用物理方法解析神经网络结构，揭示其对称性与演化规律。
Dynamic neuron approach to deep neural networks: Decoupling neurons for renormalization group analysis
- 将神经元视为独立自由度，简化网络内部交互结构。
- 发现网络存在平移对称性，支持重整化群分析。
- 为深度学习提供统计物理新视角，适合研究理论机制者。
深度神经网络架构常由重复结构组成。本文提出一种新方法，可揭示此类模式并广泛应用于深度学习研究。类似电源插座整理复杂电线，该方法将神经元视为相互作用中的额外自由度，简化结构并增强对网络内部交互的直观理解。此外，该方法揭示了深度神经网络的平移对称性，从而简化重整化群变换的应用——这是一种有效分析系统标度行为的方法。利用平移对称性和重整化群变换，可分析临界现象。该方法或为使用统计物理研究深度神经网络开辟新路径。
原文摘要 · Abstract (English)
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle and organize complex cable connections, this approach treats neurons as additional degrees of freedom in interactions, simplifying the structure and enhancing the intuitive understanding of interactions within deep neural networks. Furthermore, it reveals the translational symmetry of deep neural networks, which simplifies the application of the renormalization group transformation-a method that effectively analyzes the scaling behavior of the system. By utilizing translational symmetry and renormalization group transformations, we can analyze critical phenomena. This approach may open new avenues for studying deep neural networks using statistical physics.
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