AbstractI will show the emergence of type III_1 von Neumann algebras from large N quantum mechanical models. These are effective models constructed from gauge theories on a circle. Their partition functions are matrix models that are explicitly solved in the large N limit. The spectral densities underlying the algebras are computed in closed form, and expressed in terms of the eigenvalue densit...
AbstractIn this report, we give an overview of recent theoretical results on global performance guarantees of optimization algorithm for non convex optimization about deep neural network and data analysis