As introduced by Amari , dynamic neural fields (DNF) are a mathematical formalism aiming to describe the spatio-temporal evolution of the electrical potential of a population of cortical neurons. Various cognitive tasks have been successfully solved using this paradigm, but nevertheless, tasks requiring learning and self-organizing abilities have rarely been addressed. Aiming to extend the applicative area of DNF, we are hereby interested in using this computational model to implement such self-organizing mechanisms. Adapting the Kohonen's classical algorithm  for developing self-organizing maps (SOM), we propose a DNF-driven architecture that may deploy also a self-organizing mechanism. Benefiting from the biologically inspired features of the DNF, the advantage of such structure is that the computation is fully-distributed among its entities. Unlike the classical SOM algorithm, which requires a centralized computation of the global maximum, our proposed architecture implements a distributed decision computation, based on the local competition mechanism deployed by neural fields. Once the architecture implemented, we investigate the capacity of different neural field equations to solve simple self-organization tasks. Our analysis concludes that the considered equations (those of Amari  and Folias ) do not perform satisfactory, as seen in Figure 1, panels b and c. Highlighting the deficiencies of these equations that impeded them to behave as expected, we propose a new system of equations, enhancing that proposed by Folias  in order to handle the observed undesired effects. In summary, the novelty of these equations consist in introducing an adaptive term that triggers the re-inhibition of a so-called "unsustainable" bump of the field's activity (one that no longer is stimulated by strong input, but only but strong lateral excitation). As a conclusion, a field driven by the new equations achieves good results in solving the considered self-organizing task (as seen in Figure 1d). Our research thus opens the way to new approaches that aim using dynamic neural field to solve more complex cognitive tasks.
Figure 1. Solving a one-dimensional self-organizing task, aiming to learn the herein shown coronal shape (inner radius 0.5, outer radius 1.0), with the support provided by the 3-layer architecture described in the document. From left to right: a. Kohonen classical SOM; b. Amari DNF; c. Folias DNF; d. the new DNF system of equations.