相关论文: The Cost of Relaxation: Evaluating the Error in Co…

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…

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 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…

Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend…

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…

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…

We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization…

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…

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…

Formal verification of neural networks is essential before their deployment in safety-critical applications. However, existing methods for formally verifying neural networks are not yet scalable enough to handle practical problems under…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs…

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…

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus,…

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…

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…

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that…

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…