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It is well-known that recurrent neural networks (RNNs), although widely used,are vulnerable to adversarial attacks including one-frame attacks andmulti-frame attacks. Though a few certified defenses exist to provideguaranteed robustness against one-frame attacks, we prove that defendingagainst multi-frame attacks remains a challenging problem due to their enormousperturbation space. In this paper, we propose the first certified defenseagainst multi-frame attacks for RNNs called RNN-Guard. To address the abovechallenge, we adopt the perturb-all-frame strategy to construct perturbationspaces consistent with those in multi-frame attacks. However, theperturb-all-frame strategy causes a precision issue in linear relaxations. Toaddress this issue, we introduce a novel abstract domain called InterZono anddesign tighter relaxations. We prove that InterZono is more precise thanZonotope yet carries the same time complexity. Experimental evaluations acrossvarious datasets and model structures show that the certified robust accuracycalculated by RNN-Guard with InterZono is up to 2.18 times higher than thatwith Zonotope. In addition, we extend RNN-Guard as the first certified trainingmethod against multi-frame attacks to directly enhance RNNs' robustness. Theresults show that the certified robust accuracy of models trained withRNN-Guard against multi-frame attacks is 15.47 to 67.65 percentage pointshigher than those with other training methods.

RNN-Guard: Certified Robustness Against Multi-frame Attacks for Recurrent Neural Networks