  We propose the position-based scaled gradient (PSG) that scales the gradient
depending on the position of a weight vector to make it more
compression-friendly. First, we theoretically show that applying PSG to the
standard gradient descent (GD), which is called PSGD, is equivalent to the GD
in the warped weight space, a space made by warping the original weight space
via an appropriately designed invertible function. Second, we empirically show
that PSG acting as a regularizer to a weight vector is favorable for model
compression domains such as quantization and pruning. PSG reduces the gap
between the weight distributions of a full-precision model and its compressed
counterpart. This enables the versatile deployment of a model either as an
uncompressed mode or as a compressed mode depending on the availability of
resources. The experimental results on CIFAR-10/100 and ImageNet datasets show
the effectiveness of the proposed PSG in both domains of pruning and
quantization even for extremely low bits. The code is released in Github.
