# Connection between piecewise linear basis functions and RELU activation function

ReLU activation is defined as follows $$\sigma(x)=\max(0, x).$$ Let's assume that I have deep network of 1 hidden layer, than output from my layer has form $$f(x)= \sigma(Wx +b),$$ where matrix W represents the weights, b is bias and x stands for input data (output of previous layer).

What is connection between $$f(x)$$ and piecewise linear function, defined as $$g(x_j)=\sum_{i=N}^N \alpha_i \psi_i(x_j),$$ where $$\alpha_i$$ stands for the coefficients and $$\psi_i$$ for the basis function.

More precisely, I would like to identify basis functions and coefficients in the definition of $$f(x)$$.