Fast Detection of Phase Transitions with Multi-Task Learning-by-Confusion

Machine learning has been successfully used to study phase transitions. One of the most popular approaches to identifying critical points from data without prior knowledge of the underlying phases is the \emph{learning-by-confusion} scheme. As input, it requires system samples drawn from a grid of the parameter whose change is associated with potential phase transitions. Up to now, the scheme required training a distinct binary classifier for each possible splitting of the grid into two sides, resulting in a computational cost that scales linearly with the number of grid points. In this work, we propose and showcase an alternative implementation that only requires the training of a \emph{single} multi-class classifier. Ideally, such multi-task learning eliminates the scaling with respect to the number of grid points. In applications to the Ising model and an image dataset generated with Stable Diffusion, we find significant speedups which, apart from small deviations, correspond to this ideal case.