a conditional estimation paradigm for multimodal time series foundation model pipelines under missingness and irregular sampling, allowing incomplete target modalities to be systematically inferred from available auxiliary modalities. We evaluate TRACE on diverse multimodal benchmarks spanning healthcare and affective computing, including the MIMIC-IV clinical dataset and the CMU-MOSI and CMU-MOSEI benchmarks for multimodal sentiment analysis. Across a range of downstream prediction tasks and missing-modality settings, TRACE consistently outperforms prior multimodal fusion approaches, demonstrating improved robustness to severe modality missingness and more reliable cross-modal representations.

Multivariate time series classification (MTSC) is pivotal in high-stakes domains, such as clinical diagnosis and industrial fault detection, where safe deployment necessitates transparent decision-making. However, isolating the temporal segments that drive model predictions is challenging because discriminative signals in real-world time series are typically sparse, heterogeneous, and heavily obscured by background noise. This paper, therefore, proposes AnchorMoE, an interpretable-by-construction classification framework. Built upon a Mixture-of-Experts (MoE) architecture, AnchorMoE encodes multi-view representations of local patches and routes them to specialized experts, ensuring that the final prediction is formulated as an exact additive decomposition over the input segments, facilitating ante-hoc transparency rather than relying on post-hoc estimations. To maintain the reliability of this decomposition under sparse signal distributions, we introduce a geometric orthogonality constraint that penalizes representational redundancy, compelling distinct experts to specialize in heterogeneous predictive patterns. Furthermore, an uncertainty-aware reliability gate is designed to dynamically calibrate the contribution of each segment, effectively suppressing residual background noise. Extensive experiments on real-world and synthetic benchmarks demonstrate that AnchorMoE achieves highly competitive classification performance while faithfully grounding its decisions in the raw time series.

Many systems used in real-world environments require adding new categories and incorporating new information without forgetting what was previously learnt by the classification model. This is known as class-incremental continual learning, and in the case of multivariate time-series, is further complicated by the temporal structure of the data. In this paper, we present a novel approach for performing class incremental continual learning for the classification of multivariate time series data based upon the construction of a dual-stream feature extraction pipeline (using both deep temporal embedding features generated via a pre-trained frozen foundation model and application of statistical features). Evaluated on five benchmark datasets, the proposed system achieves competitive average accuracy across all datasets while maintaining low forgetting rates across all experimental configurations.

The ongoing digitization has led to a proliferation of time-series data streams that monitor a variety of processes, from which valuable insights may be obtained. Further, the emergence of successful foundational language models begs the question of whether it is possible to achieve time-series models with the foundational properties of handling multiple tasks, while being sufficiently lightweight to allow real-time data stream processing. Existing foundational time-series models are often large and only effective in offline settings without stringent time and computational constraints, and where repeated model calibration is not needed. However, when applied to data streams, these models are ineffective due to their size and lack of support for continual calibration, which compromise their ability to deliver accurate real-time responses, their durability, and their deployability in hardware-limited settings. We propose TimeBlocks to enable versatile time-series processing by facilitating the efficient building of lightweight models suitable for multiple tasks under variable conditions. In particular, the method maintains a pool of interchangeable and modular model blocks that can be used to construct new time-series models. When presented with specific time-series data, a routing strategy iteratively selects the most suitable blocks to construct a lightweight and accurate model for the data. We equip TimeBlocks with a method called StreamCore to build a representative small subset of the data stream, which preserves a guaranteed approximation of the stream over time, enabling continual model calibration. An experimental study on multiple data sets and covering multiple tasks shows that TimeBlocks enables to build models capable of outperforming existing baselines.