# Are FFNN (MLP) Lipschitz functions?

My question is regarding standard dense-connected feed forward neural networks with sigmoidal activation.

I am studying Bayesian Optimization for hyper-parameter selection for neural networks. There is no doubt that this is an effective method, but I just wan't to delve a little deeper into the maths.

Question: Are neural networks Lipschitz functions?

That said, this paper appears to give some conditions (specifically for dynamic ANNs) for which networks with activation function involving $$e^x$$ can be Lipschitz continuous, so possibly the above is not the whole story.