The global optimum of shallow neural network is attained by ridgelet transform
Sho Sonoda, Ishikawa, Isao, Masahiro Ikeda, Kei Hagihara, Yoshihiro Sawano, Takuo Matsubara, Noboru Murata · arXiv (Cornell University) · 2018
We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform. A series of computational experiments show that there exists an interesting similarity between the scatter plot of hidden parameters in a shallow neural network after the BP training and the spectrum of the ridgelet transform. By introducing a continuous model of neural networks, we reduce the training problem to a convex optimization in an infinite dimensional Hilbert space, and obtain the explicit expression of the global optimizer via the ridgelet transform.