Efficient Approximate k-NN Search with Cross-Encoders through Sparse Matrix Factorization

Core Concepts

This paper proposes an efficient approach to perform approximate k-nearest neighbor (k-NN) search with cross-encoder models by learning a low-dimensional embedding space that approximates the cross-encoder scores. The key innovations are: (1) a sparse matrix factorization method to compute item embeddings that align with the cross-encoder, and (2) an adaptive test-time retrieval method that incrementally refines the test query embedding to improve the approximation of cross-encoder scores.

Abstract

The paper addresses the challenge of efficiently performing k-NN search with cross-encoder models, which are computationally expensive to use directly for nearest neighbor retrieval. The authors propose two key components: Offline Indexing: The authors construct a sparse matrix G containing cross-encoder scores between a set of training queries and a subset of items. They use efficient sparse matrix factorization techniques to learn low-dimensional embeddings for the items that approximate the cross-encoder scores. This approach is more efficient than prior methods that require computing a dense matrix of cross-encoder scores or fine-tuning a dual-encoder model. Online Retrieval: At test time, the authors propose an adaptive retrieval method called AXN that incrementally refines the test query embedding to better approximate the cross-encoder scores. AXN performs retrieval over multiple rounds, alternating between (1) updating the test query embedding to improve the approximation of cross-encoder scores for items retrieved so far, and (2) retrieving additional items using the updated query embedding. This adaptive approach provides significant improvements in k-NN recall compared to retrieve-and-rerank baselines, while incurring minimal additional computational cost at test time. The authors evaluate their proposed methods on entity linking and information retrieval tasks, demonstrating substantial improvements in efficiency and effectiveness over prior approaches.

Stats

The proposed sparse matrix factorization approach can achieve up to 100x and 5x speedup over CUR-based and dual-encoder distillation-based approaches respectively. The AXN retrieval method can provide up to 5% and 54% improvement in Top-1 and Top-100 recall respectively over retrieve-and-rerank baselines.

Quotes

"Our proposed k-NN search method can achieve up to 5% and 54% improvement in k-NN recall for k = 1 and 100 respectively over the widely-used DE-based retrieve-and-rerank approach." "Furthermore, our proposed approach to index the items by aligning item embeddings with the CE achieves up to 100× and 5× speedup over CUR-based and dual-encoder distillation based approaches respectively while matching or improving k-NN search recall over baselines."

Key Insights Distilled From

Adaptive Retrieval and Scalable Indexing for k-NN Search with Cross-Encoders

by Nishant Yada... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.03651.pdf

Deeper Inquiries

How can the proposed sparse matrix factorization approach be extended to handle dynamic updates to the item set, such as adding or removing items from the index

The proposed sparse matrix factorization approach can be extended to handle dynamic updates to the item set by incorporating incremental updates to the item embeddings. When new items are added to the index, the existing item embeddings can be re-used, and only the embeddings for the new items need to be computed. This can be achieved by updating the item embeddings matrix with the embeddings of the new items and adjusting the query-item score matrix accordingly. Similarly, when items are removed from the index, their corresponding embeddings can be removed from the matrix, and the query-item score matrix can be updated accordingly. By efficiently updating the item embeddings matrix and the query-item score matrix, the system can adapt to changes in the item set without the need for a complete reindexing process.

Can the adaptive test-time retrieval method (AXN) be combined with other techniques for accelerating neural model inference, such as model quantization or early-exit strategies, to further improve the efficiency of k-NN search with cross-encoders

The adaptive test-time retrieval method (AXN) can be combined with other techniques for accelerating neural model inference to further improve the efficiency of k-NN search with cross-encoders. For example, model quantization techniques can be applied to the cross-encoder model to reduce its computational complexity and memory footprint, making it more efficient for inference during the test-time retrieval process. By quantizing the model parameters or using low-precision representations, the cross-encoder can be accelerated without compromising its performance significantly. Additionally, early-exit strategies can be integrated into the AXN method to optimize the retrieval process by terminating the search early when confident predictions are made, reducing the overall inference time. By combining these techniques with AXN, the efficiency of k-NN search with cross-encoders can be further enhanced.

What are the potential implications of the observed discrepancy between k-NN search performance and downstream task performance, and how can the training of cross-encoder models be improved to better align these two aspects

The observed discrepancy between k-NN search performance and downstream task performance can have several implications for the training of cross-encoder models. One potential implication is that the cross-encoder model may not be effectively capturing the relevant information needed for the downstream task during the k-NN search process. To address this, the training of cross-encoder models can be improved by incorporating task-specific objectives or loss functions that better align the k-NN search performance with the downstream task performance. Additionally, techniques such as curriculum learning or multi-task learning can be employed to enhance the generalization capabilities of the cross-encoder model across different tasks and datasets. By improving the training process to better align k-NN search performance with downstream task performance, the overall effectiveness of the cross-encoder model can be enhanced.