Unveiling the Mechanisms of Multi-Hop Reasoning in Transformers via Identity Bridge

Large Language Models (LLMs) excel at multi-hop reasoning in distribution, yet fail on unseen compositions, a phenomenon known as the curse of two-hop reasoning. In this work, we argue that this phenomenon can be attributed to a missing supervision on the bridge entity. We formalize this gap by introducing identity bridge, a minimal supervision that enforces a identity mapping on bridge tokens. Under this supervision, even a one-layer transformer with uniform attention (Emb-MLP) can achieve out-of-distribution (OOD) two-hop generalization. We provide a theoretical analysis demonstrating that identity bridge induces an implicit regularization effect, leading the model to establish a direct subject-to-answer association. From an empirical perspective, the performance of standard GPT-2 models aligns closely with simple Emb--MLP models across varying levels of problem complexity. Finally, analyses of fine-tuned mainstream LLMs indicate that correct two-hop predictions consistently coincide with the establishment of a subject-to-answer relationship, extending our findings to realistic settings.