Title: Deciphering Fully Connected Deep Neural Networks Through Renormalization Group Analysis on Exponential Family Distributions

Abstract: This study aims to build an interpretability framework for deep learning by linking the renormalization group (RG) technique from statistical physics with the training dynamics of deep neural networks (DNNs). While our previous work demonstrated this correspondence using one-dimensional Ising model data, we now extend these findings to continuous input data, a crucial step for applying this framework to practical, real-world scenarios. Specifically, we focus on data distributions belonging to the exponential family. We demonstrate that once fully connected (FC) DNNs reach their optimal parameter states post-training, the characteristic parameters of the network's feature layer outputs coincide with the fixed points of the input data’s characteristic parameters under the RG method for continuous fields. This equivalence implies that the DNN training process functions similarly to an RG calculation, enabling the network to distill primary features from the input much like the RG approach. Furthermore, this alignment reinforces our established correspondence framework and offers insight into the superior performance of DNNs when handling real-world data.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC