HIRA: GRADIENT-FREE RESIDUAL RETRIEVAL FOR LONG-HORIZON TIME-SERIES FORECASTING

Can a frozen time-series foundation model adapt to long-horizon forecasting without additional gradient training? We introduce Hidden-state Residual Adaptation (HIRA), which turns the backbone’s own context representations into an index of historical forecast errors. Suffix-pooled final tokens retrieve observed residuals, and horizon-wise configurations convert them into corrections without training an encoder, retriever, or fusion network. Under chronological selection with memory and configurations frozen before test, HIRA yields positive mean gains on four backbones at both 336 and 720 steps. On Chronos-2, its agreement-gated variant improves all seven datasets at the frozen-protocol 720-step horizon, reducing MSE by 13.15% on average, compared with 12.61% for the tested matched SARAFstyle control. The ungated recipe achieves long-horizon mean reductions of 4.54%, 7.00%, and 4.74% on TimesFM, Moirai 2.0, and Sundial, respectively. Mechanism controls and a recoverable-value analysis connect these gains to query-accessible historical errors and clarify transfer limits. These results establish residual memory as a competitive route to long-horizon adaptation without additional gradient training.