Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines

TL;DR

This paper compares classical energy-based Boltzmann machines and quantum state-based Born machines for unsupervised generative modeling, analyzing their theoretical bounds and empirical performance on MNIST.

Contribution

It provides a comparative analysis of Boltzmann and Born machines using information theory and empirical tests, highlighting their differences and design principles.

Findings

RBMs' information bounds are analyzed theoretically.

Performance comparison on MNIST datasets shows differences.

Design insights derived from classical and quantum information patterns.

Abstract

We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states respectively.Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the restricted Boltzmann machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches. We verify our reasonings by comparing the performance of RBMs of various architectures on the standard MNIST datasets.