🤖 AI Summary
Understanding the scaling behavior and critical phenomena in deep neural networks (DNNs) remains challenging due to the lack of principled frameworks linking their architecture to statistical-physics-inspired renormalization group (RG) analysis.
Method: We model neurons as dynamical degrees of freedom and, for the first time in DNNs, identify approximate translational symmetry. Building upon statistical physics, we develop a scalable dynamical modeling framework that unifies symmetry analysis, RG transformations, and coarse-graining of degrees of freedom.
Contribution/Results: Our approach provides a universal characterization of recurrent structural motifs across deep architectures. It bridges RG theory with deep learning by enabling rigorous analysis of critical dynamics—thereby significantly enhancing model interpretability. Most notably, it establishes the first self-consistent theoretical framework for “critical learning,” offering foundational insights into how DNNs may operate near criticality during training and inference.
📝 Abstract
Deep neural network architectures often consist of repetitive structural elements. We introduce a new approach that reveals these patterns and can be broadly applied to the study of deep learning. Similar 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.