Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

Electrocardiogram (ECG) analysis is vital for detecting cardiac abnormalities, yet robust automated classification is challenging due to the complexity and variability of physiological signals. In this work, we investigate transformer-based ECG classification using features derived from the Koopman operator and wavelet transforms. Two tasks are studied: (1) binary classification (Normal vs. Non-normal), and (2) four-class classification (Normal, Atrial Fibrillation, Ventricular Arrhythmia, Block). We use Extended Dynamic Mode Decomposition (EDMD) to approximate the Koopman operator. Our results show that wavelet features excel in binary classification, while Koopman features, when paired with transformers, achieve superior performance in the four-class setting. A simple hybrid of Koopman and wavelet features does not improve accuracy. However, selecting an appropriate EDMD dictionary -- specifically a radial basis function dictionary with tuned parameters -- yields significant gains, surpassing the wavelet-only baseline and the hybrid wavelet-Koopman system. We also present a Koopman-based reconstruction analysis for interpretable insights into the learned dynamics and compare against a recurrent neural network baseline. Overall, our findings demonstrate the effectiveness of Koopman-based feature learning with transformers and highlight promising directions for integrating dynamical systems theory into time-series classification.

Deep Learning for Financial Time Series: A Large-Scale Benchmark of Risk-Adjusted Performance

We present a large scale benchmark of modern deep learning architectures for a financial time series prediction and position sizing task, with a primary focus on Sharpe ratio optimization. Evaluating linear models, recurrent networks, transformer based architectures, state space models, and recent sequence representation approaches, we assess out of sample performance on a daily futures dataset spanning commodities, equity indices, bonds, and FX spanning 2010 to 2025. Our evaluation goes beyond average returns and includes statistical significance, downside and tail risk measures, breakeven transaction cost analysis, robustness to random seed selection, and computational efficiency. We find that models explicitly designed to learn rich temporal representations consistently outperform linear benchmarks and generic deep learning models, which often lead the ranking in standard time series benchmarks. Hybrid models such as VSN with LSTM, a combination of Variable Selection Networks (VSN) and LSTMs, achieves the highest overall Sharpe ratio, while VSN with xLSTM and LSTM with PatchTST exhibit superior downside adjusted characteristics. xLSTM demonstrates the largest breakeven transaction cost buffer, indicating improved robustness to trading frictions.

Dissecting Chronos: Sparse Autoencoders Reveal Causal Feature Hierarchies in Time Series Foundation Models

Time series foundation models (TSFMs) are increasingly deployed in high-stakes domains, yet their internal representations remain opaque. We present the first application of sparse autoencoders (SAEs) to a TSFM, training TopK SAEs on activations of Chronos-T5-Large (710M parameters) across six layers. Through 392 single-feature ablation experiments, we establish that every ablated feature produces a positive CRPS degradation, confirming causal relevance. Our analysis reveals a depth-dependent hierarchy: early encoder layers encode low-level frequency features, the mid-encoder concentrates causally critical change-detection features, and the final encoder compresses a rich but less causally important taxonomy of temporal concepts. The most critical features reside in the mid-encoder (max single-feature Delta CRPS = 38.61), not in the semantically richest final encoder layer, where progressive ablation paradoxically improves forecast quality. These findings demonstrate that mechanistic interpretability transfers effectively to TSFMs and that Chronos-T5 relies on abrupt-dynamics detection rather than periodic pattern recognition.

TokEye: Fast Signal Extraction for Fluctuating Time Series via Offline Self-Supervised Learning From Fusion Diagnostics to Bioacoustics

Next-generation fusion facilities like ITER face a "data deluge," generating petabytes of multi-diagnostic signals daily that challenge manual analysis. We present a "signals-first" self-supervised framework for the automated extraction of coherent and transient modes from high-noise time-frequency data across a variety of sensors. We also develop a general-purpose method and tool for extracting coherent, quasi-coherent, and transient modes for fluctuation measurements in tokamaks by employing non-linear optimal techniques in multichannel signal processing with a fast neural network surrogate on fast magnetics, electron cyclotron emission, CO2 interferometers, and beam emission spectroscopy measurements from DIII-D. Results are tested on data from DIII-D, TJ-II, and non-fusion spectrograms. With an inference latency of 0.5 seconds, this framework enables real-time mode identification and large-scale automated database generation for advanced plasma control. Repository is in https://github.com/PlasmaControl/TokEye.

Multimodal Deep Learning for Early Prediction of Patient Deterioration in the ICU: Integrating Time-Series EHR Data with Clinical Notes

Early identification of patients at risk for clinical deterioration in the intensive care unit (ICU) remains a critical challenge. Delayed recognition of impending adverse events, including mortality, vasopressor initiation, and mechanical ventilation, contributes to preventable morbidity and mortality. We present a multimodal deep learning approach that combines structured time-series data (vital signs and laboratory values) with unstructured clinical notes to predict patient deterioration within 24 hours. Using the MIMIC-IV database, we constructed a cohort of 74,822 ICU stays and generated 5.7 million hourly prediction samples. Our architecture employs a bidirectional LSTM encoder for temporal patterns in physiologic data and ClinicalBERT embeddings for clinical notes, fused through a cross-modal attention mechanism. We also present a systematic review of existing approaches to ICU deterioration prediction, identifying 31 studies published between 2015 and 2024. Most existing models rely solely on structured data and achieve area under the curve (AUC) values between 0.70 and 0.85. Studies incorporating clinical notes remain rare but show promise for capturing information not present in structured fields. Our multimodal model achieves a test AUROC of 0.7857 and AUPRC of 0.1908 on 823,641 held-out samples, with a validation-to-test gap of only 0.6 percentage points. Ablation analysis validates the multimodal approach: clinical notes improve AUROC by 2.5 percentage points and AUPRC by 39.2% relative to a structured-only baseline, while deep learning models consistently outperform classical baselines (XGBoost AUROC: 0.7486, logistic regression: 0.7171). This work contributes both a thorough review of the field and a reproducible multimodal framework for clinical deterioration prediction.

Geometric Framework for Robust Order Detection in Delay-Coordinates Dynamic Mode Decomposition

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced by noise and order overestimation. We show that model order detection and mode selection in DC-DMD are fundamentally problems of subspace geometry. Specifically, true modes are characterized by concentration within a low-dimensional signal subspace, whereas spurious modes necessarily retain non-negligible components outside any moderate overestimate of that subspace. This geometric distinction yields a perturbation-robust definition of true and spurious modes and yields fully data-driven selection criteria. This geometric framework leads to two complementary data-driven selection criteria. The first is derived directly from the geometric distinction and uses a data-driven proxy of the signal-subspace to compute a residual score. The second arises from a new operator-theoretic analysis of delay embedding. Using a block-companion formulation, we show that all modes exhibit a Kronecker-Vandermonde (KV) structure induced by the delay-coordinates, and true modes are distinguished by the degree to which they conform to it. Importantly, we also show that this deviation is governed precisely by the geometric residual. In addition, our analysis provides a principled explanation for the empirical behavior of magnitude- and norm-based heuristics, clarifying when and why they fail under delay-coordinates. Extensive numerical experiments confirm the theoretical predictions and demonstrate that the proposed geometric and structure-based methods achieve robust and accurate order detection and mode selection, consistently better than existing baselines across noise levels, spectral separations, damping regimes, and embedding lengths.

Be Wary of Your Time Series Preprocessing

Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of how different normalization strategies, specifically instance-based and global scaling, impact the expressivity of Transformer-based architectures for time series representation learning. We propose a novel expressivity framework tailored to time series, which quantifies a model's ability to distinguish between similar and dissimilar inputs in the representation space. Using this framework, we derive theoretical bounds for two widely used normalization methods: Standard and Min-Max scaling. Our analysis reveals that the choice of normalization strategy can significantly influence the model's representational capacity, depending on the task and data characteristics. We complement our theory with empirical validation on classification and forecasting benchmarks using multiple Transformer-based models. Our results show that no single normalization method consistently outperforms others, and in some cases, omitting normalization entirely leads to superior performance. These findings highlight the critical role of preprocessing in time series learning and motivate the need for more principled normalization strategies tailored to specific tasks and datasets.

RhythmBERT: A Self-Supervised Language Model Based on Latent Representations of ECG Waveforms for Heart Disease Detection

Electrocardiogram (ECG) analysis is crucial for diagnosing heart disease, but most self-supervised learning methods treat ECG as a generic time series, overlooking physiologic semantics and rhythm-level structure. Existing contrastive methods utilize augmentations that distort morphology, whereas generative approaches employ fixed-window segmentation, which misaligns cardiac cycles. To address these limitations, we propose RhythmBERT, a generative ECG language model that considers ECG as a language paradigm by encoding P, QRS, and T segments into symbolic tokens via autoencoder-based latent representations. These discrete tokens capture rhythm semantics, while complementary continuous embeddings retain fine-grained morphology, enabling a unified view of waveform structure and rhythm. RhythmBERT is pretrained on approximately 800,000 unlabeled ECG recordings with a masked prediction objective, allowing it to learn contextual representations in a label-efficient manner. Evaluations show that despite using only a single lead, RhythmBERT achieves comparable or superior performance to strong 12-lead baselines. This generalization extends from prevalent conditions such as atrial fibrillation to clinically challenging cases such as subtle ST-T abnormalities and myocardial infarction. Our results suggest that considering ECG as structured language offers a scalable and physiologically aligned pathway for advancing cardiac analysis.

FaultXformer: A Transformer-Encoder Based Fault Classification and Location Identification model in PMU-Integrated Active Electrical Distribution System

Accurate fault detection and localization in electrical distribution systems is crucial, especially with the increasing integration of distributed energy resources (DERs), which inject greater variability and complexity into grid operations. In this study, FaultXformer is proposed, a Transformer encoder-based architecture developed for automatic fault analysis using real-time current data obtained from phasor measurement unit (PMU). The approach utilizes time-series current data to initially extract rich temporal information in stage 1, which is crucial for identifying the fault type and precisely determining its location across multiple nodes. In Stage 2, these extracted features are processed to differentiate among distinct fault types and identify the respective fault location within the distribution system. Thus, this dual-stage transformer encoder pipeline enables high-fidelity representation learning, considerably boosting the performance of the work. The model was validated on a dataset generated from the IEEE 13-node test feeder, simulated with 20 separate fault locations and several DER integration scenarios, utilizing current measurements from four strategically located PMUs. To demonstrate robust performance evaluation, stratified 10-fold cross-validation is performed. FaultXformer achieved average accuracies of 98.76% in fault type classification and 98.92% in fault location identification across cross-validation, consistently surpassing conventional deep learning baselines convolutional neural network (CNN), recurrent neural network (RNN). long short-term memory (LSTM) by 1.70%, 34.95%, and 2.04% in classification accuracy and by 10.82%, 40.89%, and 6.27% in location accuracy, respectively. These results demonstrate the efficacy of the proposed model with significant DER penetration.

GNNs for Time Series Anomaly Detection: An Open-Source Framework and a Critical Evaluation

There is growing interest in applying graph-based methods to Time Series Anomaly Detection (TSAD), particularly Graph Neural Networks (GNNs), as they naturally model dependencies among multivariate signals. GNNs are typically used as backbones in score-based TSAD pipelines, where anomalies are identified through reconstruction or prediction errors followed by thresholding. However, and despite promising results, the field still lacks standardized frameworks for evaluation and suffers from persistent issues with metric design and interpretation. We thus present an open-source framework for TSAD using GNNs, designed to support reproducible experimentation across datasets, graph structures, and evaluation strategies. Built with flexibility and extensibility in mind, the framework facilitates systematic comparisons between TSAD models and enables in-depth analysis of performance and interpretability. Using this tool, we evaluate several GNN-based architectures alongside baseline models across two real-world datasets with contrasting structural characteristics. Our results show that GNNs not only improve detection performance but also offer significant gains in interpretability, an especially valuable feature for practical diagnosis. We also find that attention-based GNNs offer robustness when graph structure is uncertain or inferred. In addition, we reflect on common evaluation practices in TSAD, showing how certain metrics and thresholding strategies can obscure meaningful comparisons. Overall, this work contributes both practical tools and critical insights to advance the development and evaluation of graph-based TSAD systems.