[Submitted on 17 Sep 2026]
Title:MAGIC: Marginal-Guided Compression with Optimal Transport for Efficient Visual Document Retrieval
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Abstract: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: this https URL.
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Information Retrieval (cs.IR)
Cite as: arXiv:2609.21018 [cs.CV]
(or arXiv:2609.21018v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2609.21018
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Xu Yuan [view email] [v1] Thu, 17 Sep 2026 19:14:06 UTC (9,896 KB)
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