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arXiv · 2412.20195

Lower bounds on transformers with infinite precision

Alexander Kozachinskiy
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Abstract

In this note, we use the VC dimension technique to prove the first lower bound against one-layer softmax transformers with infinite precision. We do so for two tasks: function composition, considered by Peng, Narayanan, and Papadimitriou, and the SUM$_2$ task, considered by Sanford, Hsu, and Telgarsky.

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Alexander Kozachinskiy. 2024-12-28. Lower bounds on transformers with infinite precision. https://arxiv.org/abs/2412.20195

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