  This paper presents a novel differentiable method for unstructured weight
pruning of deep neural networks. Our learned-threshold pruning (LTP) method
learns per-layer thresholds via gradient descent, unlike conventional methods
where they are set as input. Making thresholds trainable also makes LTP
computationally efficient, hence scalable to deeper networks. For example, it
takes $30$ epochs for LTP to prune ResNet50 on ImageNet by a factor of $9.1$.
This is in contrast to other methods that search for per-layer thresholds via a
computationally intensive iterative pruning and fine-tuning process.
Additionally, with a novel differentiable $L_0$ regularization, LTP is able to
operate effectively on architectures with batch-normalization. This is
important since $L_1$ and $L_2$ penalties lose their regularizing effect in
networks with batch-normalization. Finally, LTP generates a trail of
progressively sparser networks from which the desired pruned network can be
picked based on sparsity and performance requirements. These features allow LTP
to achieve competitive compression rates on ImageNet networks such as AlexNet
($26.4\times$ compression with $79.1\%$ Top-5 accuracy) and ResNet50
($9.1\times$ compression with $92.0\%$ Top-5 accuracy). We also show that LTP
effectively prunes modern \textit{compact} architectures, such as EfficientNet,
MobileNetV2 and MixNet.
