Prof. Dr. Matthias Hein: From Nonlinear Eigenproblems to Neural Networks

I present our recent work on Perron-Frobenius theory for multi-homogeneous mappings. We have used a refinement of this result to show that the optimization problem behind a class of neural networks for multi-class classification can be solved globally optimal with a linear convergence rate by our nonlinear spectral method. This is the first practically feasible algorithm in the area of neural networks which is guaranteed to find the global optimum.