TAA-k: New RAG method cuts compute by orders of magnitude near oracle accuracy

Fixed Top-K retrieval fails under query-dependent similarity distributions, and existing global EVT methods are computationally prohibitive. TAA-k introduces a two-phase approach: first, it uses knee detection on the similarity curve to isolate a compact candidate region; then it applies EVT goodness-of-fit testing within that region to validate the noise tail. This coarse-to-fine design slashes complexity from O(N²M) to O(√(N log N)·M), making it practical for large-scale RAG deployments.

Across three multi-hop QA benchmarks, TAA-k achieves retrieval F1 scores within 2–3% of the theoretical oracle, while maintaining robustness across different embedding models and compression dimensions. The method is entirely training-free and adapts per query without manual tuning. For RAG systems that need to balance latency, cost, and accuracy, TAA-k offers a drop-in solution that dramatically reduces computational overhead without sacrificing retrieval quality.