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1. Certified Robustness of Graph Convolution Networks for Graph Classification under Topological Attacks

   Jin, Hongwei; Shi, Zhan; Peruri, Ashish; Zhang, Xinhua (January 2020, Advances in neural information processing systems)

   null (Ed.)

   Graph convolution networks (GCNs) have become effective models for graph classification. Similar to many deep networks, GCNs are vulnerable to adversarial attacks on graph topology and node attributes. Recently, a number of effective attack and defense algorithms have been designed, but no certificate of robustness has been developed for GCN-based graph classification under topological perturbations with both local and global budgets. In this paper, we propose the first certificate for this problem. Our method is based on Lagrange dualization and convex envelope, which result in tight approximation bounds that are efficiently computable by dynamic programming. When used in conjunction with robust training, it allows an increased number of graphs to be certified as robust. 

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2. DeepBern-Nets: Taming the Complexity of Certifying Neural Networks Using Bernstein Polynomial Activations and Precise Bound Propagation

   https://doi.org/10.1609/aaai.v38i19.30117  

   Khedr, Haitham; Shoukry, Yasser (March 2024, Proceedings of the AAAI Conference on Artificial Intelligence)

   Formal certification of Neural Networks (NNs) is crucial for ensuring their safety, fairness, and robustness. Unfortunately, on the one hand, sound and complete certification algorithms of ReLU-based NNs do not scale to large-scale NNs. On the other hand, incomplete certification algorithms are easier to compute, but they result in loose bounds that deteriorate with the depth of NN, which diminishes their effectiveness. In this paper, we ask the following question; can we replace the ReLU activation function with one that opens the door to incomplete certification algorithms that are easy to compute but can produce tight bounds on the NN's outputs? We introduce DeepBern-Nets, a class of NNs with activation functions based on Bernstein polynomials instead of the commonly used ReLU activation. Bernstein polynomials are smooth and differentiable functions with desirable properties such as the so-called range enclosure and subdivision properties. We design a novel Interval Bound Propagation (IBP) algorithm, called Bern-IBP, to efficiently compute tight bounds on DeepBern-Nets outputs. Our approach leverages the properties of Bernstein polynomials to improve the tractability of neural network certification tasks while maintaining the accuracy of the trained networks. We conduct experiments in adversarial robustness and reachability analysis settings to assess the effectiveness of the approach. Our proposed framework achieves high certified accuracy for adversarially-trained NNs, which is often a challenging task for certifiers of ReLU-based NNs. This work establishes Bernstein polynomial activation as a promising alternative for improving NN certification tasks across various NNs applications. 

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3. Adversarial Robustness of Supervised Sparse Coding

   Sulam, Jeremias; Muthukumar, Ramchandran; Arora, Raman (October 2020, Advances in neural information processing systems)

   null (Ed.)

   Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in practice. In this work, we strike a better balance by considering a model that involves learning a representation while at the same time giving a precise generalization bound and a robustness certificate. We focus on the hypothesis class obtained by combining a sparsity-promoting encoder coupled with a linear classifier, and show an interesting interplay between the expressivity and stability of the (supervised) representation map and a notion of margin in the feature space. We bound the robust risk (to $$\ell_2$$-bounded perturbations) of hypotheses parameterized by dictionaries that achieve a mild encoder gap on training data. Furthermore, we provide a robustness certificate for end-to-end classification. We demonstrate the applicability of our analysis by computing certified accuracy on real data, and compare with other alternatives for certified robustness. 

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4. Leveraging locality of reference for certificate revocation

   https://doi.org/10.1145/3359789.3359819  

   Dickinson, Luke; Smith, Trevor; Seamons, Kent (December 2019, ACSAC '19: Proceedings of the 35th Annual Computer Security Applications Conference)

   X.509 certificate revocation defends against man-in-the-middle attacks involving a compromised certificate. Certificate revocation strategies face scalability, effectiveness, and deployment challenges as HTTPS adoption rates have soared. We propose Certificate Revocation Table (CRT), a new revocation strategy that is competitive with or exceeds alternative state-of-the-art solutions in effectiveness, efficiency, certificate growth scalability, mass revocation event scalability, revocation timeliness, privacy, and deployment requirements. The CRT design assumes that locality of reference applies to the certificates accessed by an organization. The CRT periodically checks the revocation status of X.509 certificates recently used by the organization. Pre-checking the revocation status of certificates the clients are likely to use avoids the security problems of on-demand certificate revocation checking. To validate both the effectiveness and efficiency of our approach, we simulated a CRT using 60 days of TLS traffic logs from Brigham Young University to measure the effects of actively refreshing revocation status information for various certificate working set window lengths. A working set window size of 45 days resulted in an average of 99.86% of the TLS handshakes having revocation information cached in advance. The CRT storage requirements are small. The initial revocation status information requires downloading a 6.7 MB file, and subsequent updates require only 205.1 KB of bandwidth daily. Updates that include only revoked certificates require just 215 bytes of bandwidth per day. 

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5. BREAKING CERTIFIED DEFENSES: SEMANTIC ADVERSARIAL EXAMPLES WITH SPOOFED ROBUSTNESS CERTIFICATES

   Ghiasi, Amin; Shafahi, Ali; Goldstein, Tom (September 2019, International Conference on Learning Representations)

   Defenses against adversarial attacks can be classified into certified and non-certified. Certifiable defenses make networks robust within a certain -bounded radius, so that it is impossible for the adversary to make adversarial examples in the certificate bound. We present an attack that maintains the imperceptibility property of adversarial examples while being outside of the certified radius. Furthermore, the proposed "Shadow Attack" can fool certifiably robust networks by producing an imperceptible adversarial example that gets misclassified and produces a strong ``spoofed'' certificate. 

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