Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, for example, as a fast search procedure with two tower deep learning models. Graph-based methods for AKNNS in particular have received great attention due to their superior performance. These methods rely on greedy graph search to traverse the data points as embedding vectors in a database. Under this greedy search scheme, we make a key observation: many distance computations do not influence search updates so these computations can be approximated without hurting performance. As a result, we propose FINGER, a fast inference method to achieve efficient graph search. FINGER approximates the distance function by estimating angles between neighboring residual vectors with low-rank bases and distribution matching. The approximated distance can be used to bypass unnecessary computations, which leads to faster searches. Empirically, accelerating a popular graph-based method named HNSW by FINGER is shown to outperform existing graph-based methods by 20%-60% across different benchmark datasets.
