Minimax Rates for Learning Pairwise Interactions in Attention-Style Models

Shai Zucker; Xiong Wang; Fei Lu; Inbar Seroussi

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arXiv · 2510.11789

Minimax Rates for Learning Pairwise Interactions in Attention-Style Models

Shai Zucker·Xiong Wang·Fei Lu·Inbar Seroussi

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Abstract

We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a nonlinear activation function. We prove that the minimax rate is $M^{-\frac{2\beta}{2\beta+1}}$, where $M$ is the sample size and $\beta$ is the H\"older smoothness of the activation function. Importantly, this rate is independent of the embedding dimension $d$, the number of tokens $N$, and the rank $r$ of the weight matrix, provided that $rd \le (M/\log M)^{\frac{1}{2\beta+1}}$. These results highlight a fundamental statistical efficiency of attention-style models, even when the weight matrix and activation are not separately identifiable, and provide a theoretical understanding of attention mechanisms and guidance on training.

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BibTeX RIS

Shai Zucker, Xiong Wang, Fei Lu, Inbar Seroussi. 2025-10-13. Minimax Rates for Learning Pairwise Interactions in Attention-Style Models. https://arxiv.org/abs/2510.11789

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