Time-Series Classification

Multimodal irregular time series (MITS) consist of asynchronous and irregularly sampled observations from heterogeneous numerical and textual channels. In healthcare, for example, patients' electronic health records (EHR) include irregular lab measurements and clinical notes. The irregular timing and channel patterns of observations carry predictive signal alongside the numerical values and textual content. LLMs are natural candidates for processing such heterogeneous data, given their extensive pretrained knowledge spanning textual and numerical domains. We introduce MILM (Multimodal Irregular time series Language Model), which represents MITS as time-ordered triplets in Extensible Markup Language (XML) format and fine-tunes an LLM through a two-stage strategy for MITS classification. The first stage trains on value-redacted MITS to predict from sampling patterns alone, and the second stage trains on full MITS to jointly model sampling patterns and observed values. Our two-stage model (MILM-2S) and its single-stage counterpart (MILM-Direct) achieve the best and second-best average performance on multiple EHR datasets. Further value redaction evaluations confirm that sampling patterns carry predictive signal and that MILM-2S learns to exploit them. In the value pending evaluation we introduce, where some values are unavailable at prediction time, MILM-2S outperforms MILM-Direct by a larger margin compared to standard evaluation. For MILM-2S, preserving the time and channel of value-pending observations as additional sampling information further improves in-hospital mortality prediction.

While traditional time-series classifiers assume full sequences at inference, practical constraints (latency and cost) often limit inputs to partial prefixes. The absence of class-discriminative patterns in partial data can significantly hinder a classifier's ability to generalize. This work uses knowledge distillation (KD) to equip partial time series classifiers with the generalization ability of their full-sequence counterparts. In KD, high-capacity teacher transfers supervision to aid student learning on the target task. Matching with teacher features has shown promise in closing the generalization gap due to limited parameter capacity. However, when the generalization gap arises from training-data differences (full versus partial), the teacher's full-context features can be an overwhelming target signal for the student's short-context features. To provide progressive, diverse, and collective teacher supervision, we propose Generative Diffusion Prior Distillation (GDPD), a novel KD framework that treats short-context student features as degraded observations of the target full-context features. Inspired by the iterative restoration capability of diffusion models, we learn a diffusion-based generative prior over teacher features. Leveraging this prior, we posterior-sample target teacher representations that could best explain the missing long-range information in the student features and optimize the student features to be minimally degraded relative to these targets. GDPD provides each student feature with a distribution of task-relevant long-context knowledge, which benefits learning on the partial classification task. Extensive experiments across earliness settings, datasets, and architectures demonstrate GDPD's effectiveness for full-to-partial distillation.

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward-backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.

Clinical time-series data are difficult to model with methods designed for regular sequences because they exhibit irregular sampling, frequent missing values, and heterogeneous observation patterns across variables. Existing approaches commonly use observation masks and time-gap information, but they do not continuously capture the decaying reliability of past observations or consistently organize multi-resolution information within a coherent temporal context during aggregation. To address these limitations, we propose Reliability-aware Temporal Aggregation with Mamba (ReTAMamba), which reconstructs clinical time series as time-variable token sequences, estimates observation reliability from missingness and elapsed time, and augments interval summaries with statistical descriptors. Chronological Weaving is used to integrate short- and long-term temporal information within a coherent temporal context, and a budgeted token router is applied to constrain sequence length while preserving informative summaries. Experiments on MIMIC-IV, eICU, and PhysioNet 2012 show that ReTAMamba consistently improves AUPRC over strong baselines, with average relative gains of 7.51%, 7.80%, and 10.15%, respectively. Cohort-level and patient-level analyses on eICU further showed that the learned mean decay for more dynamic signals, such as heart rate and blood pressure, was 24.3% larger than that for relatively static signals, such as laboratory test variables. These findings suggest that effective prediction in irregular clinical time series requires modeling not only what was measured, but also when and how it was observed, including information freshness and observation timeliness.

In this paper, we propose the first VL$\underline{\textbf{M}}$ $\underline{\textbf{a}}$gentic $\underline{\textbf{r}}$easoning framework for few-$\underline{\textbf{s}}$hot multimodal $\underline{\textbf{T}}$ime $\underline{\textbf{S}}$eries $\underline{\textbf{C}}$lassification ($\textbf{MarsTSC}$), which introduces a self-evolving knowledge bank as a dynamic context iteratively refined via reflective agentic reasoning. The framework comprises three collaborative roles: i) Generator conducts reliable classification via reasoning; ii) Reflector diagnoses the root causes of reasoning errors to yield discriminative insights targeting the temporal features overlooked by Generator; iii) Modifier applies verified updates to the knowledge bank to prevent context collapse. We further introduce a test-time update strategy to enable cautious, continuous knowledge bank refinement to mitigate few-shot bias and distribution shift. Extensive experiments across 12 mainstream time series benchmarks demonstrate that $\textbf{MarsTSC}$ delivers substantial and consistent performance gains across 6 VLM backbones, outperforming both classical and foundation model-based time series baselines under few-shot conditions, while producing interpretable rationales that ground each classification decision in human-readable feature evidence.

Wearable sensors enable the continuous acquisition of high-resolution physiological waveforms, such as photoplethysmography and accelerometry, under free-living conditions. However, inferring health-related phenotypes from these signals presents significant challenges due to high sampling frequencies, multimodal dependencies, and extreme sequence lengths (e.g., weeks of recordings), compounded by a scarcity of ground-truth labels. To address these challenges, existing self-supervised learning (SSL) methodologies typically follow two paradigms: (1) learning rich morphological representations from short waveform segments while collapsing longitudinal dynamics through simple aggregation, or (2) modeling behavioral patterns from coarse, hand-crafted features (e.g. heart rate, step counts) spanning longer horizons but foregoing subtle, predictive signatures in raw waveforms. To bridge this gap, we propose WavesFM, a foundation model utilizing a two-stage SSL framework for longitudinal physiological data. Specifically, we decompose the learning problem into two stages: first, a segment-level encoder is pretrained to extract local embeddings from short waveforms; subsequently, a temporal encoder is trained to model the sequence of these embeddings across a multi-day horizon. This hierarchical approach overcomes the computational complexity of high-resolution, long-sequence data, allowing the overall model to capture both local signal semantics and the complex circadian and inter-day variations governing physiological dynamics. Pretrained on over 6.8M hours (N=324k individuals) of recordings for the first stage and 5.3M hours (N=10k) for the second stage, WavesFM demonstrates superior performance across 58 diverse tasks spanning demographics, lifestyle, health conditions, and medications.

In time-series domains where both predictive performance and interpretability are essential, deep neural networks achieve strong results but provide limited insight into how their predictions are made. Projection-based prototype networks address this limitation by grounding predictions in similarity to representative training examples, enabling case-based explanations and global prototype inspection. However, existing approaches rely on label supervision, tying prototypes to a specific task and requiring large labeled datasets. We introduce ProtoSSL, a novel framework for learning interpretable, projection-based prototypes from unlabeled time-series data and adapting them to downstream tasks. Our key idea is to separate motif discovery from label alignment. ProtoSSL first learns a reusable prototype bank using a self-supervised objective applied directly to prototype activations, and then aligns these prototypes to downstream tasks through an efficient assignment procedure. Across six electrocardiography (ECG) datasets, ProtoSSL improves label efficiency, outperforming supervised prototype baselines in low-data regimes with as few as 256 labeled examples; with fine-tuning, ProtoSSL outperforms supervised prototype baselines at full dataset scale. In a human evaluation study, ProtoSSL produces prototypes and prototype-based explanations that are judged more favorably than those learned with direct label supervision. We further show that the framework extends to audio classification. Thus, ProtoSSL enables both learning generalizable prototypes from unlabeled data before the downstream label space is known, and subsequent assignment of interpretable, projection-grounded prototypes to new time-series tasks.

Structured state space models (SSMs) have recently emerged as a promising foundation for sequence modeling, with Mamba-based architectures demonstrating strong performance through input-dependent state transitions, albeit at considerable complexity. However, their application to time-series classification (TSC) has been largely limited to Mamba-style architectures, leaving the broader SSM design space underexplored. We present the first systematic study spanning diagonal SSMs (S4D) and input-dependent SSMs (Mamba family) on large-scale TSC benchmarks, asking whether such complexity is necessary for top performance. Our results reveal a surprising finding: S4D consistently outperforms Mamba-based variants in both accuracy and efficiency, challenging the assumption that increased complexity translates to meaningful gains in TSC. Building on this, we introduce MS4, lightweight modifications to S4D via a linear input projection and channel-mixing mechanism, and MS4N, a normalized variant that stabilizes state dynamics with negligible overhead. Evaluated on 59 datasets across MONSTER (up to 60 million samples, 50K timesteps, 82 classes) and the UEA benchmark, against 15 baselines, MS4 and MS4N consistently outperform Mamba-based models while remaining more efficient, and MS4N matches or surpasses competing deep learning models that are roughly 2x and 10x larger in parameters. These results position lightweight structured SSMs as a compelling alternative to scaling complexity for TSC.

Accurate trend forecasting in healthcare time series is essential for planning and resource allocation. This paper proposes a Bayesian framework for predicting oncology demand trends, modeling weekly appointments as a Poisson process with a Gamma prior to the demand rate. To enhance adaptability and capture persistent directional patterns, we incorporate a residual-based boosting mechanism grounded in a Gamma-Log-Normal conjugate structure. This boosting approach allows the model to track both short- and long-term trend shifts while maintaining the analytical tractability of conjugate Bayesian updating. The methodology was evaluated on real oncology service data from Cariri, Ceara, Brazil, and compared against established baselines, including linear regression, ARIMA, naive forecasting, LSTM neural networks, and XGBoost. Results showed that the proposed model outperforms competing methods in trend detection accuracy, with gains in terms of percentage of correct direction of 38.25% in relation to the second best approach in some cases.

Learning meaningful representations from medical time series (MedTS) such as ECG or EEG signals is a critical challenge. These signals are often high-dimensional, variable-length and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs) are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact and semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of $k$ latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are \textit{sufficient statistics} for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically \textit{disentangled} representations. We present the theoretical justification for our method, framing it as a novel \textbf{Disentangled Rate-Distortion} problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.

Background: Timely, uncertainty-aware forecasting from irregular electronic health records (EHR) can support critical-care decisions, yet most approaches either impute to a grid or sacrifice interpretability. We introduce StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to uncover a sparse, ordered directed acyclic graph (DAG) of inter-variable dependencies while preserving principled uncertainty. We further propose LP-StructGP, which augments StructGP with latent pathways-shared, temporally shifted trajectories inferred via subject-specific coupling filters and a softmax gating mechanism-to capture cross-patient progression patterns. Both models are trained under sparsity and acyclicity constraints (augmented Lagrangian, Adam) using scalable low-rank updates. Results: In simulations, the approach reliably recovers ground-truth graphs (Structural Hamming Distance approaching 0 as cohorts grow) and pathway assignments (high Adjusted Rand Index). On a MIMIC-IV septic shock cohort (n=1,008; norepinephrine, creatinine, mean arterial pressure), StructGP improves short-horizon (6 h) forecasting over independent-task baselines (average RMSE 0.68 [95%CI: 0.63--0.74] vs. 0.88 [0.83-0.94]) and, with 15 additional inputs, markedly outperforms unstructured kernels (0.63 [0.58-0.69] vs. 3.02 [2.85-3.18]) with superior calibration (coverage 0.96 vs. 0.84). On the PhysioNet Challenge (12k patients, 41 variables), StructGP attains competitive accuracy (MAE 3.72e-2) relative to a state-of-the-art graph neural model while maintaining calibrated uncertainty. Conclusion: These results show that structured process convolutions with latent pathways deliver interpretable, scalable, and well-calibrated forecasting for irregular clinical time series.

Elastic distances like dynamic time warping (DTW) are central to time series machine learning because they compare sequences under local temporal misalignment. Soft-DTW is an adaptation of DTW that can be used as a gradient-based loss by replacing the hard minimum in its dynamic-programming recursion with a smooth relaxation. However, this approach does not directly extend to elastic distances whose transition costs depend on the local alignment context. Move-Split-Merge (MSM) is one such distance: it uses context-aware split and merge penalties and has often outperformed DTW in supervised and unsupervised time series machine learning tasks such as classification and clustering. We introduce Soft-MSM, a smooth relaxation of MSM and an elastic alignment loss with context-aware transition costs. Central to the formulation is a smooth gated surrogate for MSM's piecewise split/merge cost, which enables gradients through both the dynamic-programming recursion and the local transition structure. We derive the forward recursion, backward recursion, soft alignment matrix, closed-form gradient, limiting behaviour, and divergence-corrected formulation. Experiments on 112 UCR datasets show that Soft-MSM gives lower MSM barycentre loss than existing MSM barycentre methods, and yields significantly better clustering and nearest-centroid classification performance than Soft-DTW-based alternatives. An implementation is available in the open-source \texttt{aeon} toolkit.

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

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

Memristive devices present a promising foundation for next-generation information processing by combining memory and computation within a single physical substrate. This unique characteristic enables efficient, fast, and adaptive computing, particularly well suited for deep learning applications. Among recent developments, the memristive-friendly echo state network (MF-ESN) has emerged as a promising approach that combines memristive-inspired dynamics with the training simplicity of reservoir computing, where only the readout layer is learned. Building on this framework, we propose memristive-friendly parallelized reservoirs (MARS), a simplified yet more effective architecture that enables efficient scalable parallel computation and deeper model composition through novel subtractive skip connections. This design yields two key advantages: substantial training speedups of up to 21x over the inherently lightweight echo state network baseline and significantly improved predictive performance. Moreover, MARS demonstrates what is possible with parallel memristive-friendly reservoir computing: on several long sequence benchmarks our compact gradient-free models substantially outperform strong gradient-based sequence models such as LRU, S5, and Mamba, while reducing full training time from minutes or hours down seconds or even only a few hundred milliseconds. Our work positions parallel memristive-friendly computing as a promising route towards scalable neuromorphic learning systems that combine high predictive capability with radically improved computational efficiency, while providing a clear pathway to energy-efficient, low-latency implementations on emerging memristive and in-memory hardware.

Multivariate time series classification (MTSC) plays a crucial role in various domains, including biomedical signal analysis and motion monitoring. However, existing approaches, particularly deep learning models, often require high computational resources, making them unsuitable for real-time applications or deployment on low-cost hardware, such as IoT devices and wearable systems. In this paper, we propose the Univariate Channel Fusion (UCF) method to deal with MTSC efficiently. UCF transforms multivariate time series into a univariate representation through simple channel fusion strategies such as the mean, median, or dynamic time warping barycenter. This transformation enables the use of any classifier originally designed for univariate time series, providing a flexible and computationally lightweight alternative to complex models. We evaluate UCF in five case studies covering diverse application domains, including chemical monitoring, brain-computer interfaces, and human activity analysis. The results demonstrate that UCF often outperforms baseline methods and state-of-the-art algorithms tailored for MTSC, while achieving substantial gains in computational efficiency, being particularly effective in problems with high inter-channel correlation.

Medical time series, such as electrocardiograms (ECG) and electroencephalograms (EEG), exhibit complex temporal dynamics and structured cross-channel dependencies, posing fundamental challenges for automated analysis. Conventional convolutional and recurrent models struggle to capture long-range dependencies, while Transformer-based approaches incur quadratic complexity and often introduce redundant interactions that are misaligned with the intrinsic structure of physiological signals. To address these limitations, we propose MedMamba, a principle-driven multi-scale bidirectional state space architecture tailored for medical time series classification. Our design is guided by three key inductive biases of physiological signals: spatial centralization, multi-timescale temporal composition, and non-causal contextual dependency. These principles are instantiated through a lightweight channel-mixing module for cross-channel reparameterization, multi-scale convolutional tokenization for temporal decomposition, and bidirectional Mamba blocks for efficient global context modeling with linear complexity. Extensive experiments on six benchmark datasets spanning EEG, ECG, and human activity signals demonstrate that MedMamba consistently outperforms state-of-the-art methods across diverse modalities. Notably, it achieves 85.97% accuracy on PTB and establishes new state-of-the-art performance on the challenging ADFTD dataset (54.72% accuracy and 52.01% F1-score). Strong results on long-sequence benchmarks, such as SleepEDF, further validate its capability in modeling long-range dependencies. Moreover, MedMamba achieves a speedup of 4.6x in inference, highlighting its practicality for real-time clinical deployment. These results suggest that principle-guided state space modeling offers an effective and scalable alternative to Transformer-based approaches for medical time series analysis.

Despite recent advances in state space models (SSMs) such as Mamba across various sequence domains, research on their standalone capacity for time series classification (TSC) has remained limited. We propose MambaSL, a framework that minimally redesigns the selective SSM and projection layers of a single-layer Mamba, guided by four TSC-specific hypotheses. To address benchmarking limitations -- restricted configurations, partial University of East Anglia (UEA) dataset coverage, and insufficiently reproducible setups -- we re-evaluate 20 strong baselines across all 30 UEA datasets under a unified protocol. As a result, MambaSL achieves state-of-the-art performance with statistically significant average improvements, while ensuring reproducibility via public checkpoints for all evaluated models. Together with visualizations, these results demonstrate the potential of Mamba-based architectures as a TSC backbone.

The contemporary paradigm of trajectory learning operates fundamentally at the level of group dynamics, systematically reducing individual-level complexity to fit group-level models, thus rendering effective patient subtyping difficult and individual-level modeling largely out of reach. We propose a data-driven paradigm that introduces a dedicated individual-level temporal variable to capture \emph{Timing Attention} (i.e., the degree of concentration of an event's timing distribution across the patient cohort), thereby rendering timing a \emph{computable dimension} that enables individualized temporal features in trajectory learning. Instantiated as the Level-of-Individual Time Transformation (LITT) and applied to longitudinal EHR data from 3,276 breast cancer patients, the proposed paradigm demonstrates, for the first time to our knowledge: (1) automatic discovery of clinically significant patient trajectories, and (2) counterfactual timing deduction, that is, a \emph{What-If Machine}. Both results are purely data-driven, requiring no prior domain knowledge. LITT further achieves strong performance on timing prediction and survival analysis tasks.

The zero-shot evaluation of time series foundation models (TSFMs) for classification typically uses a frozen encoder followed by a task-specific classifier. However, this practice violates the training-free premise of zero-shot deployment and introduces evaluation bias due to classifier-dependent training choices. To address this issue, we propose TIC-FM, an in-context learning framework that treats the labeled training set as context and predicts labels for all test instances in a single forward pass, without parameter updates. TIC-FM pairs a time series encoder and a lightweight projection adapter with a split-masked latent memory Transformer. We further provide theoretical justification that in-context inference can subsume trained classifiers and can emulate gradient-based classifier training within a single forward pass. Experiments on 128 UCR datasets show strong accuracy, with consistent gains in the extreme low-label situation, highlighting training-free transfer for time series classification.The source code is publicly available at https://github.com/fangjuntao/TIC-FM.

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.

Electronic health Records (EHRs) have become a cornerstone in modern-day healthcare. They are a crucial part for analyzing the progression of patient health; however, their complexity, characterized by long, multivariate sequences, sparsity, and missing values poses significant challenges in traditional deep learning modeling. While Transformer-based models have demonstrated success in modeling EHR data and predicting clinical outcomes, their quadratic computational complexity and limited context length hinder their efficiency and practical applications. On the other hand, State Space Models (SSMs) like Mamba present a promising alternative offering linear-time sequence modeling and improved efficiency for handling long sequences, but focus mostly on mixing sequence-level information rather than channel-level data. To overcome these challenges, we propose HyMaTE (A Hybrid Mamba and Transformer Model for EHR Representation Learning), a novel hybrid model tailored for representing longitudinal data, combining the strengths of SSMs with advanced attention mechanisms. By testing the model on predictive tasks on multiple clinical datasets, we demonstrate HyMaTE's ability to capture an effective, richer, and more nuanced unified representation of EHR data. Additionally, the interpretability of the outcomes achieved by self-attention illustrates the effectiveness of our model as a scalable and generalizable solution for real-world healthcare applications. Codes are available at: https://github.com/healthylaife/HyMaTE.

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this paper, we propose TANDEM (Temporal Attention-guided Neural Differential Equations for Missingness), an attention-guided neural differential equation framework that effectively classifies time series data with missing values. Our approach integrates raw observation, interpolated control path, and continuous latent dynamics through a novel attention mechanism, allowing the model to focus on the most informative aspects of the data. We evaluate TANDEM on 30 benchmark datasets and a real-world medical dataset, demonstrating its superiority over existing state-of-the-art methods. Our framework not only improves classification accuracy but also provides insights into the handling of missing data, making it a valuable tool in practice.

Time series segmentation assigns a label to each part of a sequence. We formulate dense univariate segmentation as node classification on a graph whose nodes are the original time points. A local window provides node features without setting output granularity. We evaluate the approach on a TSSB-derived inductive benchmark built from disjoint UCR training and test instances. Under one fixed Graph Attention Network (GAT), visibility-based transformations achieve the highest mean ranks among eleven graph constructions. WDPVG, directed NVG, and weighted NVG form a statistically indistinguishable top group after Holm correction. On the 59-dataset Time Series Segmentation Benchmark, WDPVG+GAT reaches a weighted F1 of $0.916$, below seq2point at $0.951$ and statistically indistinguishable from same-feature MLP, random-forest, and 1-NN controls, because at this downsampled resolution each segment is short and the fixed $81$-sample window already spans most of it. At native resolution, where each segment is longer than that window, WDPVG+GAT is less sensitive to feature-window width and remains above the same-feature MLP at every tested window. The graph's advantage over these point-wise classifiers comes from context beyond the local window, which the visibility graph's long-range edges can supply, rather than from better features within it. In a separate resolution sweep, it is statistically tied with a window-searched seq2point while using about $70\times$ fewer parameters and $46\times$ less measured peak memory, although seq2point moves ahead after downsampling. This identifies a practical operating regime for finely sampled series when model size and repeated window tuning matter.

While foundation models have revolutionized various domains, their application to time series classification remains rather under-explored, with existing literature predominantly focused on forecasting. To bridge this gap, we introduce \textbf{Mantis}, a transformer-based foundation model pre-trained exclusively on synthetic data via self-supervised contrastive learning. We demonstrate that effective tokenization is critical to unlocking the full potential of transformers, proposing a novel token generator unit. Furthermore, we introduce an enhanced test-time methodology that bridges the performance gap between Mantis and strong specialized approaches by leveraging intermediate-layer representations, self-ensembling, and cross-model embedding fusion. Extensive experiments demonstrate that Mantis establishes a new state-of-the-art, outperforming existing foundation models across four diverse dataset collections covering various application domains.

The proliferation of Internet-of-Things (IoT) devices has led to an unprecedented volume of multivariate time series (MTS) data, requiring efficient and accurate processing for timely decision-making in resource-constrained edge environments. Hyperdimensional (HD) computing, with its inherent efficiency and parallelizability, has shown promise in classification tasks but struggles to capture complex temporal patterns, while Transformers excel at sequence modeling but incur high computational and memory overhead. We introduce BiHDTrans, an efficient neurosymbolic binary hyperdimensional Transformer that integrates self-attention into the HD computing paradigm, unifying the representational efficiency of HD computing with the temporal modeling power of Transformers. Empirically, BiHDTrans outperforms state-of-the-art (SOTA) HD computing models by at least 14.47% and achieves 6.67% higher accuracy on average than SOTA binary Transformers. With hardware acceleration on FPGA, our pipelined implementation leverages the independent and identically distributed properties of high-dimensional representations, delivering 39.4 times lower inference latency than SOTA binary Transformers. Theoretical analysis shows that binarizing in holographic high-dimensional space incurs significantly less information distortion than directly binarizing neural networks, explaining BiHDTrans's superior accuracy. Furthermore, dimensionality experiments confirm that BiHDTrans remains competitive even with a 64% reduction in hyperspace dimensionality, surpassing SOTA binary Transformers by 1-2% in accuracy with 4.4 times less model size, as well as further reducing the latency by 49.8% compare to the full-dimensional baseline. Together, these contributions bridge the gap between the expressiveness of Transformers and the efficiency of HD computing, enabling accurate, scalable, and low-latency MTS classification.