# Static Pruning in Dense Retrieval using Matrix Decomposition

arXiv: https://arxiv.org/abs/2412.09983 · HTML: https://mlsanity.com/paper/2412.09983/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2024.

## Built on by (most cited first, 3 of 3)

- [SECURA: Sigmoid-Enhanced CUR Decomposition with Uninterrupted Retention and Low-Rank Adaptation in Large Language Models](https://mlsanity.com/paper/2502.18168/) (2025)
- [EigenLI: Spectral Approximations to Late Interaction](https://mlsanity.com/paper/2609.07561/) (2026)
- [Simple Linear Corrections for Compression in Late Interaction](https://mlsanity.com/paper/2610.14196/) (2026)

## Abstract (arXiv)

In the era of dense retrieval, document indexing and retrieval is largely based on encoding models that transform text documents into embeddings. The efficiency of retrieval is directly proportional to the number of documents and the size of the embeddings. Recent studies have shown that it is possible to reduce embedding size without sacrificing - and in some cases improving - the retrieval effectiveness. However, the methods introduced by these studies are query-dependent, so they can't be applied offline and require additional computations during query processing, thus negatively impacting the retrieval efficiency. In this paper, we present a novel static pruning method for reducing the dimensionality of embeddings using Principal Components Analysis. This approach is query-independent and can be executed offline, leading to a significant boost in dense retrieval efficiency with a negligible impact on the system effectiveness. Our experiments show that our proposed method reduces the dimensionality of document representations by over 50% with up to a 5% reduction in NDCG@10, for different dense retrieval models.