neural networks - What is meant by “linear combination of inputs”

Question

Just starting out with MLPs. I am reading a tutorial that I found here.

It says that the disadvantages of using a linear function is that the neural net will only be restricted to learning "linear combination of inputs"

Can someone please explain via an example what a linear combination of an input is ?

I know what linearly separable functions are, but what is a linear combination of inputs ?

Answer 1

Suppose we have inputs $x, y, z$, a linear combination of inputs simply means:

$ax+by+cz$.

Ref: http://mathworld.wolfram.com/LinearCombination.html

That would be undesirable for neural networks since usually we want the network to approximate some non-linear functions.