Interpreting Grokked Transformers in Complex Modular Arithmetic

arXiv:2402.16726v2 Announce Type: replace
Abstract: Grokking has been actively explored to reveal the mystery of delayed generalization. Identifying interpretable algorithms inside the grokked models is a suggestive hint to understanding its mechanism. In this work, beyond the simplest and well-studied modular addition, we observe the internal circuits learned through grokking in complex modular arithmetic via interpretable reverse engineering, which highlights the significant difference in their dynamics: subtraction poses a strong asymmetry on Transformer; multiplication requires cosine-biased components at all the …

abstract algorithms arxiv beyond cs.ai cs.lg inside modular observe through transformers type understanding work