The dynamics of Recurrent Neural Networks trained for temporal tasks and the eigenvalue spectrum.

Different areas of the brain such as the cortex and the prefrontal cortex show great recurrence in their connections, even in early sensory areas. Several approaches and methods based on trained networks have been proposed to model and describe these systems. It is essential to understand the dynamics behind the models because they are used to build different hypotheses about the functioning of brain areas and to explain experimental results. Present work focuses on the study of the dynamics of recurrent neural networks trained to perform Boolean-like tasks with temporal stimuli that emulate being sensory signals. The contribution here is the description of the dynamics through the classification and interpretation carried out with a set of numerical simulations corresponding to networks trained to process time stimuli with AND, OR, XOR, and Flip Flop tasks. The patterns in the distribution of the eigenvalues of the recurrent weight matrix ware studied and properly related to the dynamics.