  The paper uses statistical and differential geometric motivation to acquire
prior information about the learning capability of an artificial neural network
on a given dataset. The paper considers a broad class of neural networks with
generalized architecture performing simple least square regression with
stochastic gradient descent (SGD). The system characteristics at two critical
epochs in the learning trajectory are analyzed. During some epochs of the
training phase, the system reaches equilibrium with the generalization
capability attaining a maximum. The system can also be coherent with localized,
non-equilibrium states, which is characterized by the stabilization of the
Hessian matrix. The paper proves that neural networks with higher
generalization capability will have a slower convergence rate. The relationship
between the generalization capability with the stability of the neural network
has also been discussed. By correlating the principles of high-energy physics
with the learning theory of neural networks, the paper establishes a variant of
the Complexity-Action conjecture from an artificial neural network perspective.
