# MAGIC: Marginal-Guided Compression with Optimal Transport for Efficient Visual Document Retrieval

arXiv: https://arxiv.org/abs/2609.21018 · HTML: https://mlsanity.com/paper/2609.21018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 49 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [DocVQA: A Dataset for VQA on Document Images](https://mlsanity.com/paper/2007.00398/) (2020)
- [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)
- [InfographicVQA](https://mlsanity.com/paper/2104.12756/) (2021)
- [Improving Text Embeddings with Large Language Models](https://mlsanity.com/paper/2401.00368/) (2023)
- [VisRAG: Vision-based Retrieval-augmented Generation on Multi-modality Documents](https://mlsanity.com/paper/2410.10594/) (2024)
- [Qwen3-VL-Embedding and Qwen3-VL-Reranker: A Unified Framework for State-of-the-Art Multimodal Retrieval and Ranking](https://mlsanity.com/paper/2601.04720/) (2026)
- [VLM2Vec: Training Vision-Language Models for Massive Multimodal Embedding Tasks](https://mlsanity.com/paper/2410.05160/) (2024)
- [ColPali: Efficient Document Retrieval with Vision Language Models](https://mlsanity.com/paper/2407.01449/) (2024)
- [MMLongBench-Doc: Benchmarking Long-context Document Understanding with Visualizations](https://mlsanity.com/paper/2407.01523/) (2024)
- [DeepSeek-OCR: Contexts Optical Compression](https://mlsanity.com/paper/2510.18234/) (2025)
- [SlideVQA: A Dataset for Document Visual Question Answering on Multiple Images](https://mlsanity.com/paper/2301.04883/) (2023)
- [MM-Embed: Universal Multimodal Retrieval with Multimodal LLMs](https://mlsanity.com/paper/2411.02571/) (2024)
- [VLM2Vec-V2: Advancing Multimodal Embedding for Videos, Images, and Visual Documents](https://mlsanity.com/paper/2507.04590/) (2025)
- [M3DocRAG: Multi-modal Retrieval is What You Need for Multi-page Multi-document Understanding](https://mlsanity.com/paper/2411.04952/) (2024)
- [Unifying Multimodal Retrieval via Document Screenshot Embedding](https://mlsanity.com/paper/2406.11251/) (2024)
- [Towards Complex Document Understanding By Discrete Reasoning](https://mlsanity.com/paper/2207.11871/) (2022)
- [jina-embeddings-v4: Universal Embeddings for Multimodal Multilingual Retrieval](https://mlsanity.com/paper/2506.18902/) (2025)
- [ViDoRAG: Visual Document Retrieval-Augmented Generation via Dynamic Iterative Reasoning Agents](https://mlsanity.com/paper/2502.18017/) (2025)
- [ViDoRe Benchmark V2: Raising the Bar for Visual Retrieval](https://mlsanity.com/paper/2505.17166/) (2025)
- [VDocRAG: Retrieval-Augmented Generation over Visually-Rich Documents](https://mlsanity.com/paper/2504.09795/) (2025)
- [UniME-V2: MLLM-as-a-Judge for Universal Multimodal Embedding Learning](https://mlsanity.com/paper/2510.13515/) (2025)
- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)
- [Towards Storage-Efficient Visual Document Retrieval: An Empirical Study on Reducing Patch-Level Embeddings](https://mlsanity.com/paper/2506.04997/) (2025)

## Abstract (arXiv)

Recent visual document retrieval (VDR) systems such as ColPali use multi-vector page embeddings, in which patch-level vectors enable fine-grained evidence matching but incur substantial index storage and MaxSim scoring overhead. Post-hoc merging offers a practical route to efficient VDR by reducing this cost without retraining the retriever, but its uniform reconstruction objectives are poorly aligned with the sparse, non-uniform patch usage induced by late-interaction retrieval. Under aggressive compression, this misalignment can preserve rarely used patches while concentrating retrieval activity on too few retained representatives. To address this misalignment, we propose Marginal-Guided Compression with Optimal Transport (MAGIC), a training-free post-hoc compressor for efficient retrieval with frozen multi-vector embeddings. MAGIC derives a MaxSim-induced compression surrogate and optimizes it through a two-marginal entropic optimal-transport formulation, where a retrieval-demand source marginal prioritizes high-use patches and a balanced target marginal regularizes retained-facet usage. Across ViDoRe benchmarks, keep ratios, and retrieval backbones, MAGIC consistently outperforms strong post-hoc compressors, with particularly large gains in the aggressive-compression regime; component ablations verify the complementary effects of its two marginals. We release the code at: https://github.com/xandery-geek/MAGIC.