arXiv Machine Learning June 5, 2026 By Alexandre L. M. Levada

Efficient Mean Curvature Computation on High-Dimensional Data Manifolds

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arXiv:2606. 06329v1 Announce Type: new Abstract: Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method.

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

arXiv AI

1d ago

Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning

arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.

By Alexandre L. M. Levada

rag benchmarks

arXiv Machine Learning

Jun 30

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization

arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.

By Dhruv Kohli, Sawyer J. Robertson, Gal Mishne, Alexander Cloninger

arXiv Machine Learning

Jun 24

Exact Schur-Sylvester Dimensionality Reductions for Non-Smooth Stochastic Complexity and Manifold Sampling

arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.

By Trenton Lau, Gary P. T. Choi

benchmarks

arXiv Machine Learning

Jun 26

Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity

arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.

By Haitong Liu, Deepak Narayanan Sridharan, David Steurer, Manuel Wiedmer

arXiv Machine Learning

Jun 2

Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation

arXiv:2505. 10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample.

By Alex Saad-Falcon, Brighton Ancelin, Justin Romberg

arXiv Machine Learning

Jun 19

Spectral DPPs via NEPv: A Scalable Continuous Relaxation of Determinantal MAP for Diversity-Aware Data Selection

arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.

By Richard Yi Da Xu

llms rag fine-tuning benchmarks

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Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization

Exact Schur-Sylvester Dimensionality Reductions for Non-Smooth Stochastic Complexity and Manifold Sampling

Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity

Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation

Spectral DPPs via NEPv: A Scalable Continuous Relaxation of Determinantal MAP for Diversity-Aware Data Selection