  Deep neural networks have achieved impressive performance in many
applications but their large number of parameters lead to significant
computational and storage overheads. Several recent works attempt to mitigate
these overheads by designing compact networks using pruning of connections.
However, we observe that most of the existing strategies to design compact
networks fail to preserve network robustness against adversarial examples. In
this work, we rigorously study the extension of network pruning strategies to
preserve both benign accuracy and robustness of a network. Starting with a
formal definition of the pruning procedure, including pre-training, weights
pruning, and fine-tuning, we propose a new pruning method that can create
compact networks while preserving both benign accuracy and robustness. Our
method is based on two main insights: (1) we ensure that the training
objectives of the pre-training and fine-tuning steps match the training
objective of the desired robust model (e.g., adversarial robustness/verifiable
robustness), and (2) we keep the pruning strategy agnostic to pre-training and
fine-tuning objectives. We evaluate our method on four different networks on
the CIFAR-10 dataset and measure benign accuracy, empirical robust accuracy,
and verifiable robust accuracy. We demonstrate that our pruning method can
preserve on average 93\% benign accuracy, 92.5\% empirical robust accuracy, and
85.0\% verifiable robust accuracy while compressing the tested network by
10$\times$.
