# Simple Linear Corrections for Compression in Late Interaction

arXiv: https://arxiv.org/abs/2610.14196 · HTML: https://mlsanity.com/paper/2610.14196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [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)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [ColPali: Efficient Document Retrieval with Vision Language Models](https://mlsanity.com/paper/2407.01449/) (2024)
- [On the Theoretical Limitations of Embedding-Based Retrieval](https://mlsanity.com/paper/2508.21038/) (2025)
- [PLAID: An Efficient Engine for Late Interaction Retrieval](https://mlsanity.com/paper/2205.09707/) (2022)
- [jina-embeddings-v4: Universal Embeddings for Multimodal Multilingual Retrieval](https://mlsanity.com/paper/2506.18902/) (2025)
- [Survey of Vector Database Management Systems](https://mlsanity.com/paper/2310.14021/) (2023)
- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)
- [MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encodings](https://mlsanity.com/paper/2405.19504/) (2024)
- [ViDoRe V3: A Comprehensive Evaluation of Retrieval Augmented Generation in Complex Real-World Scenarios](https://mlsanity.com/paper/2601.08620/) (2026)
- [Reducing the Footprint of Multi-Vector Retrieval with Minimal Performance Impact via Token Pooling](https://mlsanity.com/paper/2409.14683/) (2024)
- [DocPruner: A Storage-Efficient Framework for Multi-Vector Visual Document Retrieval via Adaptive Patch-Level Embedding Pruning](https://mlsanity.com/paper/2509.23883/) (2025)
- [A Study on Token Pruning for ColBERT](https://mlsanity.com/paper/2112.06540/) (2021)
- [Efficient Constant-Space Multi-Vector Retrieval](https://mlsanity.com/paper/2504.01818/) (2025)
- [Nemotron ColEmbed V2: Top-Performing Late Interaction Embedding Models for Visual Document Retrieval](https://mlsanity.com/paper/2602.03992/) (2026)
- [Sculpting the Vector Space: Towards Efficient Multi-Vector Visual Document Retrieval via Prune-then-Merge Framework](https://mlsanity.com/paper/2602.19549/) (2026)
- [Multi-Vector Index Compression in Any Modality](https://mlsanity.com/paper/2602.21202/) (2026)
- [Visual Late Chunking: An Empirical Study of Contextual Chunking for Efficient Visual Document Retrieval](https://mlsanity.com/paper/2604.10167/) (2026)
- [Multi-Vector Embeddings are Provably More Expressive than Single Vector Embeddings](https://mlsanity.com/paper/2606.23475/) (2026)
- [Near-Optimal Dimension Lower Bounds for Single-Vector Embeddings of Maximum Inner Product Similarity](https://mlsanity.com/paper/2607.20393/) (2026)
- [Static Pruning in Dense Retrieval using Matrix Decomposition](https://mlsanity.com/paper/2412.09983/) (2024)
- [M3DR: Towards Universal Multilingual Multimodal Document Retrieval](https://mlsanity.com/paper/2512.03514/) (2025)
- [A Brief Comparison of Training-Free Multi-Vector Sequence Compression Methods](https://mlsanity.com/paper/2603.22434/) (2026)
- [Quantifying and Expanding the Theoretical Capacity of Late-Interaction Retrieval Models](https://mlsanity.com/paper/2607.05803/) (2026)
- [Retrieval Needs Multivectors: An Exponential Separation](https://mlsanity.com/paper/2608.21494/) (2026)
- [Multivector Reranking in the Era of Strong First-Stage Retrievers](https://mlsanity.com/paper/2601.05200/) (2026)
- [Learn to Pool: Lightweight Fine-Tuning for Flexible Multi-Vector Compression](https://mlsanity.com/paper/2607.06036/) (2026)

## Abstract (arXiv)

Late-interaction (multi-vector) models represent documents using a set of token-level vectors, providing a middle ground between cross-encoders and dense encoders in terms of quality and cost of embedding. However, compared to the latter, the indices are costly to store and score. Pooling and pruning based compression techniques are deployed widely but deteriorate in quality noticeably with aggressive compression. We investigate whether a lightweight change to the scoring function can recover retrieval quality after document-vector compression. For each combination of encoder, compressor, and vector budget, we learn a global linear correction by distilling the uncompressed model's score distributions over candidate documents. The encoder and compressor remain frozen, and the correction can be applied to each query at search time or once, offline, to the stored vectors. We evaluate the method with ColBERTv2 and Jina v4 on MS MARCO and BEIR, and with ColPali2 on the ViDoRe v3 visual document retrieval benchmark. Experiments cover four training-free compression methods, multiple vector budgets, in-domain adaptation, and transfer from MS MARCO to BEIR. In the in-domain setting, the correction improves over baseline compression in 154 of 160 BEIR settings, while transfer from MS MARCO is more variable across models and datasets. We also find that matrices trained with synthetic queries can improve over baseline compression on ViDoRe v3. These results show that a small learned correction can recover some of the quality lost to compression without retraining the encoder or recompressing the documents.