Efficient Nearest Neighbor Search for Cross-Encoder Models using Matrix Factorization
Nishant Yadav, Nicholas Monath, Rico Angell, Manzil Zaheer, Andrew McCallum · 2022
Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP.When the similarity is measured by dot-product between dual-encoder vectors or ℓ 2 -distance, there already exist many scalable and efficient search methods.But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor.The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF.However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model.In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder.Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix.Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation.Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.