Tootfinder

Asymmetric Perturbation in Solving Bilinear Saddle-Point Optimization
Kenshi Abe, Mitsuki Sakamoto, Kaito Ariu, Atsushi Iwasaki
https://arxiv.org/abs/2506.05747

Asymmetric Perturbation in Solving Bilinear Saddle-Point Optimization
This paper proposes an asymmetric perturbation technique for solving saddle-point optimization problems, commonly arising in min-max problems, game theory, and constrained optimization. Perturbing payoffs or values are known to be effective in stabilizing learning dynamics and finding an exact solution or equilibrium. However, it requires careful adjustment of the perturbation magnitude; otherwise, learning dynamics converge to only an equilibrium. We establish an impossibility result that it a…

A critical majorant for the Khinchin-Ostrowski property
Bartosz Malman
https://arxiv.org/abs/2506.06911 https://arxiv.org/pdf/2506.06…

A critical majorant for the Khinchin-Ostrowski property
In this short note we prove an optimal version of a classical result. Given a majorant determining a growth restriction on functions in the unit disk $\mathbb{D}$, we say that a set $E$ on the unit circle $\mathbb{T}$ is a uniqueness set, or has the Khinchin-Ostrowski property, with respect to the majorant, if any sequence of analytic polynomials satisfying the growth restriction which converges in an appropriate sense to $0$ on $E$, in fact is forced to converge to $0$ in $\mathbb{D}$ also. Th…

This https://arxiv.org/abs/2502.18284 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Nested Expectations with Kernel Quadrature
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then dem…

Minimizing the Gauss map area of surfaces in $\mathbb{S}^3$
Gerard Orriols, Tristan Rivi\`ere
https://arxiv.org/abs/2506.05141 https://

Minimizing the Gauss map area of surfaces in $\mathbb{S}^3$
We establish the lower bound of $4π(1+g)$ for the area of the Gauss map of any immersion of a closed oriented surface of genus $g$ into $\mathbb{S}^3$, taking values in the Grassmannian of $2$-planes in $\mathbb{R}^4$. This lower bound is proved to be optimal for any genus $g \in \mathbb{N}$ but attained only when $g = 0$. For $g \neq 0$ we describe the behavior of any minimizing sequence of embeddings: we prove that, modulo extraction of a subsequence, the surfaces converge in the Hausdorff d…

Global well-posedness for the ILW equation in $H^s(\mathbb{T})$ for $s>-\frac12$
Louise Gassot, Thierry Laurens
https://arxiv.org/abs/2506.05149 https:/…

Global well-posedness for the ILW equation in $H^s(\mathbb{T})$ for $s>-\frac12$
We prove that the intermediate long wave (ILW) equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{T})$ for $s > -\frac12$. The previous record for well-posedness was $s\geq 0$, and the system is known to be ill-posed for $s<-\frac12$. We then demonstrate that the solutions of ILW converge to those of the Benjamin--Ono equation in $H^s(\mathbb{T})$ in the infinite-depth limit. Our methods do not rely on the complete integrability of ILW, but rather treat ILW as a perturbation o…

This https://arxiv.org/abs/2504.07552 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Uniqueness of supercritical Gaussian multiplicative chaos
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends on the choice of regularisation only through a multiplicative constant and can be characterised as an integrated atomic measure with a random intensity expressed in terms of the critical Gaussian multiplicative chaos.

From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications
Yang Cai, Haipeng Luo, Chen-Yu Wei, Weiqiang Zheng
https://arxiv.org/abs/2506.03464

From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications
The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects the actual decisions made by the learners and captures the day-to-day behavior of the learning dynamics. While many algorithms are known to converge in the average-iterate, achieving last-iterate convergence typically requires considerably more effort in both …

Ensemble-MIX: Enhancing Sample Efficiency in Multi-Agent RL Using Ensemble Methods
Tom Danino, Nahum Shimkin
https://arxiv.org/abs/2506.02841 https://

Ensemble-MIX: Enhancing Sample Efficiency in Multi-Agent RL Using Ensemble Methods
Multi-agent reinforcement learning (MARL) methods have achieved state-of-the-art results on a range of multi-agent tasks. Yet, MARL algorithms typically require significantly more environment interactions than their single-agent counterparts to converge, a problem exacerbated by the difficulty in exploring over a large joint action space and the high variance intrinsic to MARL environments. To tackle these issues, we propose a novel algorithm that combines a decomposed centralized critic with d…

This https://arxiv.org/abs/2406.04655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Bayesian Inference for Spatial-Temporal Non-Gaussian Data Using Predictive Stacking
Analysing non-Gaussian spatial-temporal data requires introducing spatial dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference is considerably encumbered by the inability to analytically integrate out the random effects and reduce the dimension of the parameter space. Iterative estimation algorithms struggle to converge due to the presence of weakly identified parameters. We devise Bayesian inference u…

This https://arxiv.org/abs/2503.13193 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The deep multi-FBSDE method: a robust deep learning method for coupled FBSDEs
We introduce the deep multi-FBSDE method for robust approximation of coupled forward-backward stochastic differential equations (FBSDEs), focusing on cases where the deep BSDE method of Han, Jentzen, and E (2018) fails to converge. To overcome the convergence issues, we consider a family of FBSDEs that are equivalent to the original problem in the sense that they satisfy the same associated partial differential equation (PDE). Our algorithm proceeds in two phases: first, we approximate the init…

Wired Scape, a new public park in Guangzhou, China, by design firm 100architects Via https://www.thisiscolossal.com/2025/04/100architects-wired-scape/

Land, Sea, and Wiry Trees Converge in 100architects' Imaginative New Playground
A new public park in Guangzhou re-envisions the possibilities of play.

Proportional Response Dynamics in Gross Substitutes Markets
Yun Kuen Cheung, Richard Cole, Yixin Tao
https://arxiv.org/abs/2506.02852 https://

Proportional Response Dynamics in Gross Substitutes Markets
Proportional response is a well-established distributed algorithm which has been shown to converge to competitive equilibria in both Fisher and Arrow-Debreu markets, for various sub-families of homogeneous utilities, including linear and constant elasticity of substitution utilities. We propose a natural generalization of proportional response for gross substitutes utilities, and prove that it converges to competitive equilibria in Fisher markets. This is the first convergence result of a propo…

I'm not shocked that Musk would try to manipulate Grok to vent his opinions. We've seen his manipulation before in the twitter recommender system.
I am kind of fascinated by how difficult it is. I think that broadly trained LLMs tend to converge to the same "worldview", which is mostly left-libertarian.
You can't really force them away from this on one issue without introducing inconsistencies, and breaking the guardrails.

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
Vinay Sharma, Sergei I Chernyshenko
https://arxiv.org/abs/2505.23430

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
With an increasing interest in the design of long and complex space missions, the search for orbits that require the least amount of fuel is of fundamental interest. This paper develops existing computational models for locating Unstable Periodic Orbits (UPOs) in polynomial dynamical systems using Sum-of-Squares (SOS) optimization technique and proposes a numerical framework to converge UPOs for the Planar Circular Restricted Three-Body Problem (PCR3BP) in astrodynamics. This is done by develop…

Particle approximation of nonlocal interaction energies
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
https://arxiv.org/abs/2506.02905 https://

Particle approximation of nonlocal interaction energies
We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies $Γ$-converge in the weak-$*$ topology to the Riesz functional defined over the space of probability measures. We also address the minimization problem for the discretized energies, and prove the existence of minimal configurations of particles in a very general and natural setting.

On the shape of the typical Poisson-Voronoi cell in high dimensions
Matthias Irlbeck, Zakhar Kabluchko, Tobias M\"uller
https://arxiv.org/abs/2506.02607

On the shape of the typical Poisson-Voronoi cell in high dimensions
We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$-th root of the intensity parameter $λ$ of the Poisson process times the volume of the unit ball, the inradius, outradius, diameter and mean width of the typical cell converge in probability to the constants $1/2, 1, 2, 2$ respectively, as the dimension $d\to\infty$. We also show that the width of the typical cell, when rescaled in the same way, is bounded between $2\sqrt{5}/(2+\sqrt{5})-o_d(1)$ …

Incremental Gain Computation and Regulation of Discrete-time Positive Lur\'e Systems using Linear Programming
Jared Miller
https://arxiv.org/abs/2505.24386

Incremental Gain Computation and Regulation of Discrete-time Positive Luré Systems using Linear Programming
This work approaches the problem of computing incremental $\ell_1$ and $\ell_\infty$ gains for discrete-time positive systems in \lure feedback with static memoryless nonlinearities, and regulating the $\ell_\infty$ gain through the design of a state-feedback controller. Finite incremental gains provide a quantitative measure of robustness for trajectories, and will ensure that all pairs of trajectories will converge to a fixed point or will diverge together in the absence of an applied input. …

Stabilization of the Gradient Method for Solving Linear Algebraic Systems - A Method Related to the Normal Equation
Ibrahima Dione
https://arxiv.org/abs/2506.00702

Stabilization of the Gradient Method for Solving Linear Algebraic Systems - A Method Related to the Normal Equation
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of the stepsize defining the new iteration. We propose here a simple and robust stabilization of the gradient method, which no longer assumes a structure on the matrix (neither symmetric, nor positive definite) to converge, and which no longer requires an approac…

This https://arxiv.org/abs/2501.11106 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$L^{1}_{loc}$-convergence of Jacobians of Sobolev homeomorphisms via area formula
We prove that given a sequence of homeomorphisms $f_k: Ω\to \mathbb{R}^n$ convergent in $W^{1,p}(Ω, \mathbb{R}^n)$, $p \geq 1$ for $n =2$ and $p > n-1$ for $n \geq 3$, to a homeomorphism $f$ which maps sets of measure zero onto sets of measure zero, Jacobians $Jf_k$ converge to $Jf$ in $L^1_{loc}(Ω)$. We prove it via Federer's area formula and investigation of when $|f_k(E)| \to |f(E)|$ as $k \to \infty$ for Borel subsets $E \Subset Ω$.

This https://arxiv.org/abs/2408.05197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal eigenfunction and show that the corresponding Rayleigh quotients converge to the principal eigenvalue. We also propose a related iterative method for an eigenvalue problem arising from a model for optimal insulation and provide some partial results.

Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations
Marco Menale, Giuseppe Toscani
https://arxiv.org/abs/2505.15526 https://

Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations
We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors. The macroscopic dynamics of their mean values follow a Lotka-Volterra system of ordinary differential equations. Unlike classical models of wealth and opinion formation, which tend to converge toward a steady-state profile, the oscillatory behavior of these …