Title: Convexified Filtered ANN via Attribute-Vector Fusion
Primary area: optimization
Keywords: Similarity Search, Hybrid Query, ANN, Convex Optimization, Vector Database

Abstract: Vector search powers transformers technology, but real-world use demands hybrid queries that combine vector similarity with attribute filters (e.g., “top document in category X, from 2023”). Current solutions trade off recall, speed, and flexibility, relying on fragile index hacks that don’t scale. We introduce fused-based ANN, a geometric framework that elevates filtering to ANN optimization constraints and introduces a convex fused space via a Lagrangian-like relaxation. Our method jointly embeds attributes and vectors through transformer-based convexification, turning hard filters into continuous, weighted penalties that preserve top‑k semantics while enabling efficient approximate search. We prove that our fused method reduces to exact filtering under high selectivity, gracefully relaxes to semantically nearest attributes when exact matches are insufficient, and preserves downstream ANN $\alpha$-approximation guarantees. Empirically, fused-based method improves query throughput by eliminating brittle filtering stages, achieving superior recall–latency trade-offs on standard hybrid benchmarks without specialized index hacks, delivering up to $3\times$ higher throughput and better recall than state-of-the-art hybrid and graph-based systems. Theoretically, we provide explicit error bounds and parameter selection rules that make the fusion practical for production. This establishes a principled, scalable, and verifiable bridge between symbolic constraints and vector similarity, unlocking a new generation of filtered retrieval systems for large, hybrid, and dynamic NLP/ML workloads.

TL;DR: Define a new geometric convex space based on transformation to fuse attribute and vectors and represent them simultaneously