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Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…

Machine Learning · Computer Science 2020-01-16 Firat Tuna

Securing networked infrastructures is important in the real world. The problem of deploying security resources to protect against an attacker in networked domains can be modeled as Network Security Games (NSGs). Unfortunately, existing…

Artificial Intelligence · Computer Science 2021-06-03 Wanqi Xue , Youzhi Zhang , Shuxin Li , Xinrun Wang , Bo An , Chai Kiat Yeo

Meta-learning often referred to as learning-to-learn is a promising notion raised to mimic human learning by exploiting the knowledge of prior tasks but being able to adapt quickly to novel tasks. A plethora of models has emerged in this…

Machine Learning · Computer Science 2022-10-17 Jicang Cai , Saeed Vahidian , Weijia Wang , Mohsen Joneidi , Bill Lin

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Machine Learning · Computer Science 2026-01-13 Chutian Huang , Chang Ma , Kaibo Wang , Yang Xiang

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

Optimization and Control · Mathematics 2024-01-30 Jiatai Tong , Junyang Cai , Thiago Serra

Network lasso is a method for solving a multi-task learning problem through the regularized maximum likelihood method. A characteristic of network lasso is setting a different model for each sample. The relationships among the models are…

Methodology · Statistics 2021-10-19 Kaito Shimamura , Shuichi Kawano

Knowledge embedded in the weights of the artificial neural network can be used to improve the network structure, such as in network compression. However, the knowledge is set up by hand, which may not be very accurate, and relevant…

Neural and Evolutionary Computing · Computer Science 2021-10-13 Mengqiao Han , Xiabi Liu , Zhaoyang Hai , Xin Duan

Purpose: We propose a novel method for continual learning based on the increasing depth of neural networks. This work explores whether extending neural network depth may be beneficial in a life-long learning setting. Methods: We propose a…

Machine Learning · Computer Science 2023-05-09 Jędrzej Kozal , Michał Woźniak

Convolutional neural networks have achieved astonishing results in different application areas. Various methods that allow us to use these models on mobile and embedded devices have been proposed. Especially binary neural networks are a…

Machine Learning · Computer Science 2018-12-06 Joseph Bethge , Marvin Bornstein , Adrian Loy , Haojin Yang , Christoph Meinel

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Numerical Analysis · Mathematics 2023-08-23 Ziad Aldirany , Régis Cottereau , Marc Laforest , Serge Prudhomme

Building on our recent research on neural heuristic quantization systems, results on learning quantized motions and resilience to channel dropouts are reported. We propose a general emulation problem consistent with the neuromimetic…

Systems and Control · Electrical Eng. & Systems 2023-05-08 Zexin Sun , John Baillieul

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

Machine Learning · Computer Science 2020-04-01 Yiquan Zhang , Bo Peng , Xiaoyi Zhou , Cheng Xiang , Dalei Wang

Despite their unprecedented performance in various domains, utilization of Deep Neural Networks (DNNs) in safety-critical environments is severely limited in the presence of even small adversarial perturbations. The present work develops a…

Machine Learning · Computer Science 2020-10-19 Fatemeh Sheikholeslami , Swayambhoo Jain , Georgios B. Giannakis

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…

Machine Learning · Computer Science 2021-06-14 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou

A sequential training method for large-scale feedforward neural networks is presented. Each layer of the neural network is decoupled and trained separately. After the training is completed for each layer, they are combined together. The…

Machine Learning · Computer Science 2019-05-21 Jongrae Kim

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…

Machine Learning · Computer Science 2018-10-26 Zhuwen Li , Qifeng Chen , Vladlen Koltun

Recently, the deep neural network (derived from the artificial neural network) has attracted many researchers' attention by its outstanding performance. However, since this network requires high-performance GPUs and large storage, it is…

Neural and Evolutionary Computing · Computer Science 2016-02-25 Song Wang , Dongchun Ren , Li Chen , Wei Fan , Jun Sun , Satoshi Naoi

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…

Numerical Analysis · Mathematics 2021-03-17 Yiqi Gu , Chunmei Wang , Haizhao Yang

This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train…

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