Optimal Machine Intelligence at the Edge of Chaos

It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural networks, the foundation of this hypothesis on generic non-linear systems remains unclear. Here we develop a general theory that reveals the exact edge of chaos is the boundary between the chaotic phase and the (pseudo)periodic phase arising from Neimark-Sacker bifurcation. This edge is analytically determined by the asymptotic Jacobian norm values of the non-linear operator and influenced by the dimensionality of the system. The optimality at the edge of chaos is associated with the highest information transfer between input and output at this point similar to that of the logistic map. As empirical validations, our experiments on the various deep learning models in computer vision demonstrate the optimality of the models near the edge of chaos, and we observe that the state-of-art training algorithms push the models towards such edge as they become more accurate. We further establishes the theoretical understanding of deep learning model generalization through asymptotic stability.