相的参数诊断和相变的神经网络学习
Parameter diagnostics of phases and phase transition learning by neural networks
摘要：
我们提出了一个基于神经网络的机器学习计划的相位和相变在理论凝聚态研究的分析，专注于神经网络与一个单一的隐藏层。这种浅层神经网络以前被发现是有效的分类阶段和定位各种基本模型系统的相变。为了使分类过程的出现合理化并且为了识别任何潜在的物理量，检查从这种浅层网络的学习过程产生的权重矩阵和卷积滤波器内核是可行的。此外，我们演示了如何学习混淆计划可以使用，结合一个简单的阈值分类方法，诊断神经网络的学习参数。特别是，我们研究了全连接和卷积神经网络的分类过程中的二维伊辛模型与扩展畴壁配置包括在低温制度。此外，我们考虑了二维XY模型，并将在裸自旋配置上训练的混淆学习方案和卷积神经网络的性能与预处理样本相对于涡旋配置的情况进行了对比。我们讨论了这些调查结果，最近类似的调查和可能的进一步应用。
英文摘要：
We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.
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