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Deep neural nets (DNNs) compression is crucial for adaptation to mobiledevices. Though many successful algorithms exist to compress naturally trainedDNNs, developing efficient and stable compression algorithms for robustlytrained DNNs remains widely open. In this paper, we focus on a co-design ofefficient DNN compression algorithms and sparse neural architectures for robustand accurate deep learning. Such a co-design enables us to advance the goal ofaccommodating both sparsity and robustness. With this objective in mind, weleverage the relaxed augmented Lagrangian based algorithms to prune the weightsof adversarially trained DNNs, at both structured and unstructured levels.Using a Feynman-Kac formalism principled robust and sparse DNNs, we can atleast double the channel sparsity of the adversarially trained ResNet20 forCIFAR10 classification, meanwhile, improve the natural accuracy by $8.69$\% andthe robust accuracy under the benchmark $20$ iterations of IFGSM attack by$5.42$\%. The code is available at\url{https://github.com/BaoWangMath/rvsm-rgsm-admm}.

Sparsity Meets Robustness: Channel Pruning for the Feynman-Kac Formalism Principled Robust Deep Neural Nets