Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models
This addresses a methodological issue for researchers studying connections between neural networks and renormalization group theory, but it is incremental as it critiques an existing framework.
The paper tackles the problem of using Restricted Boltzmann Machine flows to detect critical temperatures in Ising models, finding that a neural network thermometer is inaccurate for determining if the RBM has learned scale invariance when datasets lack topology information.
We explore alternative experimental setups for the iterative sampling (flow) from Restricted Boltzmann Machines (RBM) mapped on the temperature space of square lattice Ising models by a neural network thermometer. This framework has been introduced to explore connections between RBM-based deep neural networks and the Renormalization Group (RG). It has been found that, under certain conditions, the flow of an RBM trained with Ising spin configurations approaches in the temperature space a value around the critical one: $ k_B T_c / J \approx 2.269$. In this paper we consider datasets with no information about model topology to argue that a neural network thermometer is not an accurate way to detect whether the RBM has learned scale invariance or not.