M. Pawan Kumar

Alessandro De Palma, Rudy Bunel, Krishnamurthy Dvijotham et al.

Recent works have tried to increase the verifiability of adversarially trained networks by running the attacks over domains larger than the original perturbations and adding various regularization terms to the objective. However, these algorithms either underperform or require complex and expensive stage-wise training procedures, hindering their practical applicability. We present IBP-R, a novel verified training algorithm that is both simple and effective. IBP-R induces network verifiability by coupling adversarial attacks on enlarged domains with a regularization term, based on inexpensive interval bound propagation, that minimizes the gap between the non-convex verification problem and its approximations. By leveraging recent branch-and-bound frameworks, we show that IBP-R obtains state-of-the-art verified robustness-accuracy trade-offs for small perturbations on CIFAR-10 while training significantly faster than relevant previous work. Additionally, we present UPB, a novel branching strategy that, relying on a simple heuristic based on $β$-CROWN, reduces the cost of state-of-the-art branching algorithms while yielding splits of comparable quality.

Tom A. Lamb, Rudy Brunel, Krishnamurthy DJ Dvijotham et al.

Knowledge distillation (KD) has received much attention due to its success in compressing networks to allow for their deployment in resource-constrained systems. While the problem of adversarial robustness has been studied before in the KD setting, previous works overlook what we term the relative calibration of the student network with respect to its teacher in terms of soft confidences. In particular, we focus on two crucial questions with regard to a teacher-student pair: (i) do the teacher and student disagree at points close to correctly classified dataset examples, and (ii) is the distilled student as confident as the teacher around dataset examples? These are critical questions when considering the deployment of a smaller student network trained from a robust teacher within a safety-critical setting. To address these questions, we introduce a faithful imitation framework to discuss the relative calibration of confidences and provide empirical and certified methods to evaluate the relative calibration of a student w.r.t. its teacher. Further, to verifiably align the relative calibration incentives of the student to those of its teacher, we introduce faithful distillation. Our experiments on the MNIST, Fashion-MNIST and CIFAR-10 datasets demonstrate the need for such an analysis and the advantages of the increased verifiability of faithful distillation over alternative adversarial distillation methods.

Rudy Bunel, Krishnamurthy Dvijotham, M. Pawan Kumar et al. · deepmind

We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on neural network verification has focused on partial specifications that, even when satisfied, are not sufficient to ensure that a neural network never makes errors. We focus on applying neural network verification to computational tasks with a precise notion of correctness, where a verifiably correct neural network provably solves the task at hand with no caveats. In particular, we develop an approach to train and verify the first provably correct neural networks for compressed sensing, i.e., recovering sparse vectors from a number of measurements smaller than the dimension of the vector. We show that for modest problem dimensions (up to 50), we can train neural networks that provably recover a sparse vector from linear and binarized linear measurements. Furthermore, we show that the complexity of the network (number of neurons/layers) can be adapted to the problem difficulty and solve problems where traditional compressed sensing methods are not known to provably work.

Alessandro De Palma, Rudy Bunel, Krishnamurthy Dvijotham et al.

In order to train networks for verified adversarial robustness, it is common to over-approximate the worst-case loss over perturbation regions, resulting in networks that attain verifiability at the expense of standard performance. As shown in recent work, better trade-offs between accuracy and robustness can be obtained by carefully coupling adversarial training with over-approximations. We hypothesize that the expressivity of a loss function, which we formalize as the ability to span a range of trade-offs between lower and upper bounds to the worst-case loss through a single parameter (the over-approximation coefficient), is key to attaining state-of-the-art performance. To support our hypothesis, we show that trivial expressive losses, obtained via convex combinations between adversarial attacks and IBP bounds, yield state-of-the-art results across a variety of settings in spite of their conceptual simplicity. We provide a detailed analysis of the relationship between the over-approximation coefficient and performance profiles across different expressive losses, showing that, while expressivity is essential, better approximations of the worst-case loss are not necessarily linked to superior robustness-accuracy trade-offs.