Phase transition encoded in neural network

We discuss an aspect of neural networks for the purpose of phase transition detection. To this end, we first train the neural network by feeding Ising/Potts configurations with labels of temperature so that it can predict the temperature of the input. We do not explicitly supervise whether the configurations are in the ordered/disordered phase. Nevertheless, we can identify the critical temperature from the parameters (weights and biases) of the trained neural network. We attempt to understand how temperature-supervised neural networks capture information on the phase transition by paying attention to what quantities they learn. Our detailed analyses reveal that they learn different physical quantities depending on how well they are trained. The main observation in this study is how the weights in the trained neural network can have information on the phase transition in addition to temperature.