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Recently a number of CNN-based techniques were proposed to remove image compression artifacts. As in other restoration applications, these techniques all learn a mapping from decompressed patches to the original counterparts under the…
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable…
We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and…
We initiate the study of the inherent tradeoffs between the size of a neural network and its robustness, as measured by its Lipschitz constant. We make a precise conjecture that, for any Lipschitz activation function and for most datasets,…
Graph neural networks (GNNs) achieve the state-of-the-art on graph-relevant tasks such as node and graph classification. However, recent works show GNNs are vulnerable to adversarial perturbations include the perturbation on edges, nodes,…
Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interests in developing…
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…
Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural…
We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of…
Formal verification is only as good as the specification of a system, which is also true for neural network verification. Existing specifications follow the paradigm of data as specification, where the local neighborhood around a reference…
Deep Neural Networks (DNNs) are known to be vulnerable to adversarial attacks, i.e., an imperceptible perturbation to the input can mislead DNNs trained on clean images into making erroneous predictions. To tackle this, adversarial training…
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial…
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…
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…
The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…
Safety-critical applications are required to perform as expected in normal operations. Image processing functions are often required to be insensitive to small geometric perturbations such as rotation, scaling, shearing or translation. This…
We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with…
Deep Neural Networks (DNNs) have revolutionized a wide range of industries, from healthcare and finance to automotive, by offering unparalleled capabilities in data analysis and decision-making. Despite their transforming impact, DNNs face…
With the capability of accurately representing a functional relationship between the inputs of a physical system's model and output quantities of interest, neural networks have become popular for surrogate modeling in scientific…
Recent papers have demonstrated that ensemble stumps and trees could be vulnerable to small input perturbations, so robustness verification and defense for those models have become an important research problem. However, due to the…