Kolmogorov Neural Networks can represent discontinuous functions

Re:Kolmogorov Neural Networks can represent discontinuous fu... by ndriscoll on Sunday November 05, 2023 @12:52PM (#38153556)

I can't remember now and never gave measure theory a proper study, but isn't there a happy result that you can quotient out by a space of functions with zero integral to get an almost everywhere differentiable function or something? Maybe that's for L2:continuous, not continuous:differentiable?

Even a result like f(x) = nice(x) + evil(x) with |evil| < epsilon should be "happy enough" right?

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Re:Kolmogorov Neural Networks can represent discontinuous fu... by yorwba on Sunday November 05, 2023 @03:04PM (#38155065)

For a "happy enough" approximation to the Weierstrass function, you can cut off the series once a^n/(1 - a) < epsilon and get a function that's differentiable everywhere. But it'll have an extremely large number of local optima, which is still bad for gradient descent.

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