Geometric Deep Learning
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Geometry Of Deep Learning
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Author : Jong Chul Ye
language : en
Publisher: Springer Nature
Release Date : 2022-01-05
Geometry Of Deep Learning written by Jong Chul Ye and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-05 with Mathematics categories.
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Geometric Deep Learning
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Author : Chu Wang
language : en
Publisher:
Release Date : 2020
Geometric Deep Learning written by Chu Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
"Advances in deep learning techniques have revolutionized computer vision research and have lead to unprecedented success in visual recognition tasks. As a result, many computer vision researchers are now engaged in developing neural architectures and loss functions to handle particular computer vision problems. However, most current neural architectures cannot easily handle 3D input data and this has lead to new interest in representation learning with deep architectures, but on 3D data formats.In an early development of this thesis, we worked on abstracting features from 2.5D point clouds, interpreted as a 2D colour image and depth map pair, thus enabling the use of well studied 2D neural networks. The community had overlooked the potential of deriving higher order representations from the depth map, which could grant invariance to rigid transformations. We proposed a principled method for transforming the 2.5D input data to higher order surface geometric feature maps, including surface normals and curvatures, and applied pretrained CNNs on these new modalities for geometric feature abstraction from the 2.5D input data. However, this approach did not directly allow for the handling of unorganized 3D input. It could only work on 2.5D point clouds where the points could be mapped to pixels in a 2D image. Therefore, we took a step in this direction by working on 3D mesh representation learning. We chose to model a 3D mesh using a graph comprised of rendered 2D views. In order to abstract a global representation of the 3D mesh from the constructed view graph, we proposed a novel recursive cluster-pooling aggregation algorithm. The proposed method demonstrated nontrivial improvements over related work at the time. The empirical results we reported on the ModelNet40 categorization task ranked in second place on the associated leaderboard.Despite their effectiveness, the above methods were not native 3D approaches in that they did not directly abstract features from unorganized 3D data. Thus we moved on to representation learning directly from unorganized point clouds, using spectral graph convolution on local point neighbourhoods. Here we first sampled local point neighbourhoods from the input cloud, and inside each fix sized neighbourhood, a local graph was constructed with each point as a node. Spectral graph convolution was carried out on each local graph, followed by the application of a cluster pooling algorithm to yield a single feature vector representing this neighbourhood. This method improved point set representation learning by incorporating structural features embedded via local graphs, and boosted performance in point set classification and segmentation benchmarks. However, the local graphs remained the same once constructed, and could not be adaptively learned during the training phase.In a complementary direction, research in attention mechanisms has demonstrated that it is beneficial to parametrize the graph structures in GCN-like models, where the adjacency matrix can be learned during training to further minimize the task loss. Despite the demonstrated boost over base models, these adaptive GCN variants rely solely on the task loss to carry out graph structure learning, and as a result, the learned graph structure is usually ad hoc. Motivated by the lack of interpretability in graph structure learning, in the fourth and final contribution of this thesis we propose to explicitly supervise the graphs in GCN-like neural networks, using a novel affinity mass loss. We aim to place emphasis on designated entries in the graph adjacency matrix, which are selected by a user-specified graph supervision target. We demonstrate the effectiveness of the proposed graph supervision method on visual attention networks and regular mini-batch training. In addition to the performance boost in visual recognition tasks, the graph structures learned with the affinity loss demonstrate a much higher degree of interpretability"--
A Geometric Approach To The Unification Of Symbolic Structures And Neural Networks
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Author : Tiansi Dong
language : en
Publisher: Springer Nature
Release Date : 2020-08-24
A Geometric Approach To The Unification Of Symbolic Structures And Neural Networks written by Tiansi Dong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-24 with Technology & Engineering categories.
The unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, Tsinghua It is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science Society Both for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Geometric Deep Learning In Medical Image Analysis
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Author : Erik Bekkers
language : en
Publisher:
Release Date : 2023
Geometric Deep Learning In Medical Image Analysis written by Erik Bekkers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Graph Representation Learning
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Author : William L. William L. Hamilton
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Graph Representation Learning written by William L. William L. Hamilton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Computers categories.
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Towards Trustworthy Geometric Deep Learning For Elastoplasticity
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Author : Nikolaos Napoleon Vlassis
language : en
Publisher:
Release Date : 2021
Towards Trustworthy Geometric Deep Learning For Elastoplasticity written by Nikolaos Napoleon Vlassis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Commonly used hand-crafted homogenized microstructural descriptors (e.g. porosity or the averaged orientation of constitutes) may not adequately capture the topological structures of a material. This is overcome by introducing weighted graphs as new high-dimensional descriptors that represent topological information, such as the connectivity of anisotropic grains in an assemble. Through graph convolutional deep neural networks and graph embedding techniques, our neural networks extract low-dimensional features from the weighted graphs and, subsequently, learn the influence of these low-dimensional features on the resultant stored elastic energy functionals and plasticity models.
Human Contour Detection And Tracking
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Author : Nima Ajam Gard
language : en
Publisher:
Release Date : 2019
Human Contour Detection And Tracking written by Nima Ajam Gard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Civil engineering categories.
Finally, we investigate and propose a new geometric perspective using the notion of manifolds and differential geometry for neural network architectures. This new perspective explains the shortcomings of several methods in domain adaptation. Specifically, it sheds light on the assumptions that are made but violated by common methods in domain adaptation. Moreover, we propose a modular network for specialized task learning, advocating that domain adaptation should transfer specific tasks instead of layers of an architecture.
Information Geometry And Its Applications
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Author : Shun-ichi Amari
language : en
Publisher: Springer
Release Date : 2016-02-02
Information Geometry And Its Applications written by Shun-ichi Amari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-02 with Mathematics categories.
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Graph Neural Networks Foundations Frontiers And Applications
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Author : Lingfei Wu
language : en
Publisher: Springer Nature
Release Date : 2022-01-03
Graph Neural Networks Foundations Frontiers And Applications written by Lingfei Wu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Computers categories.
Deep Learning models are at the core of artificial intelligence research today. It is well known that deep learning techniques are disruptive for Euclidean data, such as images or sequence data, and not immediately applicable to graph-structured data such as text. This gap has driven a wave of research for deep learning on graphs, including graph representation learning, graph generation, and graph classification. The new neural network architectures on graph-structured data (graph neural networks, GNNs in short) have performed remarkably on these tasks, demonstrated by applications in social networks, bioinformatics, and medical informatics. Despite these successes, GNNs still face many challenges ranging from the foundational methodologies to the theoretical understandings of the power of the graph representation learning. This book provides a comprehensive introduction of GNNs. It first discusses the goals of graph representation learning and then reviews the history, current developments, and future directions of GNNs. The second part presents and reviews fundamental methods and theories concerning GNNs while the third part describes various frontiers that are built on the GNNs. The book concludes with an overview of recent developments in a number of applications using GNNs. This book is suitable for a wide audience including undergraduate and graduate students, postdoctoral researchers, professors and lecturers, as well as industrial and government practitioners who are new to this area or who already have some basic background but want to learn more about advanced and promising techniques and applications.
Deep Learning On Graphs
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Author : Yao Ma
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-23
Deep Learning On Graphs written by Yao Ma and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Computers categories.
A comprehensive text on foundations and techniques of graph neural networks with applications in NLP, data mining, vision and healthcare.