Deep learning and the renormalization group

Abstract

Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind the RG on the one hand and deep machine learning on the other, where depth and scale play a similar role. In order to illustrate this connection, we review a recent numerical method based on the RG---the multiscale entanglement renormalization ansatz (MERA)---and show how it can be converted into a learning algorithm based on a generative hierarchical Bayesian network model. Under the assumption---common in physics---that the distribution to be learned is fully characterized by local correlations, this algorithm involves only explicit evaluation of probabilities, hence doing away with sampling.

References in corpus (6)

• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Criticality, the area law, and the computational power of PEPS
• Quantum Criticality and the Kondo Lattice
• Practical learning method for multi-scale entangled states
• Stochastic Matrix Product States

Cited by in corpus (24)

• Machine learning and the physical sciences
• Quantum Entanglement in Neural Network States
• Machine learning quantum phases of matter beyond the fermion sign problem
• Lecture Notes of Tensor Network Contractions
• Neural Network Renormalization Group
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Deep Learning as a Parton Shower
• Nonperturbative renormalization for the neural network-QFT correspondence
• Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design
• Is Deep Learning a Renormalization Group Flow?
• Inverse Renormalization Group based on Image Super-Resolution using Deep Convolutional Networks
• Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer
• Tensor networks as conformal transformations
• Short sighted deep learning
• Geometrization of deep networks for the interpretability of deep learning systems
• Categorical Representation Learning and RG flow operators for algorithmic classifiers
• Entanglement transitions from restricted Boltzmann machines
• The Autodidactic Universe
• Wilsonian Renormalization of Neural Network Gaussian Processes
• Feature extraction of machine learning and phase transition point of Ising model
• Super-resolution of spin configurations based on flow-based generative models
• Maximum Multiscale Entropy and Neural Network Regularization