  Information maximization has been investigated as a possible mechanism of
learning governing the self-organization that occurs within the neural systems
of animals. Within the general context of models of neural systems
bidirectionally interacting with environments, however, the role of information
maximization remains to be elucidated. For bidirectionally interacting physical
systems, universal laws describing the fluctuation they exhibit and the
information they possess have recently been discovered. These laws are termed
fluctuation theorems. In the present study, we formulate a theory of learning
in neural networks bidirectionally interacting with environments based on the
principle of information maximization. Our formulation begins with the
introduction of a generalized fluctuation theorem, employing an interpretation
appropriate for the present application, which differs from the original
thermodynamic interpretation. We analytically and numerically demonstrate that
the learning mechanism presented in our theory allows neural networks to
efficiently explore their environments and optimally encode information about
them.
