arXiv:2608. 09870v1 Announce Type: cross Abstract: Uniform stability is a classical tool for controlling the generalization error of a learning algorithm.
By Thanh Nguyen-Cung, Binh T. Nguyen
arXiv:2607. 10808v1 Announce Type: new Abstract: The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed.
By Haricharan Balasundaram, Karthick Krishna Mahendran, Rahul Vaze
arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.
By Reza Ghane, Danil Akhtiamov, Babak Hassibi
arXiv:2608. 03368v1 Announce Type: new Abstract: For $n$ unit vectors $x_1,\ldots,x_n \in \mathbb{R}^d$, we study the continuous ReLU derivative Gram matrix $H$, whose entries are obtained by averaging pairwise gated inner products over a standard Gaussian direction.
By Zhao Song
arXiv:2606. 15581v1 Announce Type: cross Abstract: We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+\sigma^2}$.
By Laurent Massouli\'e, Sushil Mahavir Varma, Louis Vassaux, Ir\`ene Waldspurger
arXiv:2608. 06687v1 Announce Type: cross Abstract: We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations $\mathfrak L_\beta u=f$ using linearized ReLU$^k$ neural networks on the sphere, where $\mathfrak L_\beta$ is a positive elliptic spectral multiplier of order $\beta$.
By Xinliang Liu, Tong Mao, Jinchao Xu