The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning dynamics, in which the input vector maps to the output vector by a linear matrix whose elements are the subject of learning, has a stochastic version closely mimicking the Langevin dynamics when a full-batch gradient descent scheme is replaced by that of a stochastic gradient descent. We derive a generalized FDT for the stochastic linear learning dynamics and verify its validity among the well-known machine learning data sets such as MNIST, CIFAR-10, and EMNIST.

中文翻译：

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随机线性学习中的波动耗散型定理

波动耗散定理 (FDT) 是一阶微分方程的一个简单而强大的结果，该方程控制同时受耗散力和随机力影响的系统的动力学。线性学习动力学，其中输入向量通过一个线性矩阵映射到输出向量，其元素是学习的主题，当全批次梯度下降方案被替换为一个随机版本时，它具有密切模仿朗之万动力学的随机版本。随机梯度下降。我们推导出随机线性学习动力学的广义 FDT，并验证其在 MNIST、CIFAR-10 和 EMNIST 等知名机器学习数据集之间的有效性。