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Tropical gradient descent. [PDF]
J Glob OptimAbstract We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry—a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics, and computer science.
Talbut R, Monod A.
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Ultrametric fitting by gradient descent * [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2020 Abstract We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function to be optimized.
Giovanni Chierchia, Benjamin Perret
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Competitive Gradient Descent [PDF]
, 2019 Appeared in NeurIPS 2019. This version corrects an error in theorem 2.2. Source code used for the numerical experiments can be found under http://github.com/f-t-s/CGD. A high-level overview of this work can be found under http://f-t-s.github.io/projects/cgd/
Schäfer, Florian, Anandkumar, Anima
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Gradient-Descent-like Ghost Imaging. [PDF]
Sensors (Basel), 2021 Ghost imaging is an indirect optical imaging technique, which retrieves object information by calculating the intensity correlation between reference and bucket signals. However, in existing correlation functions, a high number of measurements is required to acquire a satisfied performance, and the increase in measurement number only leads to limited ...
Yu WK, Zhu CX, Li YX, Wang SF, Cao C.
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We consider SGD-type optimization on infinite-dimensional quadratic problems with power law spectral conditions. It is well-known that on such problems deterministic GD has loss convergence rates $L_t=O(t^{-ζ})$, which can be improved to $L_t=O(t^{-2ζ})$ by using Heavy Ball with a non-stationary Jacobi-based schedule (and the latter rate is optimal ...
Dmitry Yarotsky
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Note on the Equivalence of Orthogonalizing EM and Proximal Gradient Descent. [PDF]
TechnometricsYang J, Hastie T.
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Blind Descent: A Prequel to Gradient Descent [PDF]
, 2021 We describe an alternative learning method for neural networks, which we call Blind Descent. By design, Blind Descent does not face problems like exploding or vanishing gradients. In Blind Descent, gradients are not used to guide the learning process.
Gupta, Akshat, R, Prasad N
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Laplacian smoothing gradient descent
Research in the Mathematical Sciences, 2022 28 pages, 15 ...
Osher, Stanley +6 more
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Analysis of Natural Gradient Descent for Multilayer Neural Networks [PDF]
, 1999 Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent.
Rattray, Magnus, Saad, David
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Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent [PDF]
, 2016 First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields ...
Allen-Zhu, Zeyuan, Orecchia, Lorenzo
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