Linear and Nonlinear Judgment in Machine Learning

Linear and Nonlinear Judgment in Machine Learning

Speaking of linearity and nonlinearity, is your intuitive understanding like this:

But this intuitive understanding cannot actually answer the following question: 
So why is the convolution operation linear and ReLU non-linear?

Many people are not very clear about the definition of linearity. 
In fact, the definition of linearity is: 
F(ax+y) = aF(x) + F(y), 
where x, y are variables and a is a constant.

The convolution operation satisfies the above formula, so it is a linear operation.

The following can quickly determine the three common cases of nonlinearity:

• (变量)^n, and n is not 1
• |变量| A variable with an absolute value is nonlinear
• sgn(变量) have variables inside symbolic functions

And the ReLU looks like this:

So, it is clear that ReLU is nonlinear.