Multi-scale hypergraph meets LLMs: Aligning large language models for time series analysis

Recently, there has been great success in leveraging pre-trained large language models (LLMs) for time series analysis. The core idea lies in effectively aligning the modality between natural language and time series. However, the multi-scale structures of natural language and time series have not been fully considered, resulting in insufficient utilization of LLMs capabilities. To this end, we propose MSH-LLM, a Multi-Scale Hypergraph method that aligns Large Language Models for time series analysis. Specifically, a hyperedging mechanism is designed to enhance the multi-scale semantic information of time series semantic space. Then, a cross-modality alignment (CMA) module is introduced to align the modality between natural language and time series at different scales. In addition, a mixture of prompts (MoP) mechanism is introduced to provide contextual information and enhance the ability of LLMs to understand the multi-scale temporal patterns of time series. Experimental results on 27 real-world datasets across 5 different applications demonstrate that MSH-LLM achieves the state-of-the-art results.

Functional Continuous Decomposition

The analysis of non-stationary time-series data requires insight into its local and global patterns with physical interpretability. However, traditional smoothing algorithms, such as B-splines, Savitzky-Golay filtering, and Empirical Mode Decomposition (EMD), lack the ability to perform parametric optimization with guaranteed continuity. In this paper, we propose Functional Continuous Decomposition (FCD), a JAX-accelerated framework that performs parametric, continuous optimization on a wide range of mathematical functions. By using Levenberg-Marquardt optimization to achieve up to $C^1$ continuous fitting, FCD transforms raw time-series data into $M$ modes that capture different temporal patterns from short-term to long-term trends. Applications of FCD include physics, medicine, financial analysis, and machine learning, where it is commonly used for the analysis of signal temporal patterns, optimized parameters, derivatives, and integrals of decomposition. Furthermore, FCD can be applied for physical analysis and feature extraction with an average SRMSE of 0.735 per segment and a speed of 0.47s on full decomposition of 1,000 points. Finally, we demonstrate that a Convolutional Neural Network (CNN) enhanced with FCD features, such as optimized function values, parameters, and derivatives, achieved 16.8% faster convergence and 2.5% higher accuracy over a standard CNN.

Physics-based phenomenological characterization of cross-modal bias in multimodal models

The term 'algorithmic fairness' is used to evaluate whether AI models operate fairly in both comparative (where fairness is understood as formal equality, such as "treat like cases as like") and non-comparative (where unfairness arises from the model's inaccuracy, arbitrariness, or inscrutability) contexts. Recent advances in multimodal large language models (MLLMs) are breaking new ground in multimodal understanding, reasoning, and generation; however, we argue that inconspicuous distortions arising from complex multimodal interaction dynamics can lead to systematic bias. The purpose of this position paper is twofold: first, it is intended to acquaint AI researchers with phenomenological explainable approaches that rely on the physical entities that the machine experiences during training/inference, as opposed to the traditional cognitivist symbolic account or metaphysical approaches; second, it is to state that this phenomenological doctrine will be practically useful for tackling algorithmic fairness issues in MLLMs. We develop a surrogate physics-based model that describes transformer dynamics (i.e., semantic network structure and self-/cross-attention) to analyze the dynamics of cross-modal bias in MLLM, which are not fully captured by conventional embedding- or representation-level analyses. We support this position through multi-input diagnostic experiments: 1) perturbation-based analyses of emotion classification using Qwen2.5-Omni and Gemma 3n, and 2) dynamical analysis of Lorenz chaotic time-series prediction through the physical surrogate. Across two architecturally distinct MLLMs, we show that multimodal inputs can reinforce modality dominance rather than mitigate it, as revealed by structured error-attractor patterns under systematic label perturbation, complemented by dynamical analysis.

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.

EXCODER: EXplainable Classification Of DiscretE time series Representations

Deep learning has significantly improved time series classification, yet the lack of explainability in these models remains a major challenge. While Explainable AI (XAI) techniques aim to make model decisions more transparent, their effectiveness is often hindered by the high dimensionality and noise present in raw time series data. In this work, we investigate whether transforming time series into discrete latent representations-using methods such as Vector Quantized Variational Autoencoders (VQ-VAE) and Discrete Variational Autoencoders (DVAE)-not only preserves but enhances explainability by reducing redundancy and focusing on the most informative patterns. We show that applying XAI methods to these compressed representations leads to concise and structured explanations that maintain faithfulness without sacrificing classification performance. Additionally, we propose Similar Subsequence Accuracy (SSA), a novel metric that quantitatively assesses the alignment between XAI-identified salient subsequences and the label distribution in the training data. SSA provides a systematic way to validate whether the features highlighted by XAI methods are truly representative of the learned classification patterns. Our findings demonstrate that discrete latent representations not only retain the essential characteristics needed for classification but also offer a pathway to more compact, interpretable, and computationally efficient explanations in time series analysis.

Ill-Conditioning in Dictionary-Based Dynamic-Equation Learning: A Systems Biology Case Study

Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown considerable promise, but they face a critical challenge when candidate functions become strongly correlated: numerical ill-conditioning. Poor or restricted sampling, together with particular choices of candidate libraries, can produce strong multicollinearity and numerical instability. In such cases, measurement noise may lead to widely different recovered models, obscuring the true underlying dynamics and hindering accurate system identification. Although sparse regularization promotes parsimonious solutions and can partially mitigate conditioning issues, strong correlations may persist, regularization may bias the recovered models, and the regression problem may remain highly sensitive to small perturbations in the data. We present a systematic analysis of how ill-conditioning affects sparse identification of biological dynamics using benchmark models from systems biology. We show that combinations involving as few as two or three terms can already exhibit strong multicollinearity and extremely large condition numbers. We further show that orthogonal polynomial bases do not consistently resolve ill-conditioning and can perform worse than monomial libraries when the data distribution deviates from the weight function associated with the orthogonal basis. Finally, we demonstrate that when data are sampled from distributions aligned with the appropriate weight functions corresponding to the orthogonal basis, numerical conditioning improves, and orthogonal polynomial bases can yield improved model recovery accuracy across two baseline models.

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.

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.

Pupillometry and Brain Dynamics for Cognitive Load in Working Memory

Cognitive load, the mental effort required during working memory, is central to neuroscience, psychology, and human-computer interaction. Accurate assessment is vital for adaptive learning, clinical monitoring, and brain-computer interfaces. Physiological signals such as pupillometry and electroencephalography are established biomarkers of cognitive load, but their comparative utility and practical integration as lightweight, wearable monitoring solutions remain underexplored. EEG provides high temporal resolution of neural activity. Although non-invasive, it is technologically demanding and limited in wearability and cost due to its resource-intensive nature, whereas pupillometry is non-invasive, portable, and scalable. Existing studies often rely on deep learning models with limited interpretability and substantial computational expense. This study integrates feature-based and model-driven approaches to advance time-series analysis. Using the OpenNeuro 'Digit Span Task' dataset, this study investigates cognitive load classification from EEG and pupillometry. Feature-based approaches using Catch-22 features and classical machine learning models outperform deep learning in both binary and multiclass tasks. The findings demonstrate that pupillometry alone can compete with EEG, serving as a portable and practical proxy for real-world applications. These results challenge the assumption that EEG is necessary for load detection, showing that pupil dynamics combined with interpretable models and SHAP based feature analysis provide physiologically meaningful insights. This work supports the development of wearable, affordable cognitive monitoring systems for neuropsychiatry, education, and healthcare.

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.