How would one extract an algebraic function from the network鈥檚 weights? Why would the function the network approximates necessarily be algebraic?
For classification problems, there is often a final non-linear transformation, like a softmax.
Example with ReLu activation:
Output_i = max((input_i * weight_i),0)
In the case of a linear network, the function would be a dot product between the input and the weights: 饾懃1饾懁1+饾懃2饾懁2+饾懃3饾懁3 ... for all inputs (xi) and weights (wi)