RAGE: Reference-Guided Data Resampling via Adaptive Gradient Estimation for Time Series Foundation Models

Data allocation can improve the downstream performance of time-series foundation models by prioritizing source windows relevant to a target task. However, time-series trajectories are often delimited by data acquisition rather than semantic boundaries and can contain heterogeneous local training signals. Averaging gradients over an entire trajectory can obscure this variation, whereas computing a gradient for every overlapping window is costly. This creates a challenge of retaining useful local information for reference-guided allocation under a limited gradient budget. We propose RAGE, a reference-guided resampling method that estimates and scores local gradient shapes. RAGE places sparse gradient anchors using coverage and refinement guided by interpolation risk and direction cancellation. Neighboring anchors define linear gradient shapes on a common unit interval, encoded by jointly energy-normalized midpoint and slope components. RAGE aggregates signed source–reference shape similarities with trajectory-balanced reference weights and maps the resulting block-score ranks to source-window sampling probabilities. We evaluate RAGE on Chronos-Base, TimesFM 2.5, and TimerXL across seven forecasting tasks and two seeds, comparing against selection baselines and component ablations. Under a nominal 1.5% window-gradient budget, RAGE reduces MASE by 2.03% on average relative to random resampling and by 2.37% relative to LESS-TS. RAGE achieves the highest mean improvement among the evaluated methods and ablations overall and on each model.