Is Deep Learning an RG Flow?

Ellen de Mello Koch, Robert de Mello Koch, Ling Cheng

Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. A possible starting point suggests that deep learning performs a sophisticated coarse graining. Coarse graining is the foundation of the renormalization group (RG), which provides a systematic construction of the theory of large scales starting from an underlying microscopic theory. In this way RG can be interpreted as providing a mechanism to explain the emergence of large scale structure, which is directly relevant to deep learning. We pursue the possibility that RG may provide a useful framework within which to pursue a theoretical explanation of deep learning. A statistical mechanics model for a magnet, the Ising model, is used to train an unsupervised RBM. The patterns generated by the trained RBM are compared to the configurations generated through a RG treatment of the Ising model. We argue that correlation functions between hidden and visible neurons are capable of diagnosing RG-like coarse graining. Numerical experiments show the presence of RG-like patterns in correlators computed using the trained RBMs. The observables we consider are also able to exhibit important differences between RG and deep learning.

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