  The recent detection transformer (DETR) has advanced object detection, but
its application on resource-constrained devices requires massive computation
and memory resources. Quantization stands out as a solution by representing the
network in low-bit parameters and operations. However, there is a significant
performance drop when performing low-bit quantized DETR (Q-DETR) with existing
quantization methods. We find that the bottlenecks of Q-DETR come from the
query information distortion through our empirical analyses. This paper
addresses this problem based on a distribution rectification distillation
(DRD). We formulate our DRD as a bi-level optimization problem, which can be
derived by generalizing the information bottleneck (IB) principle to the
learning of Q-DETR. At the inner level, we conduct a distribution alignment for
the queries to maximize the self-information entropy. At the upper level, we
introduce a new foreground-aware query matching scheme to effectively transfer
the teacher information to distillation-desired features to minimize the
conditional information entropy. Extensive experimental results show that our
method performs much better than prior arts. For example, the 4-bit Q-DETR can
theoretically accelerate DETR with ResNet-50 backbone by 6.6x and achieve 39.4%
AP, with only 2.6% performance gaps than its real-valued counterpart on the
COCO dataset.
