I am about making backpropagation on a neural network that uses ReLU. In a previous project of mine, I did it on a network that was using Sigmoid activation function, but now I'm a little bit confused, since ReLU doesn't have a derivative.
Here's an image about how weight5 contributes to the total error. In this example, out/net = a*(1 - a) if I use sigmoid function.
What should I write instead of "a*(1 - a)" to make the backpropagation work?
14 Answers
since ReLU doesn't have a derivative.
No, ReLU has derivative. I assumed you are using ReLU function f(x)=max(0,x). It means if x<=0 then f(x)=0, else f(x)=x. In the first case, when x<0 so the derivative of f(x) with respect to x gives result f'(x)=0. In the second case, it's clear to compute f'(x)=1.
Relu Derivative is 1 for x >= 0 and 0 for x < 0
The relu derivative can be implemented with np.heaviside step function e.g. np.heaviside(x, 1). The second parameter defines the return value when x = 0, so a 1 means 1 when x = 0.
Coming to this from a maths standpoint it should be half on the discontinuity. Its quote common to average things like that since frouiers series act in that manner
