FusedANN is a geometric framework for hybrid queries that combines attribute filters and vector similarity. This framework elevates attributes to Approximate Nearest Neighbor (ANN) optimization constraints and introduces a convex fusion space through Lagrangian-like relaxation. Transformer-based convexification combines attributes and vectors, converting hard filters into continuous weighted penalties to preserve top-k semantics and enabling efficient approximate search. FusedANN reduces to exact filtering under high selectivity and smoothly relaxes to the semantically closest attribute when exact matches are insufficient, preserving the downstream ANN alpha-approximation guarantee. FusedANN delivers up to 3x higher throughput and improved recall compared to existing hybrid systems.