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arXiv · 2507.07814

Pay Attention to Attention Distribution: A New Local Lipschitz Bound for Transformers

Nikolay Yudin·Sergei Kudriashov·Alexander Gaponov·Maxim Rakhuba
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Abstract

We introduce a novel upper bound on the local Lipschitz constant of the dot-product self-attention block showing its dependence on the attention map distributions. The proposed bound is not only tighter than the prior art, but for the first time, reveals how the distribution of attention probabilities shapes the local Lipschitz constant of the self-attention block. The theoretical basis of the proposed upper bound lies in the refined closed-form upper bounds on singular values of the Jacobian of softmax function. Leveraging these theoretical insights, we introduce JaSMin (Jacobian Softmax norm Minimization), a lightweight regularizer that directly controls the local Lipschitz constant of each block and, consequently, the entire model. Additionally, we discuss how the nature of the attention map distribution contributes to the gradient dynamics and, consequently, transformer training stability.

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Nikolay Yudin, Sergei Kudriashov, Alexander Gaponov, Maxim Rakhuba. 2025-07-10. Pay Attention to Attention Distribution: A New Local Lipschitz Bound for Transformers. https://arxiv.org/abs/2507.07814

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