Claudius Gläser, Frank Joublin, Christian Goerick, "Intrinsically Regulated Self-Organization of Topologically Ordered Neural Maps", Frontiers in Computational Neuroscience. Conference Abstract: Bernstein Conference on Computational Neuroscience, 2009.

Dynamic field theory models the spatio-temporal evolution of activity within the cortex and has been successfully applied in various domains. However, the development of dynamic neural fields (DNFs) is only rarely explored. This is due to the fact that DNFs are sensible to the right balance between excitation and inhibition within the fields. Small changes to this balance will result in runaway excitation or quiescence. Consequently, learning most often focuses on the synaptic weights of projections to the DNF, thereby adapting the input-driven dynamics, but leaving the self-driven dynamics unchanged. Here we present a recurrent neural network model composed of excitatory and inhibitory units which overcomes these problems. Our approach differs insofar as we do not make any assumption on the connectivity of the field. In other words, synaptic weights of both, afferent projections to the field as well as lateral connections within the field, undergo Hebbian plasticity. As a direct consequence our model has to self-regulate in order to maintain a stable operation mode even in face of these experience-driven changes. We therefore incorporate recent advances in the understanding of such homeostatic processes. Firstly, we model the activity-dependent release of the neurotrophine BDNF (brain-derived neurotrophic factor) which is thought to underlie homeostatic synaptic scaling. BDNF has opposing effects on the scaling of excitatory synapses on pyramidal neurons and interneurons, thereby mediating a dynamic adjustment in the excitatory-inhibitory balance. Secondly, we adapt the intrinsic excitability of the model units by adjusting their resting potentials. In both processes the objective function of each neuron is to achieve some target firing rate. We experimentally show how homeostasis in form of such locally operating processes contributes to the global stability of the field. Due to the self-regulatory nature of our model, the number of free parameters reduces to a minimum which eases its use for applications in various domains. It is particularly suited for modeling cortical development, since the process of learning the mapping is self-organizing, intrinsically regulated, and only depends on the statistics of the input patterns. Self-organizing maps usually develop a topologically ordered representation by making use of distance-dependent lateral connections (e.g. Mexican Hat connectivity). Since our model does not rely on such an assumption, the learned mappings do not necessarily have to be topology preserving. In order to counteract this problem we propose to incorporate an additional process which aims at the minimization of the wiring length between the model units. This process relies on a purely local objective and runs in parallel to the above mentioned self-regulation. Our experiments confirm that this additional mechanism leads to a significant decrease in topological defects and further enhances the quality of the learned mappings.