(1), and write it in an analogous form to the variational free energy of some model evidence.
let log h φ (X, Y ) Cλf φ (X, Y ), then the objective can be written as Intuitively, we can view the output distribution of the neural network p(Y |X) as a prior distribution over the labels, while considering h φ (X, Y ) as defining a "likelihood" metric w.r.t the observations, making the objective analogous to a (negative) variational lower bound of the respective "model".