How to find global minima in finite times of search for multilayer perceptrons training

The authors present a novel global optimization method and a learning scheme. They first show a `magic hair-brushing´ method to eliminate any singular point while reserving the global differential structure of the rest of the singular points in the gradient field. Then global search is defined to trace a sequence of the hair-brushing flows on n-D torus T<sup>n</sup>, which is derived by `pasting´ smoothly the admissible region in Rⁿ and the gradient field at the boundary. The proposed method converges to the global minima from any initial point in finite times of search, and each search has almost the same cost as a gradient descent