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[D] Why do effective activation functions have a bounded derivative?

Is there a reason why almost every modern activation function in deep learning has a bounded derivative? ReLU, Swish, tanh, sigmoid and other activation functions mentioned here all have bounded derivatives.

My intuition says it is because we use backprop to train our networks. A bounded derivative should restrict the amount of gradient flow during the backward phase, preventing a blowup of gradients. What do you guys think?

submitted by /u/TheSilenceOfTheBakra
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.