document: Training multilayer perceptrons via minimization of sum of ridge functions Motivated by the problem of training multilayer perceptrons in neural networks , we consider the problem of minimizing E -LRB- x -RRB- = Sigma / sub i = 1 / / sup n / f/sub i / -LRB- xi / sub i / . x -RRB- , where xi / sub i / in R/sup S / , 1 < or = i < or = n , and each f/sub i / -LRB- xi / sub i / . x -RRB- is a ridge function . We show that when n is small the problem of minimizing E can be treated as one of minimizing univariate functions , and we use the gradient algorithms for minimizing E when n is moderately large . For a large n , we present the online gradient algorithms and especially show the monotonicity and weak convergence of the algorithms
doc_bio_tags: O B I O B O O O B I O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O B I I O O O O B O B I O O O