# Spatial Matryoshka Training for Multi-Granularity Visual Document Retrieval

arXiv: https://arxiv.org/abs/2608.29951 · HTML: https://mlsanity.com/paper/2608.29951/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [VLM2Vec-V2: Advancing Multimodal Embedding for Videos, Images, and Visual Documents](https://mlsanity.com/paper/2507.04590/) (2025)
- [Unifying Multimodal Retrieval via Document Screenshot Embedding](https://mlsanity.com/paper/2406.11251/) (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)
- [ViDoRe Benchmark V2: Raising the Bar for Visual Retrieval](https://mlsanity.com/paper/2505.17166/) (2025)
- [Rethinking the Role of Token Retrieval in Multi-Vector Retrieval](https://mlsanity.com/paper/2304.01982/) (2023)
- [Towards Storage-Efficient Visual Document Retrieval: An Empirical Study on Reducing Patch-Level Embeddings](https://mlsanity.com/paper/2506.04997/) (2025)
- [DocPruner: A Storage-Efficient Framework for Multi-Vector Visual Document Retrieval via Adaptive Patch-Level Embedding Pruning](https://mlsanity.com/paper/2509.23883/) (2025)
- [CITADEL: Conditional Token Interaction via Dynamic Lexical Routing for Efficient and Effective Multi-Vector Retrieval](https://mlsanity.com/paper/2211.10411/) (2022)
- [Sculpting the Vector Space: Towards Efficient Multi-Vector Visual Document Retrieval via Prune-then-Merge Framework](https://mlsanity.com/paper/2602.19549/) (2026)
- [CRISP: Clustering Multi-Vector Representations for Denoising and Pruning](https://mlsanity.com/paper/2505.11471/) (2025)
- [Unlocking Multimodal Document Intelligence: From Current Triumphs to Future Frontiers of Visual Document Retrieval](https://mlsanity.com/paper/2602.19961/) (2026)
- [Visual Late Chunking: An Empirical Study of Contextual Chunking for Efficient Visual Document Retrieval](https://mlsanity.com/paper/2604.10167/) (2026)
- [Structural Anchor Pruning: Training-Free Multi-Vector Compression for Visual Document Retrieval](https://mlsanity.com/paper/2601.20107/) (2026)
- [ReinPool: Reinforcement Learning Pooling Multi-Vector Embeddings for Retrieval System](https://mlsanity.com/paper/2601.07125/) (2026)
- [MM-Matryoshka: Towards Budget-Elastic Visual Document Retrieval via a 2D Multimodal Matryoshka Training Framework](https://mlsanity.com/paper/2606.07654/) (2026)
- [Do All Visual Tokens Matter Equally? Object-Evidence Preserving Token Merging for Vision-Language Retrieval](https://mlsanity.com/paper/2607.04605/) (2026)

## Abstract (arXiv)

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.