Toward Patch Robustness Certification and Detection for Deep Learning Systems Beyond Consistent Samples

1 Technical Report: Toward Patch Robustness Certification and Detection for Deep Learning Systems Beyond Consistent Samples Qilin Zhou, Zhengyuan Wei, Haipeng Wang, Zhuo Wang, and W.K. Chan Abstract—Patch robustness certification is an emerging kind of provable defense technique against adversarial patch attacks for deep learning systems. Certified detection ensures the detection of all patched harmful versions of certified samples, which mitigates the failures of empirical defense techniques that could (easily) be compromised. However, existing certified detection methods are ineffective in certifying samples that are misclassified or whose mutants are inconsistently predicted to different labels. This paper proposes HiCert, a novel masking-based certified detection technique. By focusing on the problem of mutants predicted with a label different from the true label with our formal analysis, HiCert formulates a novel formal relation between harmful samples generated by identified loopholes and their benign counterparts. By checking the bound of the maximum confidence among these potentially harmful (i.e., inconsistent) mutants of each benign sample, HiCert ensures that each harmful sample either has the minimum confidence among mutants that are predicted the same as the harmful sample itself below this bound, or has at least one mutant predicted with a label different from the harmful sample itself, formulated after two novel insights. As such, HiCert systematically certifies those inconsistent samples and consistent samples to a large extent. To our knowledge, HiCert is the first work capable of providing such a comprehensive patch robustness certification for certified detection. Our experiments show the high effectiveness of HiCert with a new state-of-the-art performance: It certifies significantly more benign samples, including those inconsistent and consistent, and achieves significantly higher accuracy on those samples without warnings and a significantly lower false silent ratio. Moreover, on actual patch attacks, its defense success ratio is significantly higher than its peers. Index Terms—Certification, Verification, Detection, Deep Learning Model, Patch Robustness, Worst-Case Analysis, De- terministic Guarantee NOMENCLATURE x: a benign sample • x′: x’s harmful sample • ˆx: an arbitrary sample • f: a classification model • v: a certification function • w: a warning function • P: a patch region • P: a patch region set • M: a mask • ˆxM: a mutant of ˆx for M • MP: a covering mask set for P • MP: a mask covering the patch region P • AP(x): an attack con- straint set for x • D: a certified detection defender • y0: the true label of a sample • I. INTRODUCTION © 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. R ELIABILITY of safety-critical deep learning (DL) sys- tems, such as autonomous vehicles and robots, is threat- ened by adversarial attacks [1]–[6], particularly those that are physically realizable [1] (see Fig. 1). A major stereotype is patch adversarial attacks [7]–[12], which is a threat model for a deep learning (DL) system that is tricked into misclassifying an image sample by adding additional content (called a patch) to the sample on an arbitrary region (called a patch region) to produce a label differing from the ground truth [8], [13], [14] (called harmful), consequently, producing an adversarial example. Detecting these patched samples is desirable. Yet, empirical detection and defense techniques [1], [15]–[17] often fail against patch attacks unknown to them or even the known ones if their defense strategies are exposed to attackers [18]. Certified detection for patch adversarial attacks [19]–[24] can significantly enhance the security of these systems and is emerging. Its goal is to formulate a provable framework to cover as many benign samples of a DL system as possible with the deterministic guarantee of detecting all harmful patched versions of the covered benign samples (called certified sam- ples), in the absence of the identity of these benign samples during the detection of the presence of an adversarial patch up to a given size. Certification provides a formal detection property on these certified samples with all their harmful patched versions, unachievable by pure empirical techniques. To our knowledge, almost all effective certified detection defenders against patch adversarial attacks are masking-based [19]–[23]. As harmful patched versions are considered danger- ous (e.g., for safety-critical systems [20]), they are specifically designed to detect all harmful patched versions of a certified benign sample meeting their inferable criteria while k

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