Not All History Matters: Query-Conditioned Evidence Retrieval for Time Series Forecasting

Large language models have shown promise for transferable time-series forecasting, yet most LLM-based forecasters still process the entire historical context, making long-horizon prediction vulnerable to redundant tokens, irrelevant temporal noise, and high computational cost. We aim to address the core gap of how an LLM forecaster can decide which parts of a long history are truly useful for a specific forecasting query and horizon. We propose Forecast-Conditioned Evidence Seeking (ForeSeek), a query-conditioned evidence retrieval framework that reformulates LLM-based forecasting as a retrieve-then-predict process. ForeSeek introduces Horizon-Aware Evidence Routing to select forecast-relevant historical segments, an Attention Conservation objective to preserve the predictive information flow of full-context reasoning, and a Dual-Path Forecasting design that combines evidence-based LLM reasoning with a lightweight temporal path for stable prediction. Experiments on seven benchmarks show that ForeSeek achieves strong long-term, few-shot, and zero-shot forecasting performance, while reducing LLM backbone FLOPs by 70.99% and total FLOPs by 52.56% on Time-LLM under the default Top-K ratio of 0.3. These results suggest that forecast-conditioned evidence selection offers an effective and efficient alternative to uniform full-context inference for LLM-based time-series forecasting.