SPS: Sufficient Patch Selection for Information-Preserving Time Series Forecasting

Patch-based tokenization has become a standard design choice for time series forecasting. Most existing methods treat patching as a fixed tokenization step, generating local windows and passing all resulting patches to the forecasting model regardless of their predictive utility. We instead formulate patching as a two-stage process: candidate generation followed by candidate selection. Building on this view, we propose the **Sufficient Patch Selector (SPS)**, a plug-in module for information-preserving patch selection. SPS constructs spectrally guided multi-scale candidate intervals from dominant temporal periods, then learns to retain a compact subset that preserves the predictive distribution induced by the full lookback sequence. To train SPS, we introduce an approximate posterior-preservation objective that matches the selected-patch predictive distribution to a full lookback reference, encouraging retained patches to be sufficient for prediction. We further propose Information Preservation Sufficiency (IPS), a metric that quantifies how well a patching strategy preserves full lookback predictive information. Across standard multivariate forecasting benchmarks and multiple patch-based backbones, SPS improves information preservation and achieves strong forecasting accuracy while retaining fewer patches than existing patching baselines.