Is Grokking Worthwhile? Functional Analysis and Transferability of Generalization Circuits in Transformers

While Large Language Models (LLMs) excel at factual retrieval, they often struggle with the "curse of two-hop reasoning" in compositional tasks. Recent research suggests that parameter-sharing transformers can bridge this gap by forming a "Generalization Circuit" during a prolonged "grokking" phase. A fundamental question arises: Is a grokked model superior to its non-grokked counterparts on downstream tasks? Furthermore, is the extensive computational cost of waiting for the grokking phase worthwhile? In this work, we conduct a mechanistic study to evaluate the Generalization Circuit's role in knowledge assimilation and transfer. We demonstrate that: (i) The inference paths established by non-grokked and grokked models for in-distribution compositional queries are identical. This suggests that the "Generalization Circuit" does not represent the sudden acquisition of a new reasoning paradigm. Instead, we argue that grokking is the process of integrating memorized atomic facts into an naturally established reasoning path. (ii) Achieving high accuracy on unseen cases after prolonged training and the formation of a certain reasoning path are not bound; they can occur independently under specific data regimes. (iii) Even a mature circuit exhibits limited transferability when integrating new knowledge, suggesting that "grokked" Transformers do not achieve a full mastery of compositional logic.