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arXiv · 2106.02220

Fluctuation-dissipation Type Theorem in Stochastic Linear Learning

Manhyung Han·Jeonghyeok Park·Taewoong Lee·Jung Hoon Han
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Abstract

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 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.

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Manhyung Han, Jeonghyeok Park, Taewoong Lee, Jung Hoon Han. 2021-06-04. Fluctuation-dissipation Type Theorem in Stochastic Linear Learning. https://doi.org/10.1103/physreve.104.034126

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