Minimal Training Set for Training a Successful CNN: A Case Study of the Frustrated J₁-J₂Ising Model on the Square Lattice

The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated J₁-J₂ Ising model on the square lattice. Here J₁ < 0 and J₂ > 0 are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of g ^def = J₂/|J₁| = 0.7 and employ the resulting CNN to study the phase transition of g = 0.8. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature T_c of g = 0.7, are needed to accurately determine the T_c of g = 0.8. However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the T_c of g = 0.7. Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the T_c of g = 0.8 accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.