English

Lower bounds on transformers with infinite precision

Machine Learning 2024-12-31 v1 Artificial Intelligence Machine Learning

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 SUM2_2 task, considered by Sanford, Hsu, and Telgarsky.

Cite

@article{arxiv.2412.20195,
  title  = {Lower bounds on transformers with infinite precision},
  author = {Alexander Kozachinskiy},
  journal= {arXiv preprint arXiv:2412.20195},
  year   = {2024}
}
R2 v1 2026-06-28T20:50:42.862Z