Fast Detection of Phase Transitions with Multi-Task Learning-by-Confusion
This work addresses a computational bottleneck for researchers studying phase transitions in physics and related fields, offering an incremental improvement to an existing method.
The paper tackled the computational inefficiency of the learning-by-confusion scheme for detecting phase transitions, which previously required training multiple binary classifiers scaling linearly with grid points, by proposing a single multi-class classifier that achieves significant speedups with only minor deviations from ideal scaling in tests on the Ising model and an image dataset.
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 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 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 that closely correspond to the ideal case, with only minor deviations.