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arXiv · 2605.12171

Lower bounds for one-layer transformers that compute parity

Daniel Hsu
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Abstract

This note shows that no self-attention layer post-processed by a rational function can sign-represent the parity function unless the product of the number of heads and the degree of the post-processing function grows linearly with the input length. Combining this lower bound with rational approximation of ReLU networks yields a margin-dependent extension for self-attention layers post-processed by ReLU networks.

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Daniel Hsu. 2026-05-12. Lower bounds for one-layer transformers that compute parity. https://arxiv.org/abs/2605.12171

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