Download or read book Spherical NeurO n s for Geometric Deep Learning written by Pavlo Melnyk and published by Linköping University Electronic Press. This book was released on 2024-09-03 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Felix Klein’s Erlangen Programme of 1872 introduced a methodology to unify non-Euclidean geometries. Similarly, geometric deep learning (GDL) constitutes a unifying framework for various neural network architectures. GDL is built from the first principles of geometry—symmetry and scale separation—and enables tractable learning in high dimensions. Symmetries play a vital role in preserving structural information of geometric data and allow models (i.e., neural networks) to adjust to different geometric transformations. In this context, spheres exhibit a maximal set of symmetries compared to other geometric entities in Euclidean space. The orthogonal group O(n) fully encapsulates the symmetry structure of an nD sphere, including both rotational and reflection symmetries. In this thesis, we focus on integrating these symmetries into a model as an inductive bias, which is a crucial requirement for addressing problems in 3D vision as well as in natural sciences and their related applications. In Paper A, we focus on 3D geometry and use the symmetries of spheres as geometric entities to construct neurons with spherical decision surfaces—spherical neurons—using a conformal embedding of Euclidean space. We also demonstrate that spherical neuron activations are non-linear due to the inherent non-linearity of the input embedding, and thus, do not necessarily require an activation function. In addition, we show graphically, theoretically, and experimentally that spherical neuron activations are isometries in Euclidean space, which is a prerequisite for the equivariance contributions of our subsequent work. In Paper B, we closely examine the isometry property of the spherical neurons in the context of equivariance under 3D rotations (i.e., SO(3)-equivariance). Focusing on 3D in this work and based on a minimal set of four spherical neurons (one learned spherical decision surface and three copies), the centers of which are rotated into the corresponding vertices of a regular tetrahedron, we construct a spherical filter bank. We call it a steerable 3D spherical neuron because, as we verify later, it constitutes a steerable filter. Finally, we derive a 3D steerability constraint for a spherical neuron (i.e., a single spherical decision surface). In Paper C, we present a learnable point-cloud descriptor invariant under 3D rotations and reflections, i.e., the O(3) actions, utilizing the steerable 3D spherical neurons we introduced previously, as well as vector neurons from related work. Specifically, we propose an embedding of the 3D steerable neurons into 4D vector neurons, which leverages end-to-end training of the model. The resulting model, termed TetraSphere, sets a new state-of-the-art performance classifying randomly rotated real-world object scans. Thus, our results reveal the practical value of steerable 3D spherical neurons for learning in 3D Euclidean space. In Paper D, we generalize to nD the concepts we previously established in 3D, and propose O(n)-equivariant neurons with spherical decision surfaces, which we call Deep Equivariant Hyper-spheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on the relation between two points and a sphere, which as we show, turns out to be a Gram matrix. In summary, this thesis introduces techniques based on spherical neurons that enhance the GDL framework, with a specific focus on equivariant and invariant learning on point sets.
Download or read book Lie Group Machine Learning written by Fanzhang Li and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.
Download or read book Neural Networks for Robotics written by Nancy Arana-Daniel and published by CRC Press. This book was released on 2018-09-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an insight on artificial neural networks for giving a robot a high level of autonomous tasks, such as navigation, cost mapping, object recognition, intelligent control of ground and aerial robots, and clustering, with real-time implementations. The reader will learn various methodologies that can be used to solve each stage on autonomous navigation for robots, from object recognition, clustering of obstacles, cost mapping of environments, path planning, and vision to low level control. These methodologies include real-life scenarios to implement a wide range of artificial neural network architectures. Includes real-time examples for various robotic platforms. Discusses real-time implementation for land and aerial robots. Presents solutions for problems encountered in autonomous navigation. Explores the mathematical preliminaries needed to understand the proposed methodologies. Integrates computing, communications, control, sensing, planning, and other techniques by means of artificial neural networks for robotics.
Download or read book Spherical NeurO n s for Geometric Deep Learning written by Pavlo Melnyk and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive and Intelligent Systems written by Abdelhamid Bouchachia and published by Springer Science & Business Media. This book was released on 2011-08-26 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the International Conference on Adaptive and Intelligent Systems, ICAIS 2011, held in Klagenfurt, Austria, in September 2011. The 36 full papers included in these proceedings together with the abstracts of 4 invited talks, were carefully reviewed and selected from 72 submissions. The contributions are organized under the following topical sections: incremental learning; adaptive system architecture; intelligent system engineering; data mining and pattern recognition; intelligent agents; and computational intelligence.
Download or read book The Fractal Geometry of the Brain written by Antonio Di Ieva and published by Springer Nature. This book was released on with total page 999 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Artificial Intelligence in Manufacturing written by Masoud Soroush and published by Elsevier. This book was released on 2024-01-22 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial Intelligence in Manufacturing: Concepts and Methods explains the most successful emerging techniques for applying AI to engineering problems. Artificial intelligence is increasingly being applied to all engineering disciplines, producing more insights into how we understand the world and allowing us to create products in new ways. This book unlocks the advantages of this technology for manufacturing by drawing on work by leading researchers who have successfully developed methods that can apply to a range of engineering applications. The book addresses educational challenges needed for widespread implementation of AI and also provides detailed technical instructions for the implementation of AI methods. Drawing on research in computer science, physics and a range of engineering disciplines, this book tackles the interdisciplinary challenges of the subject to introduce new thinking to important manufacturing problems. - Presents AI concepts from the computer science field using language and examples designed to inspire engineering graduates - Provides worked examples throughout to help readers fully engage with the methods described - Includes concepts that are supported by definitions for key terms and chapter summaries
Download or read book Computer Vision ECCV 2024 written by Aleš Leonardis and published by Springer Nature. This book was released on with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Visual Media written by Fang-Lue Zhang and published by Springer Nature. This book was released on with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Engineering Applications of Neural Networks written by Chrisina Jayne and published by Springer. This book was released on 2013-04-19 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Engineering Applications of Neural Networks, EANN 2012, held in London, UK, in September 2012. The 49 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers describe the applications of neural networks and other computational intelligence approaches to intelligent transport, environmental engineering, computer security, civil engineering, financial forecasting, virtual learning environments, language interpretation, bioinformatics and general engineering.
Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky and published by Psychology Press. This book was released on 2013-05-13 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
Download or read book Deep Learning on Graphs written by Yao Ma and published by Cambridge University Press. This book was released on 2021-09-23 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive text on foundations and techniques of graph neural networks with applications in NLP, data mining, vision and healthcare.
Download or read book The Spike written by Mark Humphries and published by Princeton University Press. This book was released on 2021-03-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The story of a neural impulse and what it reveals about how our brains work We see the last cookie in the box and think, can I take that? We reach a hand out. In the 2.1 seconds that this impulse travels through our brain, billions of neurons communicate with one another, sending blips of voltage through our sensory and motor regions. Neuroscientists call these blips “spikes.” Spikes enable us to do everything: talk, eat, run, see, plan, and decide. In The Spike, Mark Humphries takes readers on the epic journey of a spike through a single, brief reaction. In vivid language, Humphries tells the story of what happens in our brain, what we know about spikes, and what we still have left to understand about them. Drawing on decades of research in neuroscience, Humphries explores how spikes are born, how they are transmitted, and how they lead us to action. He dives into previously unanswered mysteries: Why are most neurons silent? What causes neurons to fire spikes spontaneously, without input from other neurons or the outside world? Why do most spikes fail to reach any destination? Humphries presents a new vision of the brain, one where fundamental computations are carried out by spontaneous spikes that predict what will happen in the world, helping us to perceive, decide, and react quickly enough for our survival. Traversing neuroscience’s expansive terrain, The Spike follows a single electrical response to illuminate how our extraordinary brains work.
Download or read book Algorithmic Advances in Riemannian Geometry and Applications written by Hà Quang Minh and published by Springer. This book was released on 2016-10-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.
Download or read book Mathematical Modeling in Biomedical Imaging I written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2009-10-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Download or read book Information Theory Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
Download or read book Textbook of Assisted Reproductive Techniques written by David K. Gardner and published by CRC Press. This book was released on 2023-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Established as the definitive reference for the IVF clinic, the sixth edition has been extensively revised, with the addition of several important new contributions on laboratory topics, including KPIs for the IVF laboratory, Quality control in the cloud, Artificial Intelligence, AI in gamete and embryo selection, Demystifying vitrification, Microfluidics, Gene editing, Disaster management, and Early human embryo development revealed by static imaging. As previously, methods, protocols, and techniques of choice are presented by IVF pioneers and eminent international experts.
