Efficient Nearest Neighbor Search for Cross-Encoder Models using Matrix Factorization

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. Score Query Embedding Item Embedding Score Joint Query-Item Embedding Linear Layer Score Contextualized Query Embedding Contextualized Item Embedding Query (q) … … … Item (i) … … … Special Tokens Query & Item Tokens a) Dual-Encoder b) [CLS]-Cross-Encoder c) [EMB]-Cross-Encoder Model (e.g. BERT) Model (e.g. BERT) Model (e.g. BERT) Model (e.g. BERT) (a) Model architecture -10 0 10 Query-Item Score 10 -3 10 -2