RAE: A Neural Network Dimensionality Reduction Method for Nearest Neighbors Preservation in Vector Search

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 reasonably preserving k-NN relationships. We provide a theoretical analysis demonstrating that the proposed regularization establishes an upper bound on the norm distortion rate of transformed vectors, thereby offering supportive guarantees for k-NN proximity. With modest training overhead, RAE achieves significantly higher recall rate compared to existing DR approaches while maintaining prompt retrieval latency.