Seeing the Forest for the Trees: Connecting Convolutional Neural Networks to Maximum Information Entropy and Correlate Product State Ansatzes

Convolutional Neural Networks(CNNs) are being increasingly used to solve quantum spin systems. Despite their success in doing so, understanding how they succeed and what physics they capture is an ongoing research area. In this talk, we show how CNNs are actually maximum entropy ansatzes (MaxEnt) in disguise. Maximizing information entropy given constraints is the optimal method for constructing a "best guess" probability distribution given little information/constraints, and as such as of great use in physics and statistical mechanics. We show the connection between CNNs and MaxEnts, as well as how they mao onto to another class ofvariational algorithms for spin systems, Entangled Plaquette Correlator Product State Ansatzes (EP-CPS). This allows us to transfer results from existing literature on each ansatz to the gaining understanding of the other. As an example of the mapping, we discuss the case of the spin-1/2 Heisenberg model on a ring. This mapping allows us to use CNNs as a stand-in where Maximum Entropy ansatzes are required, or where EP-CPS ansatzes are being applied in research.