When Do Corrective Features Help? An Agent for Corrective Feature Discovery on Black-Box Forecasters

Successful forecasting involves identifying patterns between historical and future states of the world which generalize to future observations. We apply LLMs to a variety of forecasting tasks and inspect their internal states using sparse autoencoders to understand whether they appear to rely on time-specific pieces of knowledge versus generalizable patterns. Our analyses identify features associated with both time-aware reasoning and look-ahead-biased reasoning. We then apply the LLMs to an entirely different domain and intervene on these features. We find that amplifying time-awareness features substantially reduces look-ahead bias on forecasting prompts while preserving general reasoning performance. In contrast, steering the candidate look-ahead-bias features does not produce an effect. These results suggest that interpretable temporal features can be used to causally shift LLMs toward more historically grounded reasoning.

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.

Time-series foundation models can forecast across heterogeneous domains without task-specific training, but their forecasts are fixed once produced and cannot directly incorporate task-specific expert feedback. We study expert-guided forecast editing: a frozen foundation model generates candidate future trajectories, and an expensive expert evaluator scores them to guide forecast revision. Under a tight query budget, two natural strategies sit at opposite ends: best-of-$N$ purely exploits the foundation model's predictive distribution, while optimization approaches mostly explore the forecast horizon as an unstructured high-dimensional vector. Each extreme is individually sub-optimal. We introduce \textbf{DEFT}, an expert-guided forecast editing framework that balances the two by first exploiting the foundation model's predictive samples in a decomposed trend--seasonal space, then exploring around them via component-wise refinement. DEFT queries the expert only on complete trajectories, then reuses scores for the trend and seasonal components that appeared in the queried recombinations. This lets each expert query provide structured component-level feedback while keeping the foundation model frozen. We compare DEFT against direct search approaches, including best-of-$N$, cross-entropy methods, and Bayesian optimization, under matched expert-query budgets. Across two forecasting benchmarks consisting of 78 datasets, three time-series foundation models, four feedback types, and seven query budgets, DEFT consistently improves the effectiveness of expert guidance. A molecular-dynamics case study further suggests that the same principle extends to more physically grounded feedback, supporting the hypothesis that sparse test-time guidance should be spent balancing prior exploitation with structured exploration.