We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its extrapolation over continuous ranges in parameter space. We demonstrate our proposal using the phase transition in the two-dimensional Ising model. By interpreting the output of the neural network as an order parameter, we explore connections with known observables in the system and investigate its scaling behavior. A finite-size scaling analysis is conducted based on quantities derived from the neural network that yields accurate estimates for the critical exponents and the critical temperature. The method improves the prospects of acquiring precision measurements from machine learning in physical systems without an order parameter and those where direct sampling in regions of parameter space might not be possible.

中文翻译：

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通过直方图加权扩展机器学习分类功能

我们建议使用蒙特卡罗直方图加权来推断机器学习方法的预测。在我们的方法中，我们将卷积神经网络的输出视为统计系统中的可观察值，从而可以在参数空间的连续范围内进行外推。我们使用二维伊辛模型中的相变论证了我们的建议。通过将神经网络的输出解释为有序参数，我们探索了系统中与已知可观察对象的连接，并研究了其缩放行为。基于从神经网络得出的数量进行有限大小的缩放分析，该数量可得出关键指数和关键温度的准确估计值。