TSRouter: Training-Free Capability Landscape Discovery and Routing for Growing Time-Series Foundation Model Zoos

Time-series foundation models (TSFMs) offer zero-shot forecasts, but their strengths vary across forecasting tasks and change as new models appear. This creates a two-sided selection problem: forwarding every candidate can improve task-specific selection but makes inference expensive as the model zoo grows, whereas supervised selectors avoid online forwarding but require candidate-dependent label updates and retraining after model arrivals. A practical router must retain competitive quality while keeping both inference and adaptation costs bounded. How can a router reuse capability evidence without training a selector for each evolving model zoo? We hypothesize that model preference is locally transferable: forecasting windows with similar temporal structure tend to favor similar models. We introduce TSRouter, a training-free framework for discovering, retrieving, and updating a capability landscape. Representative, source-stratified probe anchors identify model-specific capability regions. A shared representation lets unseen task windows retrieve this evidence, and window/channel rank fusion turns local preferences into a task-level choice. New models are incorporated into the same capability space using existing anchors, preserving previously discovered evidence. On 97 forecasting configurations from 23 datasets and a 20-model zoo, TSRouter achieves the best mean absolute scaled error among the evaluated deployable selectors. Holdout diagnostics and ablations support local capability transfer and evidence aggregation, while release-ordered evaluation demonstrates adaptation to changing candidates. A runtime-aware variant provides a complementary accuracy–latency trade-off.