Related papers: Computable Lipschitz Bounds for Deep Neural Networ…

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…

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…

Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead…

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years,…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. In this paper, we study two variants of pointwise robustness, the maximum safe radius problem, which for a…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

Adversarial attacks against machine learning models are a rather hefty obstacle to our increasing reliance on these models. Due to this, provably robust (certified) machine learning models are a major topic of interest. Lipschitz continuous…

Deep neural networks (DNNs) have a wide range of applications, and software employing them must be thoroughly tested, especially in safety-critical domains. However, traditional software test coverage metrics cannot be applied directly to…

We study finite-horizon optimal switching with discrete intervention dates on a general filtration, allowing continuous-time observations between decision dates, and develop a deep-learning-based dual framework with computable upper bounds.…

Adversarial robustness and generalization are both crucial properties of reliable machine learning models. In this paper, we study these properties in the context of quantum machine learning based on Lipschitz bounds. We derive…

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following:…

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…

The \(L_1/L_2\) norm ratio has gained significant attention as a measure of sparsity due to three merits: sharper approximation to the \(L_0\) norm compared to the \(L_1\) norm, being parameter-free and scale-invariant, and exceptional…

In recent years, physical informed neural networks (PINNs) have been shown to be a powerful tool for solving PDEs empirically. However, numerical analysis of PINNs is still missing. In this paper, we prove the convergence rate to PINNs for…

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected)…