Polynomial Activation Function
A neural network activation function of polynomial form, such as f(x)=x^p. Unlike non-polynomial activations such as ReLU, polynomial activation functions are theoretically easier to analyze and are often used in theoretical studies of Gaussian process approximations.
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For polynomial activation functions and arbitrary compact input sets, this lifting gives a rate of m^{-1/2} under the supremum norm, with an explicit constant.
This result is currently for polynomial activation functions and compact input sets; whether the per-sample error method can still give explicit constants for more general activation functions is not asserted in the original text.
All Facts (2)
For polynomial activation functions and arbitrary compact input sets, this lifting gives a rate of m^{-1/2} under the supremum norm, with an explicit constant.
50%UnverifiedThis result is currently for polynomial activation functions and compact input sets; whether the per-sample error method can still give explicit constants for more general activation functions is not asserted in the original text.
50%