arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
By Xiaoyang Chen, Xiang Jiang
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
arXiv:2606. 08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term.
By Ayub Kharel, Ilja Kuzborski, Patrick Rebeschini, Yasin Abbasi-Yadkori
arXiv:2606. 01596v1 Announce Type: cross Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics.
By Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
arXiv:2209. 15130v3 Announce Type: replace-cross Abstract: We study a general matrix optimization problem with a fixed-rank positive semidefinite (PSD) constraint.
By Yuetian Luo, Nicolas Garcia Trillos
arXiv:2606. 15442v1 Announce Type: cross Abstract: We design a new unconstrained coordinate system where a $p\times p$ symmetric positive definite (SPD) matrix $\Theta$ is represented by a reverse telescoping map $\Theta(x)=\rm{RT}(x)$, with $x=(v,d,r)\in\mathbb{R}\times\mathbb{R}^{(p-1)}\times\mathbb{R}^{p(p-1)/2}$, representing respectively the log volume or log determinant; and the shape, as encoded by log relative diagonal scales and partial covariances among the nodes.
By Anindya Bhadra