Effective Dataset Distillation for Spatio-Temporal Forecasting with Bi-dimensional Compression

Spatio-temporal time series are widely used in real-world applications, including traffic prediction and weather forecasting. They are sequences of observations over extensive periods and multiple locations, naturally represented as multidimensional data. Forecasting is a central task in spatio-temporal analysis, and numerous deep learning methods have been developed to address it. However, as dataset sizes and model complexities continue to grow in practice, training deep learning models has become increasingly time- and resource-intensive. A promising solution to this challenge is dataset distillation, which synthesizes compact datasets that can effectively replace the original data for model training. Although successful in various domains, including time series analysis, existing dataset distillation methods compress only one dimension, making them less suitable for spatio-temporal datasets, where both spatial and temporal dimensions jointly contribute to the large data volume. To address this limitation, we propose STemDist, the first dataset distillation method specialized for spatio-temporal time series forecasting. A key idea of our solution is to compress both temporal and spatial dimensions in a balanced manner, reducing training time and memory. We further reduce the distillation cost by performing distillation at the cluster level rather than the individual location level, and we complement this coarse-grained approach with a subset-based granular distillation technique that enhances forecasting performance. On five real-world datasets, we show empirically that, compared to both general and time-series dataset distillation methods, datasets distilled by our STemDist method enable model training (1) faster (up to 6X) (2) more memory-efficient (up to 8X), and (3) more effective (with up to 12% lower prediction error).

The Density of Cross-Persistence Diagrams and Its Applications

Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of these features across scales. While effective for analyzing individual manifolds, persistence diagrams do not account for interactions between pairs of them. Cross-persistence diagrams (cross-barcodes), introduced recently, address this limitation by characterizing relationships between topological features of two point clouds. In this work, we present the first systematic study of the density of cross-persistence diagrams. We prove its existence, establish theoretical foundations for its statistical use, and design the first machine learning framework for predicting cross-persistence density directly from point cloud coordinates and distance matrices. Our statistical approach enables the distinction of point clouds sampled from different manifolds by leveraging the linear characteristics of cross-persistence diagrams. Interestingly, we find that introducing noise can enhance our ability to distinguish point clouds, uncovering its novel utility in TDA applications. We demonstrate the effectiveness of our methods through experiments on diverse datasets, where our approach consistently outperforms existing techniques in density prediction and achieves superior results in point cloud distinction tasks. Our findings contribute to a broader understanding of cross-persistence diagrams and open new avenues for their application in data analysis, including potential insights into time-series domain tasks and the geometry of AI-generated texts. Our code is publicly available at https://github.com/Verdangeta/TDA_experiments

FreqCycle: A Multi-Scale Time-Frequency Analysis Method for Time Series Forecasting

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.

Examining the Role of YouTube Production and Consumption Dynamics on the Formation of Extreme Ideologies

The relationship between content production and consumption on algorithm-driven platforms like YouTube plays a critical role in shaping ideological behaviors. While prior work has largely focused on user behavior and algorithmic recommendations, the interplay between what is produced and what gets consumed, and its role in ideological shifts remains understudied. In this paper, we present a longitudinal, mixed-methods analysis combining one year of YouTube watch history with two waves of ideological surveys from 1,100 U.S. participants. We identify users who exhibited significant shifts toward more extreme ideologies and compare their content consumption and the production patterns of YouTube channels they engaged with to ideologically stable users. Our findings show that users who became more extreme consumed have different consumption habits from those who do not. This gets amplified by the fact that channels favored by users with extreme ideologies also have a higher affinity to produce content with a higher anger, grievance and other such markers. Lastly, using time series analysis, we examine whether content producers are the primary drivers of consumption behavior or merely responding to user demand.

TS-MLLM: A Multi-Modal Large Language Model-based Framework for Industrial Time-Series Big Data Analysis

Accurate analysis of industrial time-series big data is critical for the Prognostics and Health Management (PHM) of industrial equipment. While recent advancements in Large Language Models (LLMs) have shown promise in time-series analysis, existing methods typically focus on single-modality adaptations, failing to exploit the complementary nature of temporal signals, frequency-domain visual representations, and textual knowledge information. In this paper, we propose TS-MLLM, a unified multi-modal large language model framework designed to jointly model temporal signals, frequency-domain images, and textual domain knowledge. Specifically, we first develop an Industrial time-series Patch Modeling branch to capture long-range temporal dynamics. To integrate cross-modal priors, we introduce a Spectrum-aware Vision-Language Model Adaptation (SVLMA) mechanism that enables the model to internalize frequency-domain patterns and semantic context. Furthermore, a Temporal-centric Multi-modal Attention Fusion (TMAF) mechanism is designed to actively retrieve relevant visual and textual cues using temporal features as queries, ensuring deep cross-modal alignment. Extensive experiments on multiple industrial benchmarks demonstrate that TS-MLLM significantly outperforms state-of-the-art methods, particularly in few-shot and complex scenarios. The results validate our framework's superior robustness, efficiency, and generalization capabilities for industrial time-series prediction.

Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection

This paper introduces temporal-conditioned normalizing flows (tcNF), a novel framework that addresses anomaly detection in time series data with accurate modeling of temporal dependencies and uncertainty. By conditioning normalizing flows on previous observations, tcNF effectively captures complex temporal dynamics and generates accurate probability distributions of expected behavior. This autoregressive approach enables robust anomaly detection by identifying low-probability events within the learned distribution. We evaluate tcNF on diverse datasets, demonstrating good accuracy and robustness compared to existing methods. A comprehensive analysis of strengths and limitations and open-source code is provided to facilitate reproducibility and future research.

Towards plausibility in time series counterfactual explanations

We present a new method for generating plausible counterfactual explanations for time series classification problems. The approach performs gradient-based optimization directly in the input space. To enforce plausibility, we integrate soft-DTW (dynamic time warping) alignment with $k$-nearest neighbors from the target class, which effectively encourages the generated counterfactuals to adopt a realistic temporal structure. The overall optimization objective is a multi-faceted loss function that balances key counterfactual properties. It incorporates losses for validity, sparsity, and proximity, alongside the novel soft-DTW-based plausibility component. We conduct an evaluation of our method against several strong reference approaches, measuring the key properties of the generated counterfactuals across multiple dimensions. The results demonstrate that our method achieves competitive performance in validity while significantly outperforming existing approaches in distributional alignment with the target class, indicating superior temporal realism. Furthermore, a qualitative analysis highlights the critical limitations of existing methods in preserving realistic temporal structure. This work shows that the proposed method consistently generates counterfactual explanations for time series classifiers that are not only valid but also highly plausible and consistent with temporal patterns.

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.

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.

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.