  The DEtection TRansformer (DETR) approach, which uses a transformer
encoder-decoder architecture and a set-based global loss, has become a building
block in many transformer based applications. However, as originally presented,
the assignment cost and the global loss are not aligned, i.e., reducing the
former is likely but not guaranteed to reduce the latter. And the issue of
gradient is ignored when a combinatorial solver such as Hungarian is used. In
this paper we show that the global loss can be expressed as the sum of an
assignment-independent term, and an assignment-dependent term which can be used
to define the assignment cost matrix. Recent results on generalized gradients
of optimal assignment cost with respect to parameters of an assignment problem
are then used to define generalized gradients of the loss with respect to
network parameters, and backpropagation is carried out properly. Our
experiments using the same loss weights show interesting convergence properties
and a potential for further performance improvements.
