On the complexity of loading shallow neural networks (Q1105389)

We formalize a notion of loading information into connectionist networks that characterizes the training of feed-forward neural networks. This problem is NP-complete, so we look for tractable subcases of the problem by placing constraints on the network architecture. The focus of these constraints is on various families of ``shallow'' architectures which are defined to have bounded depth and unbounded width. We introduce a perspective on shallow networks, called the support cone interaction (SCI) graph, which is helpful in distinguishing tractable from intractable subcases: When the SCI graph is a tree or if of limited bandwidth, loading can be accomplished in polynomial time; when its bandwidth is not limited we find the problem NP-complete even if the SCI graph is a simple 2-dimensional planar grid.