圖搜索理論研究刻畫Transformer深度優勢

Computer Science > Artificial Intelligence arXiv:2611.

13594 (cs) [Submitted on 10 Nov 2026] Title:Transformers Provably Learn Graph Search: Training Dynamics and the Exponential Power of Depth Authors:Xutao Ma, Somayeh Sojoudi View a PDF of the paper titled Transformers Provably Learn Graph Search: Training Dynamics and the Exponential Power of Depth, by Xutao Ma and 1 other authors View PDF HTML (experimental) 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 two-layer transformer implements full DFS with $O(N\log(N))$ size.

Thus, a second layer is necessary and sufficient for near-linear DFS reasoning.

We then extend this expressivity analysis to deeper models: for every $k\geq3$, a $k$-layer transformer implements a bounded-reachability DFS policy with look-ahead horizon $1+2^{k-3}$, establishing an exponential increase in reachability horizon with depth.

Finally, going beyond expressivity, given appropriately curated training data, we show that two-layer transformers can provably learn to execute DFS via gradient flow and generalize to unseen graphs.

Together, our results provide a mechanistic account of how transformers implement graph search, how depth expands bounded look-ahead, and how such reasoning algorithms can emerge through training.Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2611.13594 [cs.AI] (or arXiv:2611.13594v1 [cs.

AI] for this version) https://doi.org/10.48550/arXiv.2611.

13594 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xutao Ma [view email] [v1] Tue, 10 Nov 2026 05:09:36 UTC (168 KB) Full-text links: Access Paper: View a PDF of the paper titled Transformers Provably Learn Graph Search: Training Dynamics and the Exponential Power of Depth, by Xutao Ma and 1 other authorsView PDFHTML (experimental)TeX Source view license Additional Features Audio Summary Current browse context: cs.

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