Multi-Vector Index Compression in Any Modality

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.

Multi-modal late-interaction retrievers achieve strong retrieval on visually rich documents by representing each page as per patch embeddings and matching at the token level. However, this approach incurs high storage costs. Existing compression methods typically fix a single compression level at indexing time, limiting flexibility. We present ColSNAP (Spatial Nested Average Pooling)1, a training method that generates a nested hierarchy of compression levels directly from a backbone's patch grid. By spatially pooling patch embeddings into pro- gressively coarser tiers and training all tiers simultaneously, a single model learns to support retrieval at multiple compression levels without architectural changes. Crucially, a single encoding pass yields every tier, enabling the accuracy-storage trade-off to be configured at indexing time to match avail- able storage budgets, rather than being fixed during training. We demonstrate that models trained using ColSNAP maintain near full-resolution retrieval performance under substantial compression and that ColSNAP transfers effectively across multiple late-interaction backbones, and achieves most of its improvements via a lightweight adaptation stage applied to a pre-trained retriever.

Multi-vector visual document retrieval (VDR) models such as ColPali and ColNomic achieve strong accuracy by representing each document with hundreds to thousands of patch-level embeddings, at substantial storage and latency cost. Existing compression methods either prune unimportant patches or merge similar ones into clusters; the recent state-of-the-art merging method Prune-then-Merge (PtM) consistently outperforms pruning-only baselines at high compression, but requires a per-dataset cluster budget m to be tuned by grid search. We observe that the merge-cosine sequence produced by hierarchical clustering exhibits a sharp cliff separating mergeable redundancy from salient signal, and that the location of this cliff is concentrated in a narrow band across more than 11,000 documents from 14 datasets. This suggests the merge boundary can be detected per document rather than tuned per dataset. Building on this observation, we propose AdaMerge, a plug-and-play compression method that (i) detects each document's own cliff via gap analysis on the merge-cosine trajectory, and (ii) builds attention-weighted cluster centroids to preserve salient signal. On the long-document benchmark ViDoRe-V2 (4 datasets, two backbones), AdaMerge significantly outperforms tuned PtM across the operating range (p < 10^-4); on the short-document benchmark ViDoRe-V1 (10 datasets, two backbones), where all merging methods are already near-lossless, AdaMerge matches tuned PtM without any per-dataset tuning. AdaMerge adds only about 10 ms per document and exposes a single global hyperparameter shared across all datasets and backbones.