论文标题
在伊辛相过渡的监督学习中，有限大小规模的函数的出现
Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transition
论文作者
论文摘要
我们研究了铁磁伊辛模型中二元相分类的监督学习与二阶相变的标准有限大小规模理论之间的联系。提出最小的一份参数神经网络模型，我们通过分析地制定了被用作训练数据集的规范合奏的监督学习问题。我们表明，只有一个自由参数能够足以描述网络输出中通用有限大小的尺寸尺寸函数的数据驱动的出现，该函数在大型神经网络中观察到，理论上从不同的基础晶格中验证了其对未见测试数据的临界点预测，但在同一ising关键性的同一普遍性类别中。我们还通过提出的一个参数模型来证明该解释是通过在学习Landau均值场自由能从不相关的无随机尺度图中应用于具有较大程度指数的真实数据集的临界点的示例。
We investigate the connection between the supervised learning of the binary phase classification in the ferromagnetic Ising model and the standard finite-size-scaling theory of the second-order phase transition. Proposing a minimal one-free-parameter neural network model, we analytically formulate the supervised learning problem for the canonical ensemble being used as a training data set. We show that just one free parameter is capable enough to describe the data-driven emergence of the universal finite-size-scaling function in the network output that is observed in a large neural network, theoretically validating its critical point prediction for unseen test data from different underlying lattices yet in the same universality class of the Ising criticality. We also numerically demonstrate the interpretation with the proposed one-parameter model by providing an example of finding a critical point with the learning of the Landau mean-field free energy being applied to the real data set from the uncorrelated random scale-free graph with a large degree exponent.
