Paper ID: 2412.20195

Lower bounds on transformers with infinite precision

Alexander Kozachinskiy

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.

Submitted: Dec 28, 2024