RAE: A Neural Network Dimensionality Reduction Method for Nearest Neighbors Preservation in Vector Search
Year: 2025
Type: preprint
Abstract: While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been adopted for accelerating the retrieval process due to their inability of preserving the nearest neighbor (NN) relationship among vectors. Empowered by neural networks' optimization capability and the bounding effect of Rayleigh quotient, we propose a Regularized Auto-Encoder (RAE) for k-NN preserving dimensionality reduction. RAE constrains the network parameter variation through regularization terms, adjusting singular values to control embedding magnitude changes during reduction, thus preserving k-NN relationships. We provide a rigorous mathematical analysis demonstrating that regularization establishes an upper bound on the norm distortion rate of transformed vectors, thereby offering provable guarantees for k-NN preservation. With modest training overhead, RAE achieves superior k-NN recall compared to existing DR approaches while maintaining fast retrieval efficiency.
Source: arXiv (Cornell University)
Authors: Zhang, Han, Zhao, Dongfang
Institution: University of Washington
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084448257
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