  This paper proposes a theory for understanding perceptual learning processes
within the general framework of laws of nature. Neural networks are regarded as
systems whose connections are Lagrangian variables, namely functions depending
on time. They are used to minimize the cognitive action, an appropriate
functional index that measures the agent interactions with the environment. The
cognitive action contains a potential and a kinetic term that nicely resemble
the classic formulation of regularization in machine learning. A special choice
of the functional index, which leads to forth-order differential
equations---Cognitive Action Laws (CAL)---exhibits a structure that mirrors
classic formulation of machine learning. In particular, unlike the action of
mechanics, the stationarity condition corresponds with the global minimum.
Moreover, it is proven that typical asymptotic learning conditions on the
weights can coexist with the initialization provided that the system dynamics
is driven under a policy referred to as information overloading control.
Finally, the theory is experimented for the problem of feature extraction in
computer vision.
