  This paper proposes a new algorithm based on multi-scale stochastic local
search with binary representation for training neural networks.
  In particular, we study the effects of neighborhood evaluation strategies,
the effect of the number of bits per weight and that of the maximum weight
range used for mapping binary strings to real values. Following this
preliminary investigation, we propose a telescopic multi-scale version of local
search where the number of bits is increased in an adaptive manner, leading to
a faster search and to local minima of better quality. An analysis related to
adapting the number of bits in a dynamic way is also presented. The control on
the number of bits, which happens in a natural manner in the proposed method,
is effective to increase the generalization performance. Benchmark tasks
include a highly non-linear artificial problem, a control problem requiring
either feed-forward or recurrent architectures for feedback control, and
challenging real-world tasks in different application domains.
  The results demonstrate the effectiveness of the proposed method.
