Geometric Feature Learning

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.

What is Geometric Feature Learning Geometric feature learning is a technique combining machine learning and computer vision to solve visual tasks. The main goal of this method is to find a set of representative features of geometric form to represent an object by collecting geometric features from images and learning them using efficient machine learning methods. Humans solve visual tasks and can give fast response to the environment by extracting perceptual information from what they see. Researchers simulate humans' ability of recognizing objects to solve computer vision problems. For example, M. Mata et al.(2002) applied feature learning techniques to the mobile robot navigation tasks in order to avoid obstacles. They used genetic algorithms for learning features and recognizing objects (figures). Geometric feature learning methods can not only solve recognition problems but also predict subsequent actions by analyzing a set of sequential input sensory images, usually some extracting features of images. Through learning, some hypothesis of the next action are given and according to the probability of each hypothesis give a most probable action. This technique is widely used in the area of artificial intelligence. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Geometric Feature Learning Chapter 2: Pattern Recognition Chapter 3: Hough Transform Chapter 4: Loss Function Chapter 5: Expectation-Maximization Algorithm Chapter 6: Rejection Sampling Chapter 7: Array Processing Chapter 8: Autoencoder Chapter 9: Stochastic Approximation Chapter 10: Chessboard Detection (II) Answering the public top questions about geometric feature learning. (III) Real world examples for the usage of geometric feature learning in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Geometric Feature Learning.

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.

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.

This volume develops an effective theory approach to understanding deep neural networks of practical relevance.

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

"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"--

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Summary Deep Learning with R introduces the world of deep learning using the powerful Keras library and its R language interface. The book builds your understanding of deep learning through intuitive explanations and practical examples. Continue your journey into the world of deep learning with Deep Learning with R in Motion, a practical, hands-on video course available exclusively at Manning.com (www.manning.com/livevideo/deep-​learning-with-r-in-motion). Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Machine learning has made remarkable progress in recent years. Deep-learning systems now enable previously impossible smart applications, revolutionizing image recognition and natural-language processing, and identifying complex patterns in data. The Keras deep-learning library provides data scientists and developers working in R a state-of-the-art toolset for tackling deep-learning tasks. About the Book Deep Learning with R introduces the world of deep learning using the powerful Keras library and its R language interface. Initially written for Python as Deep Learning with Python by Keras creator and Google AI researcher François Chollet and adapted for R by RStudio founder J. J. Allaire, this book builds your understanding of deep learning through intuitive explanations and practical examples. You'll practice your new skills with R-based applications in computer vision, natural-language processing, and generative models. What's Inside Deep learning from first principles Setting up your own deep-learning environment Image classification and generation Deep learning for text and sequences About the Reader You'll need intermediate R programming skills. No previous experience with machine learning or deep learning is assumed. About the Authors François Chollet is a deep-learning researcher at Google and the author of the Keras library. J.J. Allaire is the founder of RStudio and the author of the R interfaces to TensorFlow and Keras. Table of Contents PART 1 - FUNDAMENTALS OF DEEP LEARNING What is deep learning? Before we begin: the mathematical building blocks of neural networks Getting started with neural networks Fundamentals of machine learning PART 2 - DEEP LEARNING IN PRACTICE Deep learning for computer vision Deep learning for text and sequences Advanced deep-learning best practices Generative deep learning Conclusions