arXiv Machine Learning By John Chiang

Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients

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arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.

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arXiv Machine Learning
Jul 7

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).

By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
arXiv Machine Learning
Jun 16

Functional Gradient Descent with Adaptive Representations

arXiv:2606. 16926v1 Announce Type: cross Abstract: Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis.

By Daniel Csillag, Rodrigo Schuller, Pedro Dall'Antonia, Leonidas Guibas, Luiz Velho, Tiago Novello