  We introduce CQnet, a neural network with origins in the CQ algorithm for
solving convex split-feasibility problems and forward-backward splitting.
CQnet's trajectories are interpretable as particles that are tracking a
changing constraint set via its point-to-set distance function while being
elements of another constraint set at every layer. More than just a
convex-geometric interpretation, CQnet accommodates learned and deterministic
constraints that may be sample or data-specific and are satisfied by every
layer and the output. Furthermore, the states in CQnet progress toward another
constraint set at every layer. We provide proof of stability/nonexpansiveness
with minimal assumptions. The combination of constraint handling and stability
put forward CQnet as a candidate for various tasks where prior knowledge exists
on the network states or output.
