AtomGraph: Reasoning Isn't Linear, Why Should Verification Be?

Verifying the correctness and consistency of multi-step reasoning chains generated by large language models to solve reasoning problems remains a challenge. Current verification strategies treat reasoning as strictly linear chains(Chain-of-Thought) or rigid trees (Tree-of-Thought). These approaches fail to capture complex dependencies in mathematical reasoning. AtomGraph is a graph neural network approach that represents reasoning chains as directed acyclic graphs where nodes act as atomic reasoning steps and edges encode logical dependencies. AtomGraph also combines semantic embeddings with structural features then applies multi head graph attention to learn the dependencies which matter the most. On the GSM8k dataset, AtomGraph achieves 75.9\% F1 score outperforming CoT, ToT baselines by 386\%. Further analysis reveals that AtomGraph learns to assign significantly higher attention to computation nodes than reasoning nodes ($\mu = 0.70$ vs $\mu = 0.478$ ). Skip connections receive higher attention and demonstrate that reasoning verification benefits from explicit modeling of multi-hop dependencies rather than treating reasoning as linear.