A potpourri of recent results in high-dimensional dynamical systems.

This seminar will begin with a discussion of a sequence of recent results regarding our work with high-dimensional scalar neural networks. For convenience of analysis the neural networks can be partitioned via common dynamic types according to a control parameter. This stratification will be introduced, followed by a discussion of results regarding probable bifurcations from fixed points in both general dynamical systems and the specific neural networks we are employing. The discussion will also focus on a series of scaling laws that have been discovered with respect to an increase in the number of parameters and input dimensions of the neural networks. Finally, the seminar will include a discussion how these scaling laws can be used to understand topological variation with parameter change in the neural networks as the number of parameters and input dimensions becomes large.