Jethro Warnett

Publications

Most recent first. Abstracts are taken from the published version or from arXiv.

Published and accepted

1. 2026

   Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games

   Hui Huang, Jethro Warnett

   Communications on Pure and Applied Analysis, vol. 31, pp. 146–165, 2026.

   Abstract of Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games

   Recently, an earlier paper introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This paper aims to address theoretical gaps in that work, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.

   doi:10.3934/cpaa.2025101 arXiv:2505.13632 PDF of arXiv:2505.13632
2. 2023

   Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization

   Martin Heistermann, Jethro Warnett, David Bommes

   ACM Transactions on Graphics, vol. 42, no. 4, article 70, July 2023. Presented at SIGGRAPH 2023.

   Nominated for Best Paper, SIGGRAPH 2023

   Abstract of Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization

   Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.

   doi:10.1145/3592437 ACM Digital Library

Preprints

1. 2026

   Stein Variational Gradient Descent dynamics for highly concentrated kernels

   José A. Carrillo, Jakub Skrzeczkowski, Jethro Warnett

   arXiv:2605.03627 [math.AP], submitted 5 May 2026.

   Abstract of Stein Variational Gradient Descent dynamics for highly concentrated kernels

   Stein Variational Gradient Descent (SVGD) is a widely used in practice algorithm for scalable sampling with deterministic particle updates. We study its behavior in the singular limit where the kernel bandwidth tends to zero. In this regime, we show that the nonlocal SVGD dynamics converge to a local evolution equation that can be formally interpreted as a Wasserstein gradient flow with quadratic mobility. We analyze this singular limit in two settings: integrable kernels and weighted kernels. In the weighted case, the proof is supported by recently established Stein-log-Sobolev inequalities, which provide the necessary functional control. Overall, our results clarify how SVGD collapses from a nonlocal interacting particle system to a local gradient-flow dynamics as the kernel concentrates.

   arXiv:2605.03627 PDF of arXiv:2605.03627
2. 2026

   Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems

   Hui Huang, Jethro Warnett

   arXiv:2602.12886 [math.OC], submitted 13 February 2026.

   Abstract of Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems

   The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.

   arXiv:2602.12886 PDF of arXiv:2602.12886
3. 2024

   The Stein-log-Sobolev inequality and the exponential rate of convergence for the continuous Stein variational gradient descent method

   José A. Carrillo, Jakub Skrzeczkowski, Jethro Warnett

   arXiv:2412.10295 [math.AP], submitted 13 December 2024.

   Abstract of The Stein-log-Sobolev inequality and the exponential rate of convergence for the continuous Stein variational gradient descent method

   The Stein Variational Gradient Descent method is a variational inference method in statistics that has recently received a lot of attention. The method provides a deterministic approximation of the target distribution, by introducing a nonlocal interaction with a kernel. Despite the significant interest, the exponential rate of convergence for the continuous method has remained an open problem, due to the difficulty of establishing the related so-called Stein-log-Sobolev inequality. Here, we prove that the inequality is satisfied for each space dimension and every kernel whose Fourier transform has a quadratic decay at infinity and is locally bounded away from zero and infinity. Moreover, we construct weak solutions to the related PDE satisfying exponential rate of decay towards the equilibrium. The main novelty in our approach is to interpret the Stein-Fisher information, also called the squared Stein discrepancy, as a duality pairing between H⁻¹(ℝ^d) and H¹(ℝ^d), which allows us to employ the Fourier transform. We also provide several examples of kernels for which the Stein-log-Sobolev inequality fails, partially showing the necessity of our assumptions.

   arXiv:2412.10295 PDF of arXiv:2412.10295