相关论文: The Convex Relaxation Barrier, Revisited: Tightene…

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…

Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU…

In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…

Neural Networks (NNs) have increasingly apparent safety implications commensurate with their proliferation in real-world applications: both unanticipated as well as adversarial misclassifications can result in fatal outcomes. As a…

The existence of adversarial examples poses a real danger when deep neural networks are deployed in the real world. The go-to strategy to quantify this vulnerability is to evaluate the model against specific attack algorithms. This approach…

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…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

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…

A wide range of verification methods have been proposed to verify the safety properties of deep neural networks ensuring that the networks function correctly in critical applications. However, many well-known verification tools still…

Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race…

The increasing integration of deep neural networks in critical systems has spawned a theoretical and practical interest in formally guaranteeing safety properties about their behavior. To achieve this, contemporary verification algorithms…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether…

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…

Many neural network (NN) verification systems represent the network's input-output relation as a constraint program. Sound and complete, representations involve integer constraints, for simulating the activations. Recent works convexly…

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.…

State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…

In this paper, we consider the computational complexity of formally verifying the behavior of Rectified Linear Unit (ReLU) Neural Networks (NNs), where verification entails determining whether the NN satisfies convex polytopic…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…