LoRANN: Low-Rank Matrix Factorization for Approximate Nearest Neighbor Search

• URL: http://arxiv.org/abs/2410.18926v1
• Date: Thu, 24 Oct 2024 17:13:39 GMT
• Title: LoRANN: Low-Rank Matrix Factorization for Approximate Nearest Neighbor Search
• Authors: Elias Jääsaari, Ville Hyvönen, Teemu Roos,
• Abstract summary: We propose a new supervised score computation method based on the observation that inner product approximation is a multi-output regression problem. Our experiments show that the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage. We also introduce LoRANN, a clustering-based ANN library that leverages the proposed score computation method.
• Score: 4.194768796374315
• License:
• Abstract: Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score computation methods based on product quantization (PQ), are often used in industrial-scale applications due to their scalability and suitability for distributed and disk-based implementations. However, they have slower query times than the leading graph-based ANN algorithms. In this work, we propose a new supervised score computation method based on the observation that inner product approximation is a multivariate (multi-output) regression problem that can be solved efficiently by reduced-rank regression. Our experiments show that on modern high-dimensional data sets, the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage. We also introduce LoRANN, a clustering-based ANN library that leverages the proposed score computation method. LoRANN is competitive with the leading graph-based algorithms and outperforms the state-of-the-art GPU ANN methods on high-dimensional data sets.

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