Identify Dominators: The Key To Improve Large-Scale Maximum Inner Product Search
Keywords: high-dimensional vector, information retrieval, vector based retrieval, graph methods, nearest neighbor, maximum inner product search, similarity search
TL;DR: A novel graph-based method for maximum inner product search with theoretical and empirical advancement
Abstract: Maximum Inner Product Search (MIPS) is essential for machine learning and information retrieval, particularly in applications that operate on high-dimensional data, such as recommender systems and retrieval-augmented generation (RAG), using inner product or cosine similarity. While numerous techniques have been developed for efficient MIPS, their performance often suffers due to a limited understanding of the geometric properties of Inner Product (IP) space. Many approaches reduce MIPS to Nearest Neighbor Search (NNS) through nonlinear transformations, which rely on strong assumptions and can hinder performance. To address these limitations, we propose a novel approach that directly leverages the geometry of IP space. We focus on a class of special vectors called dominators and introduce the Monotonic Relative Dominator Graph MRDG, an IP-space-native, sparse, and strongly-connected graph designed for efficient MIPS, offering theoretical solid foundations. To ensure scalability, we further introduce the Approximate Relative Dominator Graph (ARDG), which retains MRDG’s benefits while significantly reducing indexing complexity. Extensive experiments on 8 public datasets demonstrate that ARDG achieves a 30% average speedup in search at high precision and reduces index size by 2x compared to state-of-the-art graph-based methods.
Supplementary Material: zip
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 1820
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