相关论文: Lipschitz-bounded 1D convolutional neural networks…

This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Convolutional neural networks (CNNs) are commonly used for image classification. Saliency methods are examples of approaches that can be used to interpret CNNs post hoc, identifying the most relevant pixels for a prediction following the…

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…

Recent research has revealed that high compression of Deep Neural Networks (DNNs), e.g., massive pruning of the weight matrix of a DNN, leads to a severe drop in accuracy and susceptibility to adversarial attacks. Integration of network…

When fine-tuning Deep Neural Networks (DNNs) to new data, DNNs are prone to overwriting network parameters required for task-specific functionality on previously learned tasks, resulting in a loss of performance on those tasks. We propose…

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…

Graph Hypernetworks (GHN) can predict the parameters of varying unseen CNN architectures with surprisingly good accuracy at a fraction of the cost of iterative optimization. Following these successes, preliminary research has explored the…

Deep Neural Networks (DNNs) are vulnerable to adversarial attacks. Existing methods are devoted to developing various robust training strategies or regularizations to update the weights of the neural network. But beyond the weights, the…

Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the…

Convolutional neural networks (CNNs) based solutions have achieved state-of-the-art performances for many computer vision tasks, including classification and super-resolution of images. Usually the success of these methods comes with a cost…

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using…

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…

Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic…

We study parameterizations of stabilizing nonlinear policies for learning-based control. We propose a structure based on a nonlinear version of the Youla-Kucera parameterization combined with robust neural networks such as the recurrent…

Despite recent success, state-of-the-art learning-based models remain highly vulnerable to input changes such as adversarial examples. In order to obtain certifiable robustness against such perturbations, recent work considers…

Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…

During the last decade, Convolutional Neural Networks (CNNs) have become the de facto standard for various Computer Vision and Machine Learning operations. CNNs are feed-forward Artificial Neural Networks (ANNs) with alternating…