  We continue our study from Lynch and Mallmann-Trenn (Neural Networks, 2021),
of how concepts that have hierarchical structure might be represented in
brain-like neural networks, how these representations might be used to
recognize the concepts, and how these representations might be learned.
  In Lynch and Mallmann-Trenn (Neural Networks, 2021), we considered simple
tree-structured concepts and feed-forward layered networks. Here we extend the
model in two ways: we allow limited overlap between children of different
concepts, and we allow networks to include feedback edges.
  For these more general cases, we describe and analyze algorithms for
recognition and algorithms for learning.
