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Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident in recent…

Machine Learning · Computer Science 2022-03-03 Daniel Bienstock , Gonzalo Muñoz , Sebastian Pokutta

In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure…

Optimization and Control · Mathematics 2025-09-16 Joey Huchette , Gonzalo Muñoz , Thiago Serra , Calvin Tsay

Deep learning has led to significant advances in artificial intelligence, in part, by adopting strategies motivated by neurophysiology. However, it is unclear whether deep learning could occur in the real brain. Here, we show that a deep…

Neurons and Cognition · Quantitative Biology 2017-04-11 Jordan Guergiuev , Timothy P. Lillicrap , Blake A. Richards

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Machine Learning · Computer Science 2025-07-28 Mohd Halim Mohd Noor , Ayokunle Olalekan Ige

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Machine Learning · Computer Science 2018-06-01 Na Lei , Zhongxuan Luo , Shing-Tung Yau , David Xianfeng Gu

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Machine Learning · Statistics 2023-10-11 Nick Polson , Vadim Sokolov

Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…

Artificial Intelligence · Computer Science 2018-02-01 Lê Nguyên Hoang , Rachid Guerraoui

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

Machine Learning · Computer Science 2013-06-10 Yoshua Bengio

Deep learning tools can incorporate all of the available information into a search for new particles, thus making the best use of the available data. This paper reviews how to optimally integrate information with deep learning and…

High Energy Physics - Phenomenology · Physics 2020-06-24 Benjamin Nachman

Deep neural networks can empirically perform efficient hierarchical learning, in which the layers learn useful representations of the data. However, how they make use of the intermediate representations are not explained by recent theories…

Machine Learning · Computer Science 2021-03-08 Minshuo Chen , Yu Bai , Jason D. Lee , Tuo Zhao , Huan Wang , Caiming Xiong , Richard Socher

The great success of deep learning shows that its technology contains profound truth, and understanding its internal mechanism not only has important implications for the development of its technology and effective application in various…

Machine Learning · Computer Science 2018-05-23 Dian Lei , Xiaoxiao Chen , Jianfei Zhao

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Machine Learning · Computer Science 2023-11-21 Andrea Apicella , Francesco Isgrò , Roberto Prevete

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

Differential Geometry · Mathematics 2025-10-22 Tsemo Aristide

In the recent time deep learning has achieved huge popularity due to its performance in various machine learning algorithms. Deep learning as hierarchical or structured learning attempts to model high level abstractions in data by using a…

Computer Vision and Pattern Recognition · Computer Science 2019-04-26 Parth Shah , Vishvajit Bakrola , Supriya Pati

Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is…

Machine Learning · Computer Science 2020-11-02 Xinshi Chen , Yufei Zhang , Christoph Reisinger , Le Song

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods…

Disordered Systems and Neural Networks · Physics 2018-10-01 Alberto Testolin , Michele Piccolini , Samir Suweis

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Machine Learning · Computer Science 2019-01-15 Giuseppe Marra , Francesco Giannini , Michelangelo Diligenti , Marco Gori

This work proposes deep network models and learning algorithms for unsupervised and supervised binary hashing. Our novel network design constrains one hidden layer to directly output the binary codes. This addresses a challenging issue in…

Computer Vision and Pattern Recognition · Computer Science 2016-07-19 Thanh-Toan Do , Anh-Dzung Doan , Ngai-Man Cheung

Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled…

Machine Learning · Computer Science 2017-11-28 Nicholas Frosst , Geoffrey Hinton

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,…

History and Overview · Mathematics 2018-01-19 Catherine F. Higham , Desmond J. Higham
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