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arXiv:2410.00396 · Physical Review Research

Dynamic neuron approach to deep neural networks: Decoupling neurons for renormalization group analysis

Donghee Lee, Hye‐Sung Lee, Jaeok Yi

Published May 30, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/tf5z-7q29

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Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T=0 to T=6 generates a flow along which the temperature approaches the critical value T_{c}=2.27. This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards T_{c} and how the RBM learns to extract features of spin configurations.