[alyxya]

No that isn’t throwing out data. Activation functions perform a nonlinear transformation to increase the expressivity of a function. If you did two matrix multiplications without ReLU in between, your function contains less information than with a ReLU in between.

[fastball]

How are you calculating "less information"?

[shwaj]

I think what they meant was:

Two linear transformations compose into a single linear transformation. If you have y = W2(W1*x) = (W2*W1)*x = W*x where W = W2*W1, you've just done one matrix multiply instead of two. The composition of linear functions is linear.

The ReLU breaks this because it's nonlinear: ReLU(W1*x) can't be rewritten as some W*x, so W2(ReLU(W1*x)) can't collapse either.

Without nonlinearities like ReLU, many layers of a neural network could be collapsed into a single matrix multiplication. This inherently limits the function approximation that it can do, because linear functions are not very good at approximating nonlinear functions. And there are many nonlinearities involved in modeling speech, video, etc.