How LLMs Learn to Reason: A Complex Network Perspective

• URL: http://arxiv.org/abs/2509.23629v1
• Date: Sun, 28 Sep 2025 04:10:37 GMT
• Title: How LLMs Learn to Reason: A Complex Network Perspective
• Authors: Sihan Hu, Xiansheng Cai, Yuan Huang, Zhiyuan Yao, Linfeng Zhang, Pan Zhang, Youjin Deng, Kun Chen,
• Abstract summary: Training large language models with Reinforcement Learning from Verifiable Rewards exhibits a set of puzzling behaviors.<n>We propose that these seemingly disparate phenomena can be explained using a single unifying theory.<n>Our work provides a new physical intuition for engineering the emergent reasoning capabilities of future AI systems.
• Score: 14.638878448692493
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Training large language models with Reinforcement Learning from Verifiable Rewards (RLVR) exhibits a set of distinctive and puzzling behaviors that remain poorly understood, including a two-stage learning curve, V-shaped response-length trajectories, and a pronounced vulnerability to catastrophic forgetting. In this work, we propose that these seemingly disparate phenomena can be explained using a single unifying theory: the model's reasoning process maps to the self-organization of a semantic complex network whose topology remains persistently sparse, with the average degree pinned close to two. This topology imposes a fundamental mechanism for forgetting and learning: it first drives the system into a maximally frustrated state where ``skill islands'' form, slow-learning happens, and forgetting is induced; then it enters a sharp growth phase where the new skills are ``bolted on'', driven by phase-transition-like learning at the web's frontier. Equipped with the theory, we propose \textit{Annealed-RLVR}, a principled algorithm that introduces an SFT-based ``heating'' step at the point of maximal frustration to resolve the competitive bottleneck and enhance the reasoning capability of the model. Experiments on a 1.5B-parameter model demonstrate that the approach outperforms standard RLVR on both in-distribution and out-of-distribution benchmarks. By recasting RLVR from black-box optimization into a predictable process of structural self-organization, our work provides a new physical intuition for engineering the emergent reasoning capabilities of future AI systems.

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