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Can multilayer neural networks -- typically constructed as highly complexstructures with many nonlinearly activated neurons across layers -- behave in anon-trivial way that yet simplifies away a major part of their complexities? Inthis work, we uncover a phenomenon in which the behavior of these complexnetworks -- under suitable scalings and stochastic gradient descent dynamics --becomes independent of the number of neurons as this number grows sufficientlylarge. We develop a formalism in which this many-neurons limiting behavior iscaptured by a set of equations, thereby exposing a previously unknown operatingregime of these networks. While the current pursuit is mathematicallynon-rigorous, it is complemented with several experiments that validate theexistence of this behavior.

Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks