Fluctuation-dissipation Type Theorem in Stochastic Linear Learning

• URL: http://arxiv.org/abs/2106.02220v1
• Date: Fri, 4 Jun 2021 02:54:26 GMT
• Title: Fluctuation-dissipation Type Theorem in Stochastic Linear Learning
• Authors: Manhyung Han, Jeonghyeok Park, Taewoong Lee, Jung Hoon Han
• Abstract summary: 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 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 verify version closely mimicking the Langevin dynamics when a full-batch gradient descent scheme is replaced by that of gradient descent. We derive a generalized verify for the linear learning dynamics and its validity among the well-known machine learning data sets such as MNIST, CIFAR-10 and
• Score: 2.8292841621378844
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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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