Refinement Symmetry in Multimodal Transformers
TL;DR
It is shown that split invariance forces the local mass factor to be linear for any fixed positive attention kernel, provided that factor is nondecreasing.
Abstract
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.
