  Recently, deep learning has become a de facto standard in machine learning
with convolutional neural networks (CNNs) demonstrating spectacular success on
a wide variety of tasks. However, CNNs are typically very demanding
computationally at inference time. One of the ways to alleviate this burden on
certain hardware platforms is quantization relying on the use of low-precision
arithmetic representation for the weights and the activations. Another popular
method is the pruning of the number of filters in each layer. While mainstream
deep learning methods train the neural networks weights while keeping the
network architecture fixed, the emerging neural architecture search (NAS)
techniques make the latter also amenable to training. In this paper, we
formulate optimal arithmetic bit length allocation and neural network pruning
as a NAS problem, searching for the configurations satisfying a computational
complexity budget while maximizing the accuracy. We use a differentiable search
method based on the continuous relaxation of the search space proposed by Liu
et al. (arXiv:1806.09055). We show, by grid search, that heterogeneous
quantized networks suffer from a high variance which renders the benefit of the
search questionable. For pruning, improvement over homogeneous cases is
possible, but it is still challenging to find those configurations with the
proposed method. The code is publicly available at
https://github.com/yochaiz/Slimmable and https://github.com/yochaiz/darts-UNIQ
