Optimization And High Dimensional Loss Landscapes In Deep Learning
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Optimization And High Dimensional Loss Landscapes In Deep Learning
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Author : Brett William Larsen
language : en
Publisher:
Release Date : 2022
Optimization And High Dimensional Loss Landscapes In Deep Learning written by Brett William Larsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Despite deep learning's impressive success, many questions remain concerning how training such high-dimensional models behaves in practice and why it reliably produces useful networks. We employ an empirical approach, performing experiments guided by theoretical predictions, to study the following through the lens of the loss landscape. (1) How do loss landscape properties affect the success or failure of weight pruning methods? Recent work on two fronts -- the lottery tickets hypothesis and training restricted to random subspaces -- has demonstrated that deep neural networks can be successfully optimized using far fewer degrees of freedom than the total number of parameters. In particular, lottery tickets, or sparse subnetworks capable of matching the full model's accuracy, can be identified via iterative pruning and retraining of the weights. We first provide a framework for the success of low-dimensional training in terms of the high-dimensional geometry of the loss landscape. We then leverage this framework both to better understand the success of lottery tickets and to predict how aggressively we can prune the weights at each iteration. (2) What are the algorithmic advantages of recurrent connections in neural networks? One of the brain's most striking anatomical features is the ubiquity of lateral and recurrent connections. Yet while the strong computational abilities of feedforward networks have been extensively studied, our understanding of the role of recurrent computations that might explain their prevalence remains an important open challenge. We demonstrate that recurrent connections are efficient for performing tasks that can be solved via repeated, local propagation of information and propose that they can be combined with feedforward architectures for efficient computation across timescales.
Geometric Aspects Of Deep Learning
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Author : Stanislav Fort
language : en
Publisher:
Release Date : 2021
Geometric Aspects Of Deep Learning written by Stanislav Fort 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.
Machine learning using deep neural networks -- deep learning -- has been extremely successful at learning solutions to a very broad suite of difficult problems across a wide range of domains spanning computer vision, game play, natural language processing and understanding, and even fundamental science. Despite this success, we still do not have a detailed, predictive understanding of how deep neural networks work, and what makes them so effective at learning and generalization. In this thesis we study the loss landscapes of deep neural networks using the lens of high-dimensional geometry. We approach the problem of understanding deep neural networks experimentally, similarly to the methods used in the natural sciences. We first discuss a phenomenological approach to modeling the large scale structure of deep neural network loss landscapes using high-dimensional geometry. Using this model, we then continue to investigate the diversity of functions neural networks learn and how it relates to the underlying geometric structure of the solution manifold. We focus on deep ensembles, robustness, and on approximate Bayesian techniques. Finally, we switch gears and investigate the role of nonlinearity in deep learning. We study deep neural networks within the Neural Tangent Kernel framework and empirically establish the role of nonlinearity for the training dynamics of finite-size networks. Using the concept of the nonlinear advantage, we empirically demonstrate the importance of nonlinearity in the very early phases of training, and its waning role farther into optimization.
High Dimensional Optimization And Probability
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Author : Ashkan Nikeghbali
language : en
Publisher: Springer Nature
Release Date : 2022-08-04
High Dimensional Optimization And Probability written by Ashkan Nikeghbali and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-04 with Mathematics categories.
This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Learning And Intelligent Optimization
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Author : Roberto Battiti
language : en
Publisher: Springer
Release Date : 2018-12-31
Learning And Intelligent Optimization written by Roberto Battiti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-31 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 12th International Conference on Learning and Intelligent Optimization, LION 12, held in Kalamata, Greece, in June 2018. The 28 full papers and 12 short papers presented have been carefully reviewed and selected from 62 submissions. The papers explore the advanced research developments in such interconnected fields as mathematical programming, global optimization, machine learning, and artificial intelligence. Special focus is given to advanced ideas, technologies, methods, and applications in optimization and machine learning.
On Optimization And Scalability In Deep Learning
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Author : Kenji Kawaguchi (Ph. D.)
language : en
Publisher:
Release Date : 2020
On Optimization And Scalability In Deep Learning written by Kenji Kawaguchi (Ph. D.) 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.
Deep neural networks have achieved significant empirical success in many fields, including computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. That is, neural networks with one hidden layer can approximate any continuous function, and deeper neural networks can approximate functions of certain classes with fewer parameters. Expressivity theory states that there exist optimal parameter vectors for neural networks of certain sizes to approximate desired target functions. However, the expressivity theory does not ensure that we can find such an optimal vector efficiently during optimization of a neural network. Optimization is one of the key steps in deep learning because learning from data is achieved through optimization, i.e., the process of optimizing the parameters of a deep neural network to make the network consistent with the data. This process typically requires nonconvex optimization, which is not scalable for high-dimensional problems in general. Indeed, in general, optimization of a neural network is not scalable without additional assumptions on its architecture. This thesis studies the non-convex optimization of various architectures of deep neural networks by focusing on some fundamental bottlenecks in the scalability, such as suboptimal local minima and saddle points. In particular, for deep neural networks, we present various guarantees for the values of local minima and critical points, as well as for points found by gradient descent. We prove that mild over-parameterization of practical degrees can ensure that gradient descent will find a global minimum for non-convex optimization of deep neural networks. Furthermore, even without over-parameterization, we show, both theoretically and empirically, that increasing the number of parameters improves the values of critical points and local minima towards the global minimum value. We also prove theoretical guarantees on the values of local minima for residual neural networks. Moreover, this thesis presents a unified theory to analyze the critical points and local minima of various deep neural networks beyond these specific architectures. These results suggest that, whereas there is the issue of scalability in the theoretical worst-case and worst architectures, we can avoid the issue and scale well for large problems with various useful architectures in practice.
Mathematical Aspects Of Deep Learning
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Author : Philipp Grohs
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-31
Mathematical Aspects Of Deep Learning written by Philipp Grohs 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 2022-12-31 with Computers categories.
A mathematical introduction to deep learning, written by a group of leading experts in the field.
High Dimensional Statistical Inference From Coarse And Nonlinear Data
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Author : Haoyu Fu
language : en
Publisher:
Release Date : 2019
High Dimensional Statistical Inference From Coarse And Nonlinear Data written by Haoyu Fu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Machine learning categories.
Moving to the context of machine learning, we study several one-hidden-layer neural network models for nonlinear regression using both cross-entropy and least-squares loss functions. The neural-network-based models have attracted a significant amount of research interest due to the success of deep learning in practical domains such as computer vision and natural language processing. Learning such neural-network-based models often requires solving a non-convex optimization problem. We propose different strategies to characterize the optimization landscape of the non-convex loss functions and provide guarantees on the statistical and computational efficiency of optimizing these loss functions via gradient descent.
An Intuitive Exploration Of Artificial Intelligence
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Author : Simant Dube
language : en
Publisher: Springer Nature
Release Date : 2021-06-21
An Intuitive Exploration Of Artificial Intelligence written by Simant Dube and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Computers categories.
This book develops a conceptual understanding of Artificial Intelligence (AI), Deep Learning and Machine Learning in the truest sense of the word. It is an earnest endeavor to unravel what is happening at the algorithmic level, to grasp how applications are being built and to show the long adventurous road in the future. An Intuitive Exploration of Artificial Intelligence offers insightful details on how AI works and solves problems in computer vision, natural language understanding, speech understanding, reinforcement learning and synthesis of new content. From the classic problem of recognizing cats and dogs, to building autonomous vehicles, to translating text into another language, to automatically converting speech into text and back to speech, to generating neural art, to playing games, and the author's own experience in building solutions in industry, this book is about explaining how exactly the myriad applications of AI flow out of its immense potential. The book is intended to serve as a textbook for graduate and senior-level undergraduate courses in AI. Moreover, since the book provides a strong geometrical intuition about advanced mathematical foundations of AI, practitioners and researchers will equally benefit from the book.
Artificial Neural Networks And Machine Learning Icann 2021
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Author : Igor Farkaš
language : en
Publisher: Springer Nature
Release Date : 2021-09-10
Artificial Neural Networks And Machine Learning Icann 2021 written by Igor Farkaš and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-10 with Computers categories.
The proceedings set LNCS 12891, LNCS 12892, LNCS 12893, LNCS 12894 and LNCS 12895 constitute the proceedings of the 30th International Conference on Artificial Neural Networks, ICANN 2021, held in Bratislava, Slovakia, in September 2021.* The total of 265 full papers presented in these proceedings was carefully reviewed and selected from 496 submissions, and organized in 5 volumes. In this volume, the papers focus on topics such as computer vision and object detection, convolutional neural networks and kernel methods, deep learning and optimization, distributed and continual learning, explainable methods, few-shot learning and generative adversarial networks. *The conference was held online 2021 due to the COVID-19 pandemic.
Deep Learning Concepts And Architectures
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Author : Witold Pedrycz
language : en
Publisher: Springer Nature
Release Date : 2019-10-29
Deep Learning Concepts And Architectures written by Witold Pedrycz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Technology & Engineering categories.
This book introduces readers to the fundamental concepts of deep learning and offers practical insights into how this learning paradigm supports automatic mechanisms of structural knowledge representation. It discusses a number of multilayer architectures giving rise to tangible and functionally meaningful pieces of knowledge, and shows how the structural developments have become essential to the successful delivery of competitive practical solutions to real-world problems. The book also demonstrates how the architectural developments, which arise in the setting of deep learning, support detailed learning and refinements to the system design. Featuring detailed descriptions of the current trends in the design and analysis of deep learning topologies, the book offers practical guidelines and presents competitive solutions to various areas of language modeling, graph representation, and forecasting.