arXiv:2608. 25273v1 Announce Type: cross Abstract: We analyze exact-metric, Metropolis-adjusted Dikin walks by keeping the proposal determinant and reverse quadratic form together.
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.
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.
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...
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...
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.
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.
arXiv:2608. 06762v1 Announce Type: new Abstract: Bisimulation metrics quantify behavioral similarity in Markov decision processes, but their Wasserstein fixed-point operator updates every state pair and incurs quadratic pairwise work.
In low-rank matrix sensing of a rank-$D$ factor $U^\ast \in \mathbb{R}^{V \times D}$, replacing isotropic Gaussian designs with power-law measurement covariance $Σ= \mathrm{diag}(j^{-s})_{j=1}^V$ leaves the Burer--Monteiro landscape free of spurious local minima, yet division-normalised first-order optimizers stall above a critical exponent $s^\ast$. We trace this failure to a numerical precision wall.
arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called \emph{smoothed Picard Hamiltonian Monte Carlo}, which combines Gaussian smoothing, Picard iteration, an...
Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories.
arXiv:2605.06866v3 Announce Type: replace Abstract: We study finite-iteration behavior of asynchronous categorical distributional temporal-difference methods, covering scalar categorical TD (CTD) in...
arXiv:2608.25279v1 Announce Type: cross Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...