RAE: A Neural Network Dimensionality Reduction Method for Nearest Neighbors Preservation in Vector Search
This addresses a bottleneck in retrieval-augmented generation and recommendation systems by enabling efficient nearest neighbor preservation, though it is an incremental improvement over existing neural network methods.
The paper tackles the problem of preserving nearest neighbor relationships in dimensionality reduction for vector search, proposing a Regularized Auto-Encoder (RAE) that achieves superior k-NN recall compared to existing methods while maintaining fast retrieval efficiency.
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.