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Geometric Aspects of Deep Learning.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric Aspects of Deep Learning./
Author:	Fort, Stanislav.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	106 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-09, Section: B.
Contained By:	Dissertations Abstracts International83-09B.
Subject:	Deep learning. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29003878
ISBN:	9798209789888

Geometric Aspects of Deep Learning.
Fort, Stanislav.

Geometric Aspects of Deep Learning. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 106 p.

Source: Dissertations Abstracts International, Volume: 83-09, Section: B.

Thesis (Ph.D.)--Stanford University, 2021.

This item must not be sold to any third party vendors.

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.

ISBN: 9798209789888Subjects--Topical Terms:

3554982
Deep learning.

Geometric Aspects of Deep Learning.
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500 $a Source: Dissertations Abstracts International, Volume: 83-09, Section: B.
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502 $a Thesis (Ph.D.)--Stanford University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a 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.
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