# EigenLI: Spectral Approximations to Late Interaction

arXiv: https://arxiv.org/abs/2609.07561 · HTML: https://mlsanity.com/paper/2609.07561/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [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)
- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)
- [FreshDiskANN: A Fast and Accurate Graph-Based ANN Index for Streaming Similarity Search](https://mlsanity.com/paper/2105.09613/) (2021)
- [Rethinking the Role of Token Retrieval in Multi-Vector Retrieval](https://mlsanity.com/paper/2304.01982/) (2023)
- [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)
- [PyLate: Flexible Training and Retrieval for Late Interaction Models](https://mlsanity.com/paper/2508.03555/) (2025)
- [WARP: An Efficient Engine for Multi-Vector Retrieval](https://mlsanity.com/paper/2501.17788/) (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)
- [Fantastic (small) Retrievers and How to Train Them: mxbai-edge-colbert-v0 Tech Report](https://mlsanity.com/paper/2510.14880/) (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)
- [ColBERT-Zero: To Pre-train Or Not To Pre-train ColBERT models](https://mlsanity.com/paper/2602.16609/) (2026)
- [On Strengths and Limitations of Single-Vector Embeddings](https://mlsanity.com/paper/2603.29519/) (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)

## Built on by (most cited first, 1 of 1)

- [Simple Linear Corrections for Compression in Late Interaction](https://mlsanity.com/paper/2610.14196/) (2026)

## Abstract (arXiv)

Late-interaction models such as ColBERT achieve strong effectiveness by representing each document with many token-level vectors, but this expressivity leads to large indexing cost, storage footprints and expensive MaxSim scoring. We show that late-interaction representations exhibit an intrinsic low-rank structure: document token embeddings concentrate in a low-dimensional subspace that preserves most of the retrieval signal. Leveraging this observation, we introduce EigenLI, a spectral approximation framework that compresses late-interaction representations via document-specific low-dimensional subspaces. Unlike clustering or pooling methods, EigenLI identifies the dominant eigendirections of each document and uses them to construct reduced interaction representations. Empirically, k-EigenLI with k ≤ 32 outperforms k-means and Ward clustering based pooling methods on ColBERTv2 and AnswerAI-ColBERT-small; GTE-ModernColBERT exhibits a different tradeoff at k=32, where clustering methods perform better. The same spectral construction also yields EigenLI-SV, an ANN-compatible single-vector representation derived from the second-order summary of the reduced structure. Across multiple datasets and all three text models, EigenLI-SV consistently outperforms comparable single-vector surrogates such as MUVERA.