# Visual Text Compression as Measure Transport

arXiv: https://arxiv.org/abs/2605.06708 · HTML: https://mlsanity.com/paper/2605.06708/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Visual token pruning and efficiency, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 4 of its 54 references that are in the map.
- First posted on arXiv 6 May 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Visual token pruning and efficiency](https://mlsanity.com/mllm/visual-token-pruning-and-efficiency/)

## Builds on (most cited first, 4 of 4)

- [Routers in Vision Mixture of Experts: An Empirical Study](https://mlsanity.com/paper/2401.15969/) (2024)
- [Enhancing CLIP Robustness via Cross-Modality Alignment](https://mlsanity.com/paper/2510.24038/) (2025)
- [OTPrune: Distribution-Aligned Visual Token Pruning via Optimal Transport](https://mlsanity.com/paper/2602.20205/) (2026)
- [Selective Sinkhorn Routing for Improved Sparse Mixture of Experts](https://mlsanity.com/paper/2511.08972/) (2025)

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

- [FocusVTC: Efficient and High-Performance Visual Text Compression with Adaptive Resolution](https://mlsanity.com/paper/2609.36651/) (2026)

## Abstract (arXiv)

Visual text compression (VTC) promises efficient long-context processing by rendering text into an image and re-encoding it with a vision-language model, often producing 3--20× fewer decoder tokens than subword tokenization. Yet token savings do not translate predictably into downstream utility: on some tasks the visual path matches or exceeds the text path, on others it collapses, and the compression ratio itself does not predict which regime will occur. The missing quantity is therefore not another summary of efficiency, but a principled measure of task-relevant information loss induced by visual encoding. We address this problem by formulating VTC in the language of measure transport. Treating text and visual tokens as empirical probability measures, we show that the ViT patch encoder induces a push-forward map whose transport cost decomposes into a precision cost from within-patch aggregation and a coverage cost from cross-patch fragmentation. Both terms are estimable from downstream-label-free probes. This formulation yields two operational consequences: a downstream-label-free routing criterion that selects whether to use the visual path for a given input or benchmark instance, and a transport-informed foveation mechanism that re-encodes high-cost regions at higher resolution. Across 24 NLP datasets at Qwen3-4B, our label-free rule matches the per-dataset oracle on 17/24 datasets (70.8%), and improves the average task score by +3.3% with -10.3% average tokens relative to a pure-LLM.