Personalized Federated Sparse Adaptation of Time-Series Foundation Models

Time-series foundation models (TSFMs) such as Chronos have demonstrated strong forecasting capabilities across domains, yet adapting them to institutionally fragmented settings, where data cannot be centralized due to regulatory, competitive, or sovereignty constraints, remains unexplored. We introduce FedChronos, a framework for federated parameter-efficient fine-tuning of an already pre-trained TSFM, a setting that existing federated time-series work has not addressed, since prior methods either pre-train from scratch or align prototypes rather than adapt a fixed backbone. Our approach applies Low-Rank Adaptation (LoRA) to the Chronos-T5 backbone and trains across distributed clients using FedAvg and FedProx, transmitting only lightweight adapter weights (384~KB per round, an 86$\times$ reduction over full-model exchange). We evaluate FedChronos on daily commodity prices from 15 Indian agricultural markets across 9 states, a naturally non-IID federated setting, and find that naïve LoRA fine-tuning overfits substantially on small per-client datasets, dropping below zero-shot performance. We further observe that differential privacy (DP) noise can act as implicit regularization and counteract this overfitting: in our experiments the strongest configuration ($\varepsilon = 5$) reduces mean absolute percentage error (MAPE) by 31% over zero-shot and 26% over the best traditional baseline, while bounding each round's information leakage via per-round $(\varepsilon, δ)$-differential privacy. Because the model is compact and the updates are small, the approach also suits edge AI deployments where both the network link and the client device are constrained. Overall, our findings suggest that privacy and accuracy can be complementary rather than competing objectives in federated TSFM fine-tuning.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.