Further Theoretical Investigations of the Trion Model of Cortical Organization

The trion model represents a mathematical realization of Mountcastle's columnar organization principle of cortex. A trion represents a localized group of neurons with three levels of firing which are interconnected to form trion networks. The striking results of Fisher's ANNNI spin model were incorporated by using connections that are localized, highly structured in space and time, and competing by having a balance between excitation and inhibition. These networks have large repertoires of spatial-temporal patterns, MPs, that can be readily learned using a Hebb learning rule with only small changes in the connections. As the synaptic noise, or temperature T, is varied a series of phase transitions at precise values T(n) were found giving new repertoires of MPs, and the average time for any initial firing configuration to project onto an MP shows a quite sharp change at each T(n). Near a phase transition, in a Monte Carlo simulation, the temporal evolution wanders back and forth between sets of MPs in contrast to the more structured sequential evolutions far from a T(n). Thresholds and learning are shown to be enhanced near the transition points. The temporal dependence of the Hebb learning rule was investigated and shown to be predominantly inhibitory for correlations that are out of phase and excitatory for correlations that are in phase. This type of learning proceeds by a selectional principle which can proceed much more rapidly than instructional learning and with comparatively small changes in connectivity. A novel treatment for epilepsy is proposed and experimental support on the elimination of an epileptic focus by patterned electrical stimulation would have fundamental scientific importance in addition to the enormous clinical relevance. The information processing by these cortical networks is shown to be performing various symmetry operations as the network evolves into sequences of the various spatial -temporal patterns. Rotation, time-reversal, parity, charge conjugation, and combinations of these symmetry operations are shown to occur in the Monte Carlo simulations of trion networks. A cortical column is thus proposed to perform computations by symmetry operations. A higher level architecture is discussed which necessitates a hardware implementation.