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This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a Simulated Annealing (SA) algorithm tailored to operate within constrained domains and ensure convergence towards…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…
Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability…
Existing deep neural network (DNN) based wireless localization approaches typically do not capture uncertainty inherent in their estimates. In this work, we propose and evaluate variational and scalable DNN approaches to measure the…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…
Deep neural networks (DNNs) may outperform human brains in complex tasks, but the lack of transparency in their decision-making processes makes us question whether we could fully trust DNNs with high stakes problems. As DNNs' operations…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
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…
The increasing demand on precision and throughput within high-precision mechatronics industries requires a new generation of feedforward controllers with higher accuracy than existing, physics-based feedforward controllers. As neural…
It is well-known that the training of Deep Neural Networks (DNN) can be formalized in the language of optimal control. In this context, this paper leverages classical turnpike properties of optimal control problems to attempt a quantifiable…
Deep Neural Networks (DNNs) and their accelerators are being deployed ever more frequently in safety-critical applications leading to increasing reliability concerns. A traditional and accurate method for assessing DNNs' reliability has…
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of $L^p$ norms of NNs and their derivatives. When combined with…
Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the…
The expressiveness of deep neural network (DNN) is a perspective to understandthe surprising performance of DNN. The number of linear regions, i.e. pieces thata piece-wise-linear function represented by a DNN, is generally used to…
Determining the optimal depth of a neural network is a fundamental yet challenging problem, typically resolved through resource-intensive experimentation. This paper introduces a formal theoretical framework to address this question by…
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the behaviors of neural network systems will be crucial for…
Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are being increasingly deployed in real-world safety-critical domains. Despite the widespread success, their complex architecture makes proving any formal guarantees about…
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…
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…