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 $f(x)$.


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