Transformers Provably Learn Graph Search: Training Dynamics and the Exponential Power of Depth

arXiv:2611.13594v1 Announce Type: new Abstract: Large Language Models (LLMs) have achieved remarkable progress on complex reasoning tasks, yet the mechanisms by which they acquire reasoning capabilities and the efficiency of their reasoning remain poorly understood. In this paper, we investigate the path-finding problem over directed graphs, a symbolic abstraction of multi-step reasoning. We first characterize the architectural requirements for this task, proving that one-layer transformers require $\Omega(N^2)$ size on dense graphs to implement the key DFS child-selection primitive. While a t

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