CINN Learning

Abstract

Solutions of the continuum model can be studied using the “method of characteristics” (see appendix C). Characteristics are trajectories in the Cartesian product of the LTM space and time axis (also called (w, t)-space) along which the neural density is constant. They provide a convenient way of studying the continuum model’s solutions. This section derives the characteristic trajectories for the continuum model. It will be shown that under certain restrictions called the “clustering constraints”, the CINN clusters LTM states about the modes of a smoothed source density. It will also be shown that there exist cases when these clusters form about all of the source density’s modes. This last property has been called the CINN’s “global search property” and arises as a direct consequence of mild competitive interactions between neurons. The implication of these analyses is that the CINN’s LTM states act as estimates for the source density’s modes. Since modal estimation constitutes a form of machine learning, we can say that the continuum model represents a model for “CINN learning”.