  Existing feature distillation methods commonly adopt the One-to-one
Representation Matching between any pre-selected teacher-student layer pair. In
this paper, we present N-to-One Representation (NORM), a new two-stage
knowledge distillation method, which relies on a simple Feature Transform (FT)
module consisting of two linear layers. In view of preserving the intact
information learnt by the teacher network, during training, our FT module is
merely inserted after the last convolutional layer of the student network. The
first linear layer projects the student representation to a feature space
having N times feature channels than the teacher representation from the last
convolutional layer, and the second linear layer contracts the expanded output
back to the original feature space. By sequentially splitting the expanded
student representation into N non-overlapping feature segments having the same
number of feature channels as the teacher's, they can be readily forced to
approximate the intact teacher representation simultaneously, formulating a
novel many-to-one representation matching mechanism conditioned on a single
teacher-student layer pair. After training, such an FT module will be naturally
merged into the subsequent fully connected layer thanks to its linear property,
introducing no extra parameters or architectural modifications to the student
network at inference. Extensive experiments on different visual recognition
benchmarks demonstrate the leading performance of our method. For instance, the
ResNet18|MobileNet|ResNet50-1/4 model trained by NORM reaches
72.14%|74.26%|68.03% top-1 accuracy on the ImageNet dataset when using a
pre-trained ResNet34|ResNet50|ResNet50 model as the teacher, achieving an
absolute improvement of 2.01%|4.63%|3.03% against the individually trained
counterpart. Code is available at https://github.com/OSVAI/NORM
