Lower bounds for one-layer transformers that compute parity
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914559410831360 |
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| author | Hsu, Daniel |
| author_facet | Hsu, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower bounds for one-layer transformers that compute parity Hsu, Daniel Machine Learning 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. |
| title | Lower bounds for one-layer transformers that compute parity |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.12171 |