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A personal and informal account of what a pure mathematician might expect when using tools from deep learning in their research.

Representation Theory · Mathematics 2023-05-29 Geordie Williamson

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

Machine Learning · Computer Science 2017-06-13 Kaifeng Lv , Shunhua Jiang , Jian Li

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures…

Machine Learning · Computer Science 2025-07-17 Arnulf Jentzen , Benno Kuckuck , Philippe von Wurstemberger

Deep learning with neural networks is applied by an increasing number of people outside of classic research environments, due to the vast success of the methodology on a wide range of machine perception tasks. While this interest is fueled…

Deep learning's great success motivates many practitioners and students to learn about this exciting technology. However, it is often challenging for beginners to take their first step due to the complexity of understanding and applying…

Human-Computer Interaction · Computer Science 2020-10-15 Zijie J. Wang , Robert Turko , Omar Shaikh , Haekyu Park , Nilaksh Das , Fred Hohman , Minsuk Kahng , Duen Horng Chau

This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…

Machine Learning · Statistics 2021-10-20 Jan-Willem van de Meent , Brooks Paige , Hongseok Yang , Frank Wood

In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph…

Machine Learning · Computer Science 2023-05-10 R. Fioresi , F. Zanchetta

Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…

Computational Physics · Physics 2018-08-29 Brian K. Spears

Originally inspired by neurobiology, deep neural network models have become a powerful tool of machine learning and artificial intelligence, where they are used to approximate functions and dynamics by learning from examples. Here we give a…

Neurons and Cognition · Quantitative Biology 2019-04-12 Nikolaus Kriegeskorte , Tal Golan

This is an introductory machine-learning course specifically developed with STEM students in mind. Our goal is to provide the interested reader with the basics to employ machine learning in their own projects and to familiarize themself…

Computational Physics · Physics 2022-06-23 Titus Neupert , Mark H Fischer , Eliska Greplova , Kenny Choo , M. Michael Denner

Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…

Neurons and Cognition · Quantitative Biology 2019-03-06 Katherine R. Storrs , Nikolaus Kriegeskorte

Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a…

Machine learning is a modern approach to problem-solving and task automation. In particular, machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive…

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

Several recent works have shown separation results between deep neural networks, and hypothesis classes with inferior approximation capacity such as shallow networks or kernel classes. On the other hand, the fact that deep networks can…

Machine Learning · Computer Science 2021-07-20 Eran Malach , Gilad Yehudai , Shai Shalev-Shwartz , Ohad Shamir

It is a common belief that training deep transformers from scratch requires large datasets. Consequently, for small datasets, people usually use shallow and simple additional layers on top of pre-trained models during fine-tuning. This work…

Computation and Language · Computer Science 2021-06-01 Peng Xu , Dhruv Kumar , Wei Yang , Wenjie Zi , Keyi Tang , Chenyang Huang , Jackie Chi Kit Cheung , Simon J. D. Prince , Yanshuai Cao

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…

Machine Learning · Statistics 2018-08-06 Nicholas G. Polson , Vadim O. Sokolov

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…

Machine Learning · Statistics 2025-06-09 Van Minh Nguyen , Cristian Ocampo , Aymen Askri , Louis Leconte , Ba-Hien Tran

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of…

Image and Video Processing · Electrical Eng. & Systems 2021-03-09 Jeffrey M. Ede

Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…

Machine Learning · Computer Science 2021-06-10 Daniel T. Chang