Related papers: Enabling certification of verification-agnostic ne…
Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications. Semidefinite programming (SDP)-based…
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…
Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…
The robustness of a neural network to adversarial examples can be provably certified by solving a convex relaxation. If the relaxation is loose, however, then the resulting certificate can be too conservative to be practically useful.…
Semidefinite programming (SDP) relaxation has emerged as a promising approach for neural network verification, offering tighter bounds than other convex relaxation methods for deep neural networks (DNNs) with ReLU activations. However, we…
In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…
Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but…
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a…
This paper presents a novel approach to training neural networks with formal safety guarantees using semidefinite programming (SDP) for verification. Our method focuses on verifying safety over large, high-dimensional input regions,…
The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…
We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the…
Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…
In the field of formal verification, Neural Networks (NNs) are typically reformulated into equivalent mathematical programs which are optimized over. To overcome the inherent non-convexity of these reformulations, convex relaxations of…
Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e.,…
Neural networks are central to many emerging technologies, but verifying their correctness remains a major challenge. It is known that network outputs can be sensitive and fragile to even small input perturbations, thereby increasing the…
Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…
Training neural networks which are robust to adversarial attacks remains an important problem in deep learning, especially as heavily overparameterized models are adopted in safety-critical settings. Drawing from recent work which…