2014/10/14 by Pankaj Mehta, David J. Schwab, Mehta, Pankaj +1 · 8 voices · 17 citations
Physics and Astronomy · Materials Science · #Quantum many-body systems #Machine Learning in Materials Science #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1410.3831
Deep learning is a broad set of techniques that uses multiple layers of\nrepresentation to automatically learn relevant features directly from\nstructured data. Recently, such techniques have yielded record-breaking results\non a diverse set of difficult machine learning tasks in computer vision, speech\nrecognition, and natural language processing. Despite the enormous success of\ndeep learning, relatively little is understood theoretically about why these\ntechniques are so successful at feature learning and compression. Here, we show\nthat deep learning is intimately related to one of the most important and\nsuccessful techniques in theoretical physics, the renormalization group (RG).\nRG is an iterative coarse-graining scheme that allows for the extraction of\nrelevant features (i.e. operators) as a physical system is examined at\ndifferent length scales. We construct an exact mapping from the variational\nrenormalization group, first introduced by Kadanoff, and deep learning\narchitectures based on Restricted Boltzmann Machines (RBMs). We illustrate\nthese ideas using the nearest-neighbor Ising Model in one and two-dimensions.\nOur results suggests that deep learning algorithms may be employing a\ngeneralized RG-like scheme to learn relevant features from data.\n