# Efficient k-NN Search with Cross-Encoders using Adaptive Multi-Round CUR Decomposition

arXiv: https://arxiv.org/abs/2305.02996 · HTML: https://mlsanity.com/paper/2305.02996/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 4 May 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Atlas: Few-shot Learning with Retrieval Augmented Language Models](https://mlsanity.com/paper/2208.03299/) (2022)
- [RocketQA: An Optimized Training Approach to Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2010.08191/) (2020)
- [Improving Efficient Neural Ranking Models with Cross-Architecture Knowledge Distillation](https://mlsanity.com/paper/2010.02666/) (2020)
- [Zero-Shot Entity Linking by Reading Entity Descriptions](https://mlsanity.com/paper/1906.07348/) (2019)
- [Efficient Nearest Neighbor Search for Cross-Encoder Models using Matrix Factorization](https://mlsanity.com/paper/2210.12579/) (2022)
- [MuVER: Improving First-Stage Entity Retrieval with Multi-View Entity Representations](https://mlsanity.com/paper/2109.05716/) (2021)

## Built on by (most cited first, 2 of 2)

- [Adaptive Retrieval and Scalable Indexing for k-NN Search with Cross-Encoders](https://mlsanity.com/paper/2405.03651/) (2024)
- [Relevance-Based Embeddings: Lightweight Candidate Retrieval via Heavy-Ranker Calls](https://mlsanity.com/paper/2607.03515/) (2026)

## Abstract (arXiv)

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.