Fiber-Navigable Search: A Geometric Approach to Filtered ANN

TL;DR

This paper introduces a geometric framework for filtered ANN search that leverages local signals and a lightweight anchor structure to improve search efficiency and failure handling.

Contribution

It proposes a novel two-phase search algorithm and failure classification method based on geometric properties of filtered proximity graphs.

Findings

Outperforms FAISS HNSW on filtered search tasks.

Effectively classifies search failures into three regimes.

Failure regimes shift predictably with filter selectivity.

Abstract

We present a geometric framework for filtered approximate nearest neighbor (ANN) search. Filtering a proximity graph by a metadata predicate produces a subgraph, a fiber, whose connectivity and geometry can differ sharply from the full graph. Using local signals, we propose a two-phase search algorithm that combines full-graph exploration with filtered-neighbor descent when the local geometry is favorable. These signals also classify search failures into three regimes: topological cuts, geometric folds, and genuine basins. A key observation is that all three share a common resolution: restarting the search in a fiber-present cluster near the query. To support this, we introduce a lightweight anchor structure that identifies such regions and restarts the search accordingly. We show empirically that the method outperforms FAISS HNSW on filtered search and the three failure regimes separate cleanly and shift predictably with filter selectivity.