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.

利用机器学习研究相变，提出了一种基于混淆学习的方案，通过训练一个多类别分类器而不是多个二分类器来减少计算成本，实现了与理想情况相近的速度提升，适用于伊辛模型和具有稳定扩散生成的图像数据集。