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Gradient Descent Theory Extended for Complex Minima and Vector Outputs

By PulseAugur Editorial · [2 sources] ·

This paper extends the theory of gradient descent (GD) with large step sizes to more complex scenarios. It addresses overparameterized least-squares problems with vector-valued outputs and analyzes neighborhoods of manifolds of flat minima, which are crucial for applications like matrix factorization. The research generalizes existing normal forms and convergence theorems, introducing a novel method to solve a singular partial differential equation. AI

IMPACT Advances theoretical understanding of optimization algorithms crucial for training complex AI models.

RANK_REASON The cluster contains an academic paper detailing theoretical advancements in gradient descent.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Gradient Descent Theory Extended for Complex Minima and Vector Outputs

COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Lachlan Ewen MacDonald, Ren\'e Vidal ·

    Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

    arXiv:2607.08380v1 Announce Type: new Abstract: An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian. Classical analyses typically require the step size to be uniformly smaller than twice …

  2. arXiv cs.LG TIER_1 English(EN) · René Vidal ·

    Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

    An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian. Classical analyses typically require the step size to be uniformly smaller than twice the reciprocal of the sharpness, but this condit…

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