A very informative article by Shalev-Shwartz, Shamir and Shammah about critical problems faced when solving some simple problems via neural networks trained with gradient-based methods. Find the article here.
In recent years, Deep Learning has become the go-to solution for a broad range of applications, often outperforming state-of-the-art. However, it is important, for both theoreticians and practitioners, to gain a deeper understanding of the difﬁculties and limitations associated with common approaches and algorithms. We describe four types of simple problems, for which the gradient-based algorithms commonly used in deep learning either fail or suffer from signiﬁcant difﬁculties. We illustrate the failures through practical experiments, and provide theoretical insights explaining their source, and how they might be remedied.