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Researchers propose novel second-order method for Stiefel manifold optimization

By PulseAugur Editorial · Summary by gemini-2.5-flash-lite from 3 sources

Researchers have developed a novel second-order optimization method for the Stiefel manifold that avoids retractions, offering improved efficiency for high-accuracy requirements. This method combines a tangent component to reduce the objective function and a normal component, constructed using the Newton-Schulz iteration for orthogonalization, to decrease infeasibility. Numerical experiments demonstrated superior performance compared to existing methods on problems like orthogonal Procrustes and principal component analysis. AI

Summary written by gemini-2.5-flash-lite from 3 sources. How we write summaries →

IMPACT Introduces a more efficient optimization technique for problems involving orthogonal matrices, potentially benefiting machine learning algorithms that rely on such structures.

RANK_REASON This is a research paper detailing a new mathematical optimization method.

Read on arXiv cs.LG →

COVERAGE [3]

  1. arXiv cs.LG TIER_1 · Xinhui Xiong, Bin Gao, P. -A. Absil ·

    A second-order method on the Stiefel manifold via Newton$\unicode{x2013}$Schulz

    arXiv:2605.02838v1 Announce Type: cross Abstract: Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we prop…

  2. arXiv cs.AI TIER_1 · P. -A. Absil ·

    A second-order method on the Stiefel manifold via Newton$\unicode{x2013}$Schulz

    Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a second-order method landing on the Stiefel m…

  3. Hugging Face Daily Papers TIER_1 ·

    A second-order method on the Stiefel manifold via Newton$\unicode{x2013}$Schulz

    Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a second-order method landing on the Stiefel m…

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