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On the asymptotics of wide networks with polynomial activations

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arxiv 2006.06687 v1 pith:2ULNVNRN submitted 2020-06-11 cs.LG hep-thstat.ML

Kyle Aitken , Guy Gur-Ari This is my paper · ORCID
classification cs.LGhep-thstat.ML
keywords networksbehaviorconjectureactivationactivationsasymptoticfunctionspolynomial
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We consider an existing conjecture addressing the asymptotic behavior of neural networks in the large width limit. The results that follow from this conjecture include tight bounds on the behavior of wide networks during stochastic gradient descent, and a derivation of their finite-width dynamics. We prove the conjecture for deep networks with polynomial activation functions, greatly extending the validity of these results. Finally, we point out a difference in the asymptotic behavior of networks with analytic (and non-linear) activation functions and those with piecewise-linear activations such as ReLU.

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