An equality condition for the Dobrushin bound on attention rollout and how often it holds in trained transformers

Abstract:The Dobrushin coefficient of each attention-rollout factor satisfies $\kappa(\frac12(I+A))\le\frac12(1+\kappa(A))$, and multiplying these inequalities over layers bounds the coefficient of the whole rollout. We characterise exactly when the layerwise bound is tight: equality holds if and only if some token pair attaining $\kappa(A)$ is mutually self-dominant - each of the two attends to itself at least as strongly as the other attends to it. The condition is far from automatic: uniformly random stochastic matrices satisfy it only 24-30% of the time. When tested on the head-averaged attention of each individual input and restricted to content tokens - image patches, words or tabular features, excluding cls, register and separator tokens - the condition holds for essentially every input at every layer of DINOv2 (three model sizes), RoBERTa and DistilBERT. In the supervised models DeiT-B and ViT-B/16 it holds for 91% and 64% of input-layer pairs respectively, with all failures occurring late in depth. In FT-Transformer trained on two standard tabular benchmarks it holds for only 11-44% of input-layer pairs. The special tokens account for almost all failures in DINOv2 and the language models: when they are included, the condition holds for only 82-97% of input-layer pairs.

Machine Learning (cs.LG); Probability (math.PR)

arXiv:2610.05558 [cs.LG]

(or arXiv:2610.05558v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.05558 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.