Revisiting Landscape Analysis in Deep Neural Networks: Eliminating Decreasing Paths to Infinity

DOI10.1137/19M1299074OpenAlexW4309184205MaRDI QIDQ5051381

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Publication date: 23 November 2022

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.13472

zbMATH Keywords

local minimumdeep neural networklandscapedecreasing paths to infinity

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30)

Uses Software

• ImageNet
• Wirtinger Flow
• AlexNet

Cites Work

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• A geometric analysis of phase retrieval
• Gradient descent optimizes over-parameterized deep ReLU networks
• Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval
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• Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks
• A mean field view of the landscape of two-layer neural networks
• Convergence Results for Neural Networks via Electrodynamics
• Mean Field Analysis of Deep Neural Networks
• Effect of Depth and Width on Local Minima in Deep Learning
• Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization
• Matrix Completion From a Few Entries
• Convergence of a block coordinate descent method for nondifferentiable minimization

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