Mainly because in high-dimensional space saddle points are much more common and many local minima have very close fitness. Look for example http://arxiv.org/abs

Mainly because in high-dimensional space saddle points are much more common and many local minima have very close fitness. Look for example http://arxiv.org/abs/1405.4604 http://arxiv.org/abs/1405.4604 and following papers.