To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the training process itself (e.g., min-max optimization, constrained learning, or regularization). These approaches, however, might not be effective at increasing the margin in the input (feature) space. In this paper, we propose a differentiable regularizer that is a lower bound on the distance of the data points to the classification boundary. The proposed regularizer requires knowledge of the model's Lipschitz constant along certain directions. To this end, we develop a scalable method for calculating guaranteed differentiable upper bounds on the Lipschitz constant of neural networks accurately and efficiently. The relative accuracy of the bounds prevents excessive regularization and allows for more direct manipulation of the decision boundary. Furthermore, our Lipschitz bounding algorithm exploits the monotonicity and Lipschitz continuity of the activation layers, and the resulting bounds can be used to design new layers with controllable bounds on their Lipschitz constant. Experiments on the MNIST, CIFAR-10, and Tiny-ImageNet data sets verify that our proposed algorithm obtains competitively improved results compared to the state-of-the-art.

Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the prediction confidence, i.e., the higher confidence from a smoothed classifier implies the better robustness. This motivates us to rethink the fundamental trade-off between accuracy and robustness in terms of calibrating confidences of a smoothed classifier. In this paper, we propose a simple training scheme, coined SmoothMix, to control the robustness of smoothed classifiers via self-mixup: it trains on convex combinations of samples along the direction of adversarial perturbation for each input. The proposed procedure effectively identifies over-confident, near off-class samples as a cause of limited robustness in case of smoothed classifiers, and offers an intuitive way to adaptively set a new decision boundary between these samples for better robustness. Our experimental results demonstrate that the proposed method can significantly improve the certified $\ell_2$-robustness of smoothed classifiers compared to existing state-of-the-art robust training methods.

Recent studies show that training deep neural networks (DNNs) with Lipschitz constraints are able to enhance adversarial robustness and other model properties such as stability. In this paper, we propose a layer-wise orthogonal training method (LOT) to effectively train 1-Lipschitz convolution layers via parametrizing an orthogonal matrix with an unconstrained matrix. We then efficiently compute the inverse square root of a convolution kernel by transforming the input domain to the Fourier frequency domain. On the other hand, as existing works show that semi-supervised training helps improve empirical robustness, we aim to bridge the gap and prove that semi-supervised learning also improves the certified robustness of Lipschitz-bounded models. We conduct comprehensive evaluations for LOT under different settings. We show that LOT significantly outperforms baselines regarding deterministic l2 certified robustness, and scales to deeper neural networks. Under the supervised scenario, we improve the state-of-the-art certified robustness for all architectures (e.g. from 59.04% to 63.50% on CIFAR-10 and from 32.57% to 34.59% on CIFAR-100 at radius $\rho=36/255$ for 40-layer networks). With semi-supervised learning over unlabelled data, we are able to improve state-of-the-art certified robustness on CIFAR-10 at $\rho=108/255$ from 36.04% to 42.39%. In addition, LOT consistently outperforms baselines on different model architectures with only 1/3 evaluation time.

A recent technique of randomized smoothing has shown that the worst-case (adversarial) l2-robustness can be transformed into the average-case Gaussian-robustness by smoothing a classifier, i.e., by considering the averaged prediction over Gaussian noise. In this paradigm, one should rethink the notion of adversarial robustness in terms of generalization ability of a classifier under noisy observations. We found that the trade-off between accuracy and certified robustness of smoothed classifiers can be greatly controlled by simply regularizing the prediction consistency over noise. This relationship allows us to design a robust training objective without approximating a non-existing smoothed classifier, e.g., via soft smoothing. Our experiments under various deep neural network architectures and datasets show that the certified l2-robustness can be dramatically improved with the proposed regularization, even achieving better or comparable results to the state-of-the-art approaches with significantly less training costs and hyperparameters.

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.

Today's state-of-the-art certifications make optimal

We use the notations defined in Section 2 of the main text throughout this section. E.1 SmoothAdv Recall that a smoothed classifier ˆ f is defined from a hard classifier f: R

Let, y be a point in that intersection. The rest of the procedure remains the same as algorithm 1. (figure 3). However, models trained without noise also produce non-trivial certificates.

While certified robustness is widely promoted as a solution to adversarial examples in Artificial Intelligence systems, significant challenges remain before these techniques can be meaningfully deployed in real-world applications. We identify critical gaps in current research, including the paradox of detection without distinction, the lack of clear criteria for practitioners to evaluate certification schemes, and the potential security risks arising from users' expectations surrounding ``guaranteed" robustness claims. These create an alignment issue between how certifications are presented and perceived, relative to their actual capabilities. This position paper is a call to arms for the certification research community, proposing concrete steps to address these fundamental challenges and advance the field toward practical applicability.