# Are there any commonly used discontinuous activation functions?

Are there any commonly used activation functions (e.g. that take values in $$(0,.5)\cup (.5,1)$$)? Preferably for classification?

Why? I was looking for commonly used activation functions on Google, and I noticed that all activation functions are continuous. However, I believe this is not needed in Hornik's paper.

When I did a bit of testing myself, with a discontinuous activation function on the MNIST dataset, the results were good. So I was curious if anyone else used this kind of activation function.

• The example you provide is discontinuous in strict mathematical sense, but in an informal way not really discontinuous (as far as I understand). So what exactly do you mean by discontinuous? Also can you link this paper. – DuttaA Apr 1 '20 at 1:30
• I'm looking for a commonly used discontinuous bounded activation function. Somethign I can use for classification.. – BLBA Apr 1 '20 at 6:49