Graph families that best support fiber descent

Characterize which classes of proximity graphs used for approximate nearest neighbor indexing most effectively support drift-guided fiber descent for filtered queries, by identifying structural properties (e.g., local connectivity, degree distribution, symmetrization) that ensure navigability of the filter-induced subgraph and favorable drift behavior during search.

Background

The paper proposes a geometric framework for filtered ANN search and introduces drift-guided fiber descent, where search preferentially follows filtered neighbors when the local drift signal is negative. While the method is index-agnostic and demonstrated on both a custom α-kNN graph and the base layer of FAISS HNSW, the authors note that different graph constructions may variably support the fiber descent procedure.

Identifying which graph constructions inherently preserve navigability on filter-induced subgraphs (fibers) and yield favorable drift profiles would guide both algorithm choice and index design for filtered search, especially at scale.