Related papers: Algorithms for Verifying Deep Neural Networks

Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks. We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges,…

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…

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks…

We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…

Deep neural networks are becoming more and more popular due to their revolutionary success in diverse areas, such as computer vision, natural language processing, and speech recognition. However, the decision-making processes of these…

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Recent years have shown that deep learned neural networks are a valuable tool in the field of computer vision. This paper addresses the use of two different kinds of network architectures, namely LeNet and Network in Network (NiN). They…

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation and the vision of the Internet-of-Things fuel the interest in resource efficient approaches. These approaches require a carefully…

In recent years, deep neural network is introduced in recommender systems to solve the collaborative filtering problem, which has achieved immense success on computer vision, speech recognition and natural language processing. On one hand,…

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…

Computer-aided detection has been a research area attracting great interest in the past decade. Machine learning algorithms have been utilized extensively for this application as they provide a valuable second opinion to the doctors.…

Developing Intelligent Systems involves artificial intelligence approaches including artificial neural networks. Here, we present a tutorial of Deep Neural Networks (DNNs), and some insights about the origin of the term "deep"; references…

Deep supervision, or known as 'intermediate supervision' or 'auxiliary supervision', is to add supervision at hidden layers of a neural network. This technique has been increasingly applied in deep neural network learning systems for…

Deep learning based on artificial neural networks is a powerful machine learning method that, in the last few years, has been successfully used to realize tasks, e.g., image classification, speech recognition, translation of languages,…

Recent developments in deep neural networks (DNNs) have led to their adoption in safety-critical systems, which in turn has heightened the need for guaranteeing their safety. These safety properties of DNNs can be proven using tools…

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…