Optimal Machine Intelligence at the Edge of Chaos
This provides a foundational theoretical understanding of deep learning generalization and optimality, potentially impacting all of ML/AI by linking model performance to dynamical systems theory.
The paper tackles the problem of understanding why optimal machine intelligence might occur at the edge of chaos, developing a general theory that analytically determines this edge based on asymptotic Jacobian norms and dimensionality, and empirically validates it by showing that state-of-the-art deep learning models in computer vision achieve optimal performance near this edge as they become more accurate.
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.