arXiv Machine Learning July 28, 2026 By George A Kevrekidis

When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization

Read the original on arXiv Machine Learning →

arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

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arXiv Machine Learning

Jul 14

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response

arXiv:2607. 07204v2 Announce Type: replace-cross Abstract: Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to reach a useful metric.

By Zavier Li

arXiv Machine Learning

Jul 16

Beyond the $d^{2.5}$-mixing bound for Dikin walks on polytopes

arXiv:2607. 13943v1 Announce Type: cross Abstract: Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009.

By Yunbum Kook

arXiv Machine Learning

Jul 7

A Near-Linear-Time Solver for Graph $p$-Laplacian Semi-Supervised Learning via Continuation in $p$

arXiv:2607. 03503v1 Announce Type: new Abstract: Graph-based semi-supervised learning (SSL) propagates a few labels over a similarity graph by minimizing a Dirichlet-type energy.

By Oren E. Livne

arXiv Machine Learning

Jul 10

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization

arXiv:2605. 23391v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens.

By Youngjae Park, Jaemin Kim, Junghwa Hong

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arXiv Machine Learning

Jun 4

Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent

arXiv:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.

By Ahanaf Hasan Ariq

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arXiv Machine Learning

Jul 9

Optimization Geometrodynamics: A Framework for Dynamic Geometric Optimization

arXiv:2607. 06723v1 Announce Type: cross Abstract: Most gradient-based optimization methods move parameters through a fixed background geometry, even when their internal states implicitly define changing notions of length, curvature, and preconditioning.

By Zavier Li

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Related stories

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response

Beyond the $d^{2.5}$-mixing bound for Dikin walks on polytopes

A Near-Linear-Time Solver for Graph $p$-Laplacian Semi-Supervised Learning via Continuation in $p$

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization

Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent

Optimization Geometrodynamics: A Framework for Dynamic Geometric Optimization