  By and large the behavior of stochastic gradient is regarded as a challenging
problem, and it is often presented in the framework of statistical machine
learning. This paper offers a novel view on the analysis of on-line models of
learning that arises when dealing with a generalized version of stochastic
gradient that is based on dissipative dynamics. In order to face the complex
evolution of these models, a systematic treatment is proposed which is based on
energy balance equations that are derived by means of the Caldirola-Kanai (CK)
Hamiltonian. According to these equations, learning can be regarded as an
ordering process which corresponds with the decrement of the loss function.
Finally, the main results established in this paper is that in the case of
quasi-periodic environments, where the pattern novelty is progressively limited
as time goes by, the system dynamics yields an asymptotically consistent
solution in the weight space, that is the solution maps similar patterns to the
same decision.
