标题： 通过统计系统构型系综的深度学习揭示临界温度的逻辑推理 显示英文标题

标题： Logical reasoning of revealing the critical temperature through deep learning of configuration ensemble of statistical systems

摘要： 最近有很多关于深度学习统计系综和温度的工作，可能找出可能相变的临界温度。 我们分析了优化的深度学习机器的详细结构，并证明了优化机器参数与物理量之间的基本等式。 根据这些等式，我们得出结论，最终全连接层的偏置参数将自由能作为温度的函数刻录下来。 我们在一维和二维自旋模型中验证了这些等式，并实际展示了深度学习机器可以通过这些偏置参数的二阶导数，即比热，揭示相变的临界温度。 我们的结果非常新颖，并完全否定了之前的说法，即全连接层的权重参数起到类似于自旋期望的序参量的作用。 显示英文摘要

摘要： Recently there have been many works on that deep learning of statistical ensemble and temperature may find out the critical temperature of possible phase transition. We analyze the detailed structure of the optimized deep leaning machine and prove the basic equalities between the optimized machine parameters ant the physical quantities. According to these equalities we conclude that the bias parameters of the final full connection layer are engraved the free energy of the statistical system as a function of temperature. We confirm these equalities in one and two dimensional spin models and actually show that the deep learning machine may reveal the critical temperature of the phase transition through the second derivative of these bias parameters, that is, the specific heat. Our results are quite new and completely deny the previous statements that the weight parameters of the full connection play a role of the order parameter like the spin expectation.