arXiv Statistics ML October 27, 2026 By Yingzhen Yang, Ping Li

Sharp Generalization for Nonparametric Regression in Interpolation Space by Over-Parameterized Neural Networks Trained with Preconditioned Gradient Descent and Early Stopping

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arXiv Machine Learning

Jun 16

Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model

arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?

By Siyu Chen, Beining Wu, Miao Lu, Zhuoran Yang, Tianhao Wang

efficiency

arXiv Machine Learning

Sep 11

Configuration-Dependent Lower Bounds for Approximation by Shallow ReLU$^k$ Networks on the Sphere

arXiv:2510. 04060v3 Announce Type: replace-cross Abstract: We establish two related but logically distinct results for shallow ReLU$^k$ neural networks on the unit sphere $\SS^d$.

By Tong Mao, Jinchao Xu

arXiv Machine Learning

Jun 30

Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model

arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.

By Andrea Montanari, Kangjie Zhou

arXiv Machine Learning

Oct 23

Phase Transition from Random Features to Fully Trainable Networks

arXiv:2610. 31663v1 Announce Type: cross Abstract: Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing.

By Xin He, Huan Lao, Xiliang Lu, Shijun Zhang

arXiv Machine Learning

Jun 3

Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression

arXiv:2606. 03559v1 Announce Type: new Abstract: For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition.

By Yohei Kakimoto, Yuto Omae, Hirotaka Takahashi

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

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Related stories

Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model

Configuration-Dependent Lower Bounds for Approximation by Shallow ReLU$^k$ Networks on the Sphere

Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model

Phase Transition from Random Features to Fully Trainable Networks

Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression

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