Associative Memories to Accelerate Approximate Nearest Neighbor Search

Abstract

Nearest neighbor search is a very active field in machine learning. It appears in many application cases, including classification and object retrieval. In its naive implementation, the complexity of the search is linear in the product of the dimension and the cardinality of the collection of vectors into which the search is performed. Recently, many works have focused on reducing the dimension of vectors using quantization techniques or hashing, while providing an approximate result. In this paper, we focus instead on tackling the cardinality of the collection of vectors. Namely, we introduce a technique that partitions the collection of vectors and stores each part in its own associative memory. When a query vector is given to the system, associative memories are polled to identify which one contains the closest match. Then, an exhaustive search is conducted only on the part of vectors stored in the selected associative memory. We study the effectiveness of the system when messages to store are generated from i.i.d. uniform ±1 random variables or 0–1 sparse i.i.d. random variables. We also conduct experiments on both synthetic data and real data and show that it is possible to achieve interesting trade-offs between complexity and accuracy.

Keywords

• similarity search
• vector search
• associative memory
• exponential inequalities