Rix: Reusable Attention Indexing

Indexer-based sparse attention replaces full O(L^2) attention with a learned index plus a top-k pass, but as contexts grow longer the indexer's own score computation becomes the bottleneck. Existing accelerations cluster keys into blocks or share indices across layers. Reusing indices across query positions is orthogonal to both, yet unsafe to exploit directly. We observe that adjacent queries' index sets coincide strongly, but rare query pairs drift sharply, so query-side reuse requires a safety assurance. Our proposed method, Reusable Indexing (Rix), provides one with an O(Hd) closed-form reusability metric, derived from attention score estimation under a uniform key model, and applies reusable indexing coherently: an indexer design the metric mandates, a distillation recipe that keeps the metric faithful across reuse rates, and an inference-time scheduler that places fresh anchors only where the metric demands. In our evaluation, Rix consistently outperforms fixed reuse scheduling at matched reuse rates.