A Renormalization Group Framework for Scale-Invariant Feature Learning in Deep Neural Networks (Student Abstract)

Abstract We propose a framework that uses renormalization group (RG) theory from statistical physics to analyze and optimize the hierarchical feature learning process in deep neural networks. Here, the layer-wise transformations in deep networks can be viewed as analogous to RG transformations, with each layer implementing a coarse-graining operation that extracts increasingly abstract features. We propose an approach to enforce scale invariance in neural networks, introduce scale-aware activation functions, and derive RG flow equations for network parameters. We show that our approach leads to fixed points corresponding to scale-invariant feature representations. Finally, we propose an RG-guided training procedure that converges to these fixed points while minimizing the loss function.