Harmonic Dataset Distillation for Time Series Forecasting

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).

Time series foundation models rely on large-scale pretraining over diverse datasets across domains, yet their heterogeneity in temporal patterns could hinder the effectiveness of training and learning transferable time series representations. Inspired a fundamental concept, normalized power spectral density (PSD) in signal processing, we assume harmonizing datasets via PSDs in the spectral domain could reduce mismatches and enhance pretraining. We then go beyond the direct intractable minimization optimization and innovatively reformulate it as a principled harmonization approach. Specifically, we propose Harmonizer, a module that reshapes spectral structures and implicitly harmonizing PSDs across datasets, which theoretically corresponds to a shared reparameterization of second-order temporal correlations. Our theoretical analysis further reveals token interactions with Harmonizer can be efficiently mediated by a compact set of resonators, motivating a HarmonicAttention design that performs self-attention in a low-dimensional interaction space. Then, we propose Olivia, a novel time series foundation model built upon these harmonization mechanisms. Extensive experiments on two large-scale benchmarks (TSLib and GIFT-Eval) and extra 6 datasets from GluonTS, demonstrate Olivia consistently achieves state-of-the-art performance under zero-shot, few-shot, and full-shot forecasting scenarios. Our code is available at https://github.com/TSTS13/Olivia.

Self-supervised pre-training of time series models is currently dominated by next-token prediction and reconstruction objectives. In continuous-valued domains, these paradigms often waste model capacity on high-frequency, point-wise noise at the expense of learning invariant structure. While invariance-based self-distillation has proven highly effective in computer vision, its application to temporal data remains largely underexplored. Effectively adapting such methods to time series requires carefully designed augmentations: spatial operations like cropping can shift the timing of repeating cycles or distort the signal, while basic jittering may provide limited variation. We introduce Wavelet-based self-distillation for time series (WinoTS), an invariance-based pre-training paradigm designed specifically for temporal signals. At its core, WinoTS leverages time-frequency augmentations to construct multi-scale structural views without distorting underlying signal dynamics. Across extensive evaluations, WinoTS outperforms state-of-the-art baselines in long-term forecasting, cross-domain zero-shot transfer, and unsupervised anomaly detection. Notably, linear probing on frozen WinoTS representations frequently surpasses fully supervised models trained from scratch. Systematic ablations demonstrate that WinoTS is a flexible, architecture-agnostic framework yielding gains across time series backbones, and establish that time-frequency transformations provide a principled alternative to vision-style spatial augmentations.