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1. 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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2. LRS: Enhancing Adversarial Transferability through Lipschitz Regularized Surrogate

   https://doi.org/10.1609/aaai.v38i6.28430  

   Wu, Tao ; Luo, Tie ; Wunsch_II, Donald C ( March 2024 , Proceedings of the AAAI Conference on Artificial Intelligence)

   The transferability of adversarial examples is of central importance to transfer-based black-box adversarial attacks. Previous works for generating transferable adversarial examples focus on attacking given pretrained surrogate models while the connections between surrogate models and adversarial trasferability have been overlooked. In this paper, we propose Lipschitz Regularized Surrogate (LRS) for transfer-based black-box attacks, a novel approach that transforms surrogate models towards favorable adversarial transferability. Using such transformed surrogate models, any existing transfer-based black-box attack can run without any change, yet achieving much better performance. Specifically, we impose Lipschitz regularization on the loss landscape of surrogate models to enable a smoother and more controlled optimization process for generating more transferable adversarial examples. In addition, this paper also sheds light on the connection between the inner properties of surrogate models and adversarial transferability, where three factors are identified: smaller local Lipschitz constant, smoother loss landscape, and stronger adversarial robustness. We evaluate our proposed LRS approach by attacking state-of-the-art standard deep neural networks and defense models. The results demonstrate significant improvement on the attack success rates and transferability. Our code is available at https://github.com/TrustAIoT/LRS. 

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3. Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks

   Mahyar Fazlyab, Alexander Robey ( December 2019 , Advances in Neural Information Processing Systems 32 (NeurIPS 2019))

   Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant suffer from either lack of accuracy or poor scalability. In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently. Our main idea is to interpret activation functions as gradients of convex potential functions. Hence, they satisfy certain properties that can be described by quadratic constraints. This particular description allows us to pose the Lipschitz constant estimation problem as a semidefinite program (SDP). The resulting SDP can be adapted to increase either the estimation accuracy (by capturing the interaction between activation functions of different layers) or scalability (by decomposition and parallel implementation). We illustrate the utility of our approach with a variety of experiments on randomly generated networks and on classifiers trained on the MNIST and Iris datasets. In particular, we experimentally demonstrate that our Lipschitz bounds are the most accurate compared to those in the literature. We also study the impact of adversarial training methods on the Lipschitz bounds of the resulting classifiers and show that our bounds can be used to efficiently provide robustness guarantees. 

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4. Adversarial Robustness of Flow-Based Generative Models

   Pope, Phillip ; Balaji, Yogesh ; Feizi, Soheil ( January 2020 , International Conference on Artificial Intelligence and Statistics (AISTATS))

   null (Ed.)

   Flow-based generative models leverage invertible generator functions to fit a distribution to the training data using maximum likelihood. Despite their use in several application domains, robustness of these models to adversarial attacks has hardly been explored. In this paper, we study adversarial robustness of flow-based generative models both theoretically (for some simple models) and empirically (for more complex ones). First, we consider a linear flow-based generative model and compute optimal sample-specific and universal adversarial perturbations that maximally decrease the likelihood scores. Using this result, we study the robustness of the well-known adversarial training procedure, where we characterize the fundamental trade-off between model robustness and accuracy. Next, we empirically study the robustness of two prominent deep, non-linear, flow-based generative models, namely GLOW and RealNVP. We design two types of adversarial attacks; one that minimizes the likelihood scores of in-distribution samples, while the other that maximizes the likelihood scores of out-of-distribution ones. We find that GLOW and RealNVP are extremely sensitive to both types of attacks. Finally, using a hybrid adversarial training procedure, we significantly boost the robustness of these generative models. 

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5. Improved Estimation of Concentration Under ℓp-Norm Distance Metrics Using Half Spaces

   Prescott, Jack ; Zhang, Xiao ; Evans, David ( January 2021 , International Conference on Learning Representations (ICLR))

   Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. (2019) presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find lower bounds on intrinsic robustness for several benchmark datasets. However, it remains unclear whether these lower bounds are tight enough to provide a useful approximation for the intrinsic robustness of a dataset. To gain a deeper understanding of the concentration of measure phenomenon, we first extend the Gaussian Isoperimetric Inequality to non-spherical Gaussian measures and arbitrary ℓp-norms (p ≥ 2). We leverage these theoretical insights to design a method that uses half-spaces to estimate the concentration of any empirical dataset under ℓp-norm distance metrics. Our proposed algorithm is more efficient than Mahloujifar et al. (2019)‘s, and experiments on synthetic datasets and image benchmarks demonstrate that it is able to find much tighter intrinsic robustness bounds. These tighter estimates provide further evidence that rules out intrinsic dataset concentration as a possible explanation for the adversarial vulnerability of state-of-the-art classifiers. 

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