A free from local minima algorithm for training regressive MLP neural
  networks
Augusto Montisci
In this article an innovative method for training regressive MLP networks is
presented, which is not subject to local minima. The Error-Back-Propagation
algorithm, proposed by William-Hinton-Rummelhart, has had the merit of
favouring the development of machine learning techniques, which has permeated
every branch of research and technology since the mid-1980s. This extraordinary
success is largely due to the black-box approach, but this same factor was also
seen as a limitation, as soon more challenging problems were approached. One of
the most critical aspects of the training algorithms was that of local minima
of the loss function, typically the mean squared error of the output on the
training set. In fact, as the most popular training algorithms are driven by
the derivatives of the loss function, there is no possibility to evaluate if a
reached minimum is local or global. The algorithm presented in this paper
avoids the problem of local minima, as the training is based on the properties
of the distribution of the training set, or better on its image internal to the
neural network. The performance of the algorithm is shown for a well-known
benchmark.