# Refinement Symmetry in Multimodal Transformers

arXiv: https://arxiv.org/abs/2609.32669 · HTML: https://mlsanity.com/paper/2609.32669/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [MVBench: A Comprehensive Multi-modal Video Understanding Benchmark](https://mlsanity.com/paper/2311.17005/) (2023)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [Qwen2.5-Omni Technical Report](https://mlsanity.com/paper/2503.20215/) (2025)
- [An Image is Worth 1/2 Tokens After Layer 2: Plug-and-Play Inference Acceleration for Large Vision-Language Models](https://mlsanity.com/paper/2403.06764/) (2024)
- [LLaVA-PruMerge: Adaptive Token Reduction for Efficient Large Multimodal Models](https://mlsanity.com/paper/2403.15388/) (2024)
- [Patch n' Pack: NaViT, a Vision Transformer for any Aspect Ratio and Resolution](https://mlsanity.com/paper/2307.06304/) (2023)
- [VideoChat-Flash: Hierarchical Compression for Long-Context Video Modeling](https://mlsanity.com/paper/2501.00574/) (2024)
- [Audio Flamingo 3: Advancing Audio Intelligence with Fully Open Large Audio Language Models](https://mlsanity.com/paper/2507.08128/) (2025)
- [WorldSense: Evaluating Real-world Omnimodal Understanding for Multimodal LLMs](https://mlsanity.com/paper/2502.04326/) (2025)
- [Byte Latent Transformer: Patches Scale Better Than Tokens](https://mlsanity.com/paper/2412.09871/) (2024)
- [How Smooth Is Attention?](https://mlsanity.com/paper/2312.14820/) (2023)
- [Continuum Attention for Neural Operators](https://mlsanity.com/paper/2406.06486/) (2024)
- [Accelerating Transformers with Spectrum-Preserving Token Merging](https://mlsanity.com/paper/2405.16148/) (2024)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [On the Regularity of Attention](https://mlsanity.com/paper/2102.05628/) (2021)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [nD-RoPE: A Generalized RoPE for n-Dimensional Position Embedding](https://mlsanity.com/paper/2606.12146/) (2026)

## Abstract (arXiv)

Attention weights depend on token counts, which change with the representation of a signal. We study refinement symmetry: splitting a representation while preserving content, position, visible context, and total mass should preserve its contribution. Building on proportional and quadrature attention, we show that split invariance forces the local mass factor to be linear for any fixed positive attention kernel, provided that factor is nondecreasing. For changed representations, a physical coupling bounds attention error by separating feature change from weight reallocation. In Qwen2.5-Omni-7B, duplicating half the visual tokens threefold changes 255 of 3,586 MVBench answers under standard attention; measure weighting preserves every answer under matched visibility. Under natural frame resampling, it reduces distributional drift. At twofold merging of a frozen video encoding, a five-seed evaluation shows an all-partition-correct accuracy gain of 1.04 percentage points over global count weighting (average group mass) and 0.93 points over standard attention. The advantage over global count also holds on WorldSense but depends on the compression budget. The result is a representation principle with a measured benefit in robustness across partitions.