Scale-Aware Pretraining of Time Series Foundation Models via Multi-Patch Token Alignment and Hybrid Masking

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.

Time Series Foundation Models (TSFMs) have achieved remarkable zero-shot performance through extensive pre-training on massive time series datasets. Nevertheless, due to the low-dimensional properties and diverse structural patterns of time series data, performing naive fine-tuning on TSFMs often leads to overfitting and falling into the mean-prediction trap. To address these challenges, we propose SIFT, a robust adaptation method that enhances time series foundation models by preserving Semantic Invariance and structural Fidelity throughout the fine-Tuning process. We employ semantic-invariant adversarial augmentation, which utilizes semantic spectrum decomposition to partition the semantic space and then generates perturbations within the non-core semantic subspace to bolster the model's robustness against these perturbations, mitigating overfitting. We implement a component-based structural fidelity enhancement, which facilitates component-wise mixup and imposes a reconstruction objective to improve the model's ability to preserve structural fidelity, alleviating the mean-prediction trap. Extensive experiments on representative TSFMs covering 10 real-world datasets demonstrate that SIFT can significantly enhance the performance of TSFMs.

Inherent temporal heterogeneity, such as varying sampling densities and periodic structures, has posed substantial challenges in zero-shot generalization for Time Series Foundation Models (TSFMs). Existing TSFMs predominantly rely on massive parameterization to absorb such heterogeneity, as their static tokenization and positional encoding schemes entangle diverse temporal patterns into a fixed representation space, encouraging memorization rather than adaptation. To address this limitation, we propose Kairos, a flexible and parameter-efficient TSFM dedicated to forecasting tasks, which decouples temporal heterogeneity from model capacity through a novel tokenization perspective. Kairos introduces a dynamic patching tokenizer and a mixture-of-size encoding that adapt observational granularity to local information density, enabling fine-grained temporal abstraction without increasing model width or depth. In addition, we design a multi-granularity positional embedding based on dynamic rotary encodings, which conditions on instance-level spectral features and temporal structure induced by dynamic patching tokenization, allowing robust modeling of diverse temporal dependencies. Trained on a novel Predictability-Stratified Time-Series (PreSTS) corpus, Kairos achieves superior zero-shot performance with substantially fewer parameters on two mainstream benchmarks, GIFT-Eval and Time-Series-Library. The project page is at https://foundation-model-research.github.io/Kairos .