Efficient k-NN Search with Cross-Encoders using Adaptive Multi-Round CUR Decomposition
This work addresses a bottleneck in information retrieval systems by improving recall accuracy for top-k search tasks, though it is incremental as it builds on existing CUR decomposition methods.
The paper tackles the problem of efficient k-nearest neighbor search using cross-encoders, which are computationally expensive, by proposing ADACUR, an adaptive iterative method that reduces recall error by up to 70% compared to previous approaches while maintaining similar computational costs.
Cross-encoder models, which jointly encode and score a query-item pair, are prohibitively expensive for direct k-nearest neighbor (k-NN) search. Consequently, k-NN search typically employs a fast approximate retrieval (e.g. using BM25 or dual-encoder vectors), followed by reranking with a cross-encoder; however, the retrieval approximation often has detrimental recall regret. This problem is tackled by ANNCUR (Yadav et al., 2022), a recent work that employs a cross-encoder only, making search efficient using a relatively small number of anchor items, and a CUR matrix factorization. While ANNCUR's one-time selection of anchors tends to approximate the cross-encoder distances on average, doing so forfeits the capacity to accurately estimate distances to items near the query, leading to regret in the crucial end-task: recall of top-k items. In this paper, we propose ADACUR, a method that adaptively, iteratively, and efficiently minimizes the approximation error for the practically important top-k neighbors. It does so by iteratively performing k-NN search using the anchors available so far, then adding these retrieved nearest neighbors to the anchor set for the next round. Empirically, on multiple datasets, in comparison to previous traditional and state-of-the-art methods such as ANNCUR and dual-encoder-based retrieve-and-rerank, our proposed approach ADACUR consistently reduces recall error-by up to 70% on the important k = 1 setting-while using no more compute than its competitors.