arXiv:2607. 13943v1 Announce Type: cross Abstract: Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009.
By Yunbum Kook
The paper investigates the mixing time of weighted Dikin walks used for sampling from exponential distributions on polytopes and truncated positive-semidefinite cones. It presents a general total-variation mixing bound under conditions of strong self-concordance, ν-symmetry, and mixed-trace regularity, achieving an “~O(d^2)" bound for polytopes and “~O(d^4)" for truncated PSD cones. A second result introduces a fourth-order bootstrap condition that yields stronger χ^2-divergence guarantees and an improved “~O(d^2)" mixing bound for a scaled Lee–Sidford metric.
By Yuansi Chen, Yunbum Kook
arXiv:2610.15829v2 Announce Type: replace
Abstract: Hard-margin SVM training is the distance problem between two convex hulls, which the Triangle Algorithm (TA) solves with a certified duality gap. W...
By Mayank Gupta
arXiv:2610.27550v1 Announce Type: new
Abstract: Low curvature trace, an effective rank condition, is a common explanation for why randomized zeroth-order methods scale to high-dimensional tasks such...
By Yuxing Peng, Zhiqing Tang, Weijia Jia
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
arXiv:2606. 20082v1 Announce Type: cross Abstract: The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins, Lee and Yang (COLT 2019) to its successors [WY24, CLS+25], all reaching a $(1+\varepsilon)$-approximation in $\Theta(\varepsilon^{-1}\log(n/d))$ iterations.
By Xiaoyu Li, Junwei Yu, Jiaojiao Jiang, Junbin Gao, Andi Han