We wish that our neural network manages to minimize a given cost function.
A reformulation of out equation, (6), must therefore be done, such that it describes the problem a neural network can solve for.
The neural network must find the set of weights and biases \( P \) such that the trial solution in (7) satisfies (6).
The trial solution
$$ g_t(x, P) = g_0 + x \cdot N(x, P) $$has been chosen such that it already solves the condition \( g(0) = g_0 \). What remains, is to find \( P \) such that
$$ \begin{equation} \tag{8} g_t'(x, P) = - \gamma g_t(x, P) \end{equation} $$is fulfilled as best as possible.