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Most methods for neural network verification focus on bounding the image, i.e., set of outputs for a given input set. This can be used to, for example, check the robustness of neural network predictions to bounded perturbations of an input.…

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Throughout the past five years, the susceptibility of neural networks to minimal adversarial perturbations has moved from a peculiar phenomenon to a core issue in Deep Learning. Despite much attention, however, progress towards more robust…

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly…

Robustness against adversarial attack in neural networks is an important research topic in the machine learning community. We observe one major source of vulnerability of neural nets is from overparameterized fully-connected layers. In this…

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network…

A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…

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,…

Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples. Thus, considerable effort has been invested into…

For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through…

Beyond the traditional neural network training methods based on gradient descent and its variants, state estimation techniques have been proposed to determine a set of ideal weights from a control-theoretic perspective. Hence, the concept…

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern…

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…

Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time. In this work we highlight the benefits of natural low rank representations that often exist for real data…

We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike…