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In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

Machine Learning · Computer Science 2018-03-01 Raman Arora , Amitabh Basu , Poorya Mianjy , Anirbit Mukherjee

As deep learning systems are widely adopted in safety- and security-critical applications, such as autonomous vehicles, banking systems, etc., malicious faults and attacks become a tremendous concern, which potentially could lead to…

Cryptography and Security · Computer Science 2018-10-02 Jakub Breier , Xiaolu Hou , Dirmanto Jap , Lei Ma , Shivam Bhasin , Yang Liu

Deep neural networks (DNNs) have succeeded in many different perception tasks, e.g., computer vision, natural language processing, reinforcement learning, etc. The high-performed DNNs heavily rely on intensive resource consumption. For…

Machine Learning · Computer Science 2022-10-10 Zhongnan Qu

Deep Neural Network (DNN) workloads are quickly moving from datacenters onto edge devices, for latency, privacy, or energy reasons. While datacenter networks can be protected using conventional cybersecurity measures, edge neural networks…

Cryptography and Security · Computer Science 2019-11-28 Mihailo Isakov , Vijay Gadepally , Karen M. Gettings , Michel A. Kinsy

Deep neural networks (DNNs) are vulnerable to subtle adversarial perturbations applied to the input. These adversarial perturbations, though imperceptible, can easily mislead the DNN. In this work, we take a control theoretic approach to…

Machine Learning · Computer Science 2019-11-13 Arash Rahnama , Andre T. Nguyen , Edward Raff

Semidefinite programming (SDP) relaxation has emerged as a promising approach for neural network verification, offering tighter bounds than other convex relaxation methods for deep neural networks (DNNs) with ReLU activations. However, we…

Machine Learning · Computer Science 2025-06-13 Ryota Ueda , Takami Sato , Ken Kobayashi , Kazuhide Nakata

The ubiquity of deep neural networks (DNNs), cloud-based training, and transfer learning is giving rise to a new cybersecurity frontier in which unsecure DNNs have `structural malware' (i.e., compromised weights and activation pathways). In…

Machine Learning · Computer Science 2021-02-05 N. Benjamin Erichson , Dane Taylor , Qixuan Wu , Michael W. Mahoney

Deep neural networks (DNNs) have substantial computational requirements, which greatly limit their performance in resource-constrained environments. Recently, there are increasing efforts on optical neural networks and optical computing…

Machine Learning · Computer Science 2021-04-05 Yingjie Li , Ruiyang Chen , Berardi Sensale Rodriguez , Weilu Gao , Cunxi Yu

Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the…

Machine Learning · Statistics 2018-09-25 Konstantin Eckle , Johannes Schmidt-Hieber

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…

Artificial Intelligence · Computer Science 2022-10-11 Zhen Liang , Dejin Ren , Wanwei Liu , Ji Wang , Wenjing Yang , Bai Xue

Attribution explanation is a typical approach for explaining deep neural networks (DNNs), inferring an importance or contribution score for each input variable to the final output. In recent years, numerous attribution methods have been…

Machine Learning · Computer Science 2025-08-12 Huiqi Deng , Hongbin Pei , Quanshi Zhang , Mengnan Du

Formal verification has emerged as a powerful approach to ensure the safety and reliability of deep neural networks. However, current verification tools are limited to only a handful of properties that can be expressed as first-order…

Artificial Intelligence · Computer Science 2022-03-03 Xuan Xie , Kristian Kersting , Daniel Neider

Deep neural networks (DNN) have been a de facto standard for nowadays biometric recognition solutions. A serious, but still overlooked problem in these DNN-based recognition systems is their vulnerability against adversarial attacks.…

Computer Vision and Pattern Recognition · Computer Science 2019-02-26 Renjie Xie , Yanzhi Chen , Yan Wo , Qiao Wang

The stringent requirements for the Deep Neural Networks (DNNs) accelerator's reliability stand along with the need for reducing the computational burden on the hardware platforms, i.e. reducing the energy consumption and execution time as…

Hardware Architecture · Computer Science 2024-01-19 Mahdi Taheri , Natalia Cherezova , Mohammad Saeed Ansari , Maksim Jenihhin , Ali Mahani , Masoud Daneshtalab , Jaan Raik

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

Machine Learning · Statistics 2021-11-03 Lu Lu , Yanhui Su , George Em Karniadakis

As Graph Neural Networks (GNNs) are increasingly being employed in critical real-world applications, several methods have been proposed in recent literature to explain the predictions of these models. However, there has been little to no…

Machine Learning · Computer Science 2022-02-23 Chirag Agarwal , Marinka Zitnik , Himabindu Lakkaraju

Deep neural networks (DNNs) are increasingly used in safety-critical autonomous systems as perception components processing high-dimensional image data. Formal analysis of these systems is particularly challenging due to the complexity of…

Computer Vision and Pattern Recognition · Computer Science 2023-02-13 Corina S. Pasareanu , Ravi Mangal , Divya Gopinath , Sinem Getir Yaman , Calum Imrie , Radu Calinescu , Huafeng Yu

Deep neural networks (DNNs) have become an enabling component for a myriad of artificial intelligence applications. DNNs have shown sometimes superior performance, even compared to humans, in cases such as self-driving, health applications,…

Neural and Evolutionary Computing · Computer Science 2023-07-12 Ghada Alsuhli , Vasileios Sakellariou , Hani Saleh , Mahmoud Al-Qutayri , Baker Mohammad , Thanos Stouraitis

As neural networks (NNs) are increasingly introduced into safety-critical domains, there is a growing need to formally verify NNs before deployment. In this work we focus on the formal verification problem of NN equivalence which aims to…

Machine Learning · Computer Science 2021-12-14 Samuel Teuber , Marko Kleine Büning , Philipp Kern , Carsten Sinz

Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard…

Machine Learning · Computer Science 2021-10-19 Hangcheng Dong , Jingxiao Liao , Yan Wang , Yixin Chen , Bingguo Liu , Dong Ye , Guodong Liu
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