arXiv Machine Learning
2d ago

How Accurate Is Accurate Enough?

arXiv:2609.38785v1 Announce Type: new Abstract: How accurate must a numerical approximation be within a learning system? Primitive error alone cannot answer this question: errors of the same magnitud...

By Ningkang Peng, Qianfeng Yu, Jingyang Mao, Xiaoqian Peng, Yanhui Gu
arXiv Machine Learning
Sep 4

A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations

arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.

By Ruiyang Hong, Hrad Ghoukasian, Anastasis Kratsios
arXiv Machine Learning
Sep 15

Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels

The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.

By Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
arXiv Machine Learning
Jun 30

Learning from samples: inverse problems over measures

arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon