Tootfinder

Contraction and entropy production in continuous-time Sinkhorn dynamics
Anand Srinivasan, Jean-Jacques Slotine
https://arxiv.org/abs/2510.12639 https://arx…

Contraction and entropy production in continuous-time Sinkhorn dynamics
Recently, the vanishing-step-size limit of the Sinkhorn algorithm at finite regularization parameter $\varepsilon$ was shown to be a mirror descent in the space of probability measures. We give $L^2$ contraction criteria in two time-dependent metrics induced by the mirror Hessian, which reduce to the coercivity of certain conditional expectation operators. We then give an exact identity for the entropy production rate of the Sinkhorn flow, which was previously known only to be nonpositive. Exam…

Physics-informed learning under mixing: How physical knowledge speeds up learning
Anna Scampicchio, Leonardo F. Toso, Rahel Rickenbach, James Anderson, Melanie N. Zeilinger
https://arxiv.org/abs/2509.24801

Physics-informed learning under mixing: How physical knowledge speeds up learning
A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one w…

Event-Driven Control via Sparsity-Promoting Regularization: A Rollout Approach with Performance Guarantees
Shumpei Nishida, Kunihisa Okano
https://arxiv.org/abs/2509.24799 https…

Event-Driven Control via Sparsity-Promoting Regularization: A Rollout Approach with Performance Guarantees
This paper presents a controller design method aiming to balance control performance and actuation frequency. In this framework, actuation timings are determined in an event-driven manner, resulting in intermittent control actions. Control performance is measured by an infinite-horizon average cost, and input sparsity is promoted through actuation-rate regularization. Since the formulated optimal control problem has a combinatorial nature, we employ a rollout algorithm to find a suboptimal solu…

General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems
Jiaping Yang, Yunxin Zhang
https://arxiv.org/abs/2510.02489 https://

General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of dimensionality, which prevents its application in high-dimensional spaces. While entropic regularization has been proven to effectively mitigate the curse of dimensionality and achieve a parametric convergence rate under mild conditions, these statistical gua…

Generalization Analysis for Classification on Korobov Space
Yuqing Liu
https://arxiv.org/abs/2509.22748 https://arxiv.org/pdf/2509.22748

Generalization Analysis for Classification on Korobov Space
In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex $η$-norm loss function $ϕ(v)=(1 - v)_{+}^η$, $η\geq1$. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of $L_p$ approximation of functions from Korobov space $X^{2, p}([-1,1]^{d})$, $1\leq p \leq \infty$, by the s…