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We currently witness the spectacular success of artificial intelligence in both science and public life. However, the development of a rigorous mathematical foundation is still at an early stage. In this survey article, which is based on an…

Machine Learning · Computer Science 2022-03-18 Gitta Kutyniok

The Artificial Neural network is a functional imitation of simplified model of the biological neurons and their goal is to construct useful computers for real world problems. The ANN applications have increased dramatically in the last few…

Neural and Evolutionary Computing · Computer Science 2007-05-23 Nitin Malik

Recently, stemming from the rapid development of artificial intelligence, which has gained expansive success in pattern recognition, robotics, and bioinformatics, neuroscience is also gaining tremendous progress. A kind of spiking neural…

Neural and Evolutionary Computing · Computer Science 2024-07-02 Shengjie Zheng , Lang Qian , Pingsheng Li , Chenggang He , Xiaoqin Qin , Xiaojian Li

Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…

Neurons and Cognition · Quantitative Biology 2025-07-22 David Papo , Javier M. Buldú

This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…

Optimization and Control · Mathematics 2023-12-25 Andreas Habring , Martin Holler

The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…

Numerical Analysis · Mathematics 2025-10-28 Matthias J. Ehrhardt , Davide Murari , Ferdia Sherry

An exhaustive study on neural network language modeling (NNLM) is performed in this paper. Different architectures of basic neural network language models are described and examined. A number of different improvements over basic neural…

Computation and Language · Computer Science 2017-08-25 Dengliang Shi

With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…

Social and Information Networks · Computer Science 2018-07-20 Daokun Zhang , Jie Yin , Xingquan Zhu , Chengqi Zhang

The field of machine learning has taken a dramatic twist in recent times, with the rise of the Artificial Neural Network (ANN). These biologically inspired computational models are able to far exceed the performance of previous forms of…

Neural and Evolutionary Computing · Computer Science 2015-12-03 Keiron O'Shea , Ryan Nash

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

Classical Physics · Physics 2025-07-14 Sergej Pankratow

The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…

Networking and Internet Architecture · Computer Science 2007-05-23 Jeffrey B. Smith

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

Computer Vision and Pattern Recognition · Computer Science 2021-12-03 Yizeng Han , Gao Huang , Shiji Song , Le Yang , Honghui Wang , Yulin Wang

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…

Statistical Mechanics · Physics 2023-07-21 Guillermo B. Morales , Serena Di Santo , Miguel A. Muñoz

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

Computer Vision and Pattern Recognition · Computer Science 2019-09-05 Yucong Shen , Xin Zhong , Frank Y. Shih

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

Machine Learning · Statistics 2020-11-09 Tom Charnock , Laurence Perreault-Levasseur , François Lanusse

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…

Neural and Evolutionary Computing · Computer Science 2022-05-23 Fabien Furfaro , Avner Bar-Hen , Geoffroy Berthelot

Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…

Social and Information Networks · Computer Science 2026-05-18 Takaaki Fujita , Florentin Smarandache

Artificial neural networks have diverged far from their early inspiration in neurology. In spite of their technological and commercial success, they have several shortcomings, most notably the need for a large number of training examples…

Neural and Evolutionary Computing · Computer Science 2019-12-04 J. Campbell Scott , Thomas F. Hayes , Ahmet S. Ozcan , Winfried W. Wilcke

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic…

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…

Computation and Language · Computer Science 2021-10-15 Oana-Maria Camburu