The approach addresses computational bottlenecks that emerge when conducting exhaustive searches over millions of high-dimensional vectors. Prepared for ICML 2026, the technique utilizes small input convex neural networks trained offline through standard regression on sampled query-output pairs. These networks approximate mathematical support functions whose gradients point directly to the best-matching keys in a fixed database. Consequently, the method tailors query routing to actual user behavior, preventing routing errors common in traditional clustering approximations.
Key points
Traditional centroid-based clustering introduces frequent routing errors because user que…: Traditional centroid-based clustering introduces frequent routing errors because user queries differ substantially from long stored documents.
Small neural networks learn to route queries by using gradients that point directly towar…: Small neural networks learn to route queries by using gradients that point directly toward the best-matching database keys.
Investing in upfront offline training reduces computational overhead and accelerates infe…: Investing in upfront offline training reduces computational overhead and accelerates inference retrieval across high-dimensional vector databases.
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Maximum inner product search (MIPS) sits at the core of recommendation systems, search, and retrieval-augmented generation (RAG). Given a query vector, MIPS systems search within a database of millions of candidate key vectors for the one that best matches the query. The original data point associated with that best-matching key is then used to handle the query: in RAG, the document that is best suited to answer the question is typically prefixed to the query.
As the number of keys grows to millions and vector dimensions reach thousands, the computational cost of running an exhaustive comparison of the query to all keys grows dramatically. Numerous approximate methods have been proposed to trade off accuracy for speed using clustering and quantization. While these baseline methods focus on the properties of the set of keys to build up clever indexing structures, their geometric arguments loosely assume that the set of queries itself will resemble that found in keys, or bypass any considerations about what the queries will look like. This can be problematic on two fronts: In the crucial RAG case, queries…
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