Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis

• URL: http://arxiv.org/abs/2106.02588v1
• Date: Fri, 4 Jun 2021 16:34:32 GMT
• Title: Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
• Authors: Stephan Wojtowytsch
• Abstract summary: We show that in a certain noise regime, the optimization algorithm prefers 'flat' minima of the objective function in a sense which is different from the flat minimum selection of continuous time SGD with homogeneous noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient descent (SGD) or an advanced SGD-based algorithm. In a continuous time model for SGD with noise that follows the 'machine learning scaling', we show that in a certain noise regime, the optimization algorithm prefers 'flat' minima of the objective function in a sense which is different from the flat minimum selection of continuous time SGD with homogeneous noise.

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