We analyze the problem of supervised learning of ferromagnetic phase transitions from the statistical physics perspective. We consider two systems in two universality classes, the two-dimensional Ising model and two-dimensional Baxter-Wu model, and perform careful finite-size analysis of the results of the supervised learning of the phases of each model. We find that the variance of the neural network (NN) output function (VOF) as a function of temperature has a peak in the critical region. Qualitatively, the VOF is related to the classification rate of the NN. We find that the width of the VOF peak displays the finite-size scaling governed by the correlation length exponent $\nu$ of the universality class of the model. We check this conclusion using several NN architectures—a fully connected NN, a convolutional NN, and several members of the ResNet family—and discuss the accuracy of the extracted critical exponents $\nu$.

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• Critical phenomena
• Artificial neural networks
• Monte Carlo methods