  As deep neural networks make their ways into different domains, their compute
efficiency is becoming a first-order constraint. Deep quantization, which
reduces the bitwidth of the operations (below 8 bits), offers a unique
opportunity as it can reduce both the storage and compute requirements of the
network super-linearly. However, if not employed with diligence, this can lead
to significant accuracy loss. Due to the strong inter-dependence between layers
and exhibiting different characteristics across the same network, choosing an
optimal bitwidth per layer granularity is not a straight forward. As such, deep
quantization opens a large hyper-parameter space, the exploration of which is a
major challenge. We propose a novel sinusoidal regularization, called SINAREQ,
for deep quantized training. Leveraging the sinusoidal properties, we seek to
learn multiple quantization parameterization in conjunction during
gradient-based training process. Specifically, we learn (i) a per-layer
quantization bitwidth along with (ii) a scale factor through learning the
period of the sinusoidal function. At the same time, we exploit the
periodicity, differentiability, and the local convexity profile in sinusoidal
functions to automatically propel (iii) network weights towards values
quantized at levels that are jointly determined. We show how SINAREQ balance
compute efficiency and accuracy, and provide a heterogeneous bitwidth
assignment for quantization of a large variety of deep networks (AlexNet,
CIFAR-10, MobileNet, ResNet-18, ResNet-20, SVHN, and VGG-11) that virtually
preserves the accuracy. Furthermore, we carry out experimentation using fixed
homogenous bitwidths with 3- to 5-bit assignment and show the versatility of
SINAREQ in enhancing quantized training algorithms (DoReFa and WRPN) with about
4.8% accuracy improvements on average, and then outperforming multiple
state-of-the-art techniques.
