Action function approach to network dynamics and the meaning of representations

This study examines the potential for neural networks to perform decompostion procedures. The approach that is taken uses action functionals constrained to preserve symmetries identified in cognitive processes. In this scheme the temporal aspect of these procedures, even after learning, reflects the sequential analysis of information contained in the input. By using appropriately constrained action functionals, variation principles can be used to derive expressions for the dynamics of the system even though the exact nature of all the interactions are unknown. The geometry of the energy space obtained is therefore modified by the symmetry constraints placed on the action functional. As a result the relationships between representations in this space are such that their physical attributes encorporate semantic meanings.