  Pruning-quantization joint learning always facilitates the deployment of deep
neural networks (DNNs) on resource-constrained edge devices. However, most
existing methods do not jointly learn a global criterion for pruning and
quantization in an interpretable way. In this paper, we propose a novel physics
inspired criterion for pruning-quantization joint learning (PIC-PQ), which is
explored from an analogy we first draw between elasticity dynamics (ED) and
model compression (MC). Specifically, derived from Hooke's law in ED, we
establish a linear relationship between the filters' importance distribution
and the filter property (FP) by a learnable deformation scale in the physics
inspired criterion (PIC). Furthermore, we extend PIC with a relative shift
variable for a global view. To ensure feasibility and flexibility, available
maximum bitwidth and penalty factor are introduced in quantization bitwidth
assignment. Experiments on benchmarks of image classification demonstrate that
PIC-PQ yields a good trade-off between accuracy and bit-operations (BOPs)
compression ratio e.g., 54.96X BOPs compression ratio in ResNet56 on CIFAR10
with 0.10% accuracy drop and 53.24X in ResNet18 on ImageNet with 0.61% accuracy
drop). The code will be available at https://github.com/fanxxxxyi/PIC-PQ.
