  Quantization and pruning are core techniques used to reduce the inference
costs of deep neural networks. State-of-the-art quantization techniques are
currently applied to both the weights and activations; however, pruning is most
often applied to only the weights of the network. In this work, we jointly
apply novel uniform quantization and unstructured pruning methods to both the
weights and activations of deep neural networks during training. Using our
methods, we empirically evaluate the currently accepted prune-then-quantize
paradigm across a wide range of computer vision tasks and observe a
non-commutative nature when applied to both the weights and activations of deep
neural networks. Informed by these observations, we articulate the
non-commutativity hypothesis: for a given deep neural network being trained for
a specific task, there exists an exact training schedule in which quantization
and pruning can be introduced to optimize network performance. We identify that
this optimal ordering not only exists, but also varies across discriminative
and generative tasks. Using the optimal training schedule within our training
framework, we demonstrate increased performance per memory footprint over
existing solutions.
