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The representation of functions by artificial neural networks depends on alarge number of parameters in a non-linear fashion. Suitable parameters ofthese are found by minimizing a 'loss functional', typically by stochasticgradient descent (SGD) or an advanced SGD-based algorithm.  In a continuous time model for SGD with noise that follows the 'machinelearning scaling', we show that in a certain noise regime, the optimizationalgorithm prefers 'flat' minima of the objective function in a sense which isdifferent from the flat minimum selection of continuous time SGD withhomogeneous noise.

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