  We explore conditions for when the gradient of a deep declarative node can be
approximated by ignoring constraint terms and still result in a descent
direction for the global loss function. This has important practical
application when training deep learning models since the approximation is often
computationally much more efficient than the true gradient calculation. We
provide theoretical analysis for problems with linear equality constraints and
normalization constraints, and show examples where the approximation works well
in practice as well as some cautionary tales for when it fails.
