The function/mathematics in an NN (neural network) is meaningless unless there is an outside observer to attribute meaning to it. There is no such thing as a meaningful mathematical expression without a conscious observer to give it meaning. Fundamentally there is no objective difference between one instance of a NN with one parameter, f(θ), evaluated on some input, f(θ)(x), and another instance of the same network with a small perturbation of the parameter, f(θ+ε), evaluated on the same input, f(θ+ε)(x), unless a conscious observer perceives the output and attributes meaning to the differences because the arithmetic operations performed by the network are the same in both networks in terms of their objective complexity and energy utilization.