Recursive Inference for Test-Time Compute Allocation in Time-Series Foundation Models

In time-series forecasting tasks, some forecasts require carrying seasonal demand \em months into the future whereas in other settings, one must anticipate changes in electricity load over the \em next few hours. Still, a pretrained forecasting model typically runs the same sequence of blocks \em once for each task. In this paper, we ask whether a small amount of additional inference budget can be utilized for tangible performance gains, in a way that leaves the model’s parameters frozen. A fixed budget can be variously used to distribute compute. We explore these choices through compute programs that revisit selected consecutive blocks, control the size of each update, and determine which token representations can change. Their cost in encoder-block evaluations is known in advance. But their impact on forecast error for the particular task must be measured. Recursive inference uses a reasoning model to propose programs, read their results on historical forecasting windows, and revise subsequent proposals. Held-out later windows decide whether to deploy a program, and it then stays \em fixed throughout testing. We find that this simple idea, across 56 tasks from 14 datasets, reduces test MSE by 4.02% on average, at only 1.28 times the baseline encoder-block evaluations per forecast.