Tootfinder

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 …

Self-ensemble: Mitigating Confidence Distortion for Large Language Models
Zicheng Xu, Guanchu Wang, Guangyao Zheng, Yu-Neng Chuang, Alexander Szalay, Xia Hu, Vladimir Braverman
https://arxiv.org/abs/2506.01951

Self-ensemble: Mitigating Confidence Distortion for Large Language Models
Although Large Language Models (LLMs) perform well in general fields, they exhibit a confidence distortion problem on multi-choice question-answering (MCQA), particularly as the number of answer choices increases. Specifically, on MCQA with many choices, LLMs suffer from under-confidence in correct predictions and over-confidence in incorrect ones, leading to a substantially degraded performance. To solve this problem, we propose Self-ensemble in this work. Our method splits the choices into se…

Spherically Symmetric Accretion with Self-Gravity: Analytical Formulae and Numerical Validation
Cheng-Liang Jiao, Er-gang Zhao, Liying Zhu, Xiang-dong Shi
https://arxiv.org/abs/2507.02621

Spherically Symmetric Accretion with Self-Gravity: Analytical Formulae and Numerical Validation
Spherically symmetric accretion incorporating self-gravity constitutes a three-point boundary value problem (TPBVP) governed by constraints at the outer boundary, sonic point, and accretor surface. Previous studies have two limitations: either employing an incorrect formula for self-gravity potential in analytical treatments, or introducing additional input parameters in numerical implementations to circumvent solving the full TPBVP. To address these issues, we present a self-consistent TPBVP f…

This https://arxiv.org/abs/2406.15909 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fibred surfaces and their unitary rank
Let $f\colon S\to B$ a complex fibred surface with fibres of genus $g\geq 2$. Let $u_f$ be its unitary rank, i.e., the rank of the maximal unitary summand of the Hodge bundle $f_*ω_f$. We prove many new slope inequalities involving $u_f$ and some other invariants of the fibration. As applications: (1) we prove a new Xiao-type bound on $u_f$ with respect to $g$ for non-isotrivial fibrations: \[ u_f< g\frac{5g-2}{6g-3}. \] In particular this implies that if $f$ is not locally trivial and $u_f=…

Topology induced modifications in the critical behavior of the Yaldram Khan catalytic reaction model
Paulo F. Gomes, Henrique A. Fernandes, Roberto da Silva
https://arxiv.org/abs/2506.04485

Topology induced modifications in the critical behavior of the Yaldram Khan catalytic reaction model
In this work, we investigated how the use of complex networks as catalytic surfaces can affect the phase diagram of the Yaldram-Khan model, as well as how the order of the phase transitions present in the seminal work behaves when the randomness is added to the model. The study was conducted by taking into consideration two well-known random networks, the Erdos-Renyi network (ERN), with its long-range randomness, and the random geometric graph (RGG), with its spatially constrained randomness. W…

Operator-Theoretic Methods for Differential Games
Craig Bakker, Adam T. Rupe, Alexander Von Moll, Adam R. Gerlach
https://arxiv.org/abs/2507.02203 https://…

Operator-Theoretic Methods for Differential Games
Differential game theory offers an approach for modeling interactions between two or more agents that occur in continuous time. The goal of each agent is to optimize its objective cost functional. In this paper, we present two different methods, based on the Koopman Operator (KO), to solve a zero-sum differential game. The first approach uses the resolvent of the KO to calculate a continuous-time global feedback solution over the entire domain. The second approach uses a discrete-time, data-dri…

Self-correcting Reward Shaping via Language Models for Reinforcement Learning Agents in Games
Ant\'onio Afonso, Iolanda Leite, Alessandro Sestini, Florian Fuchs, Konrad Tollmar, Linus Gissl\'en
https://arxiv.org/abs/2506.23626

Self-correcting Reward Shaping via Language Models for Reinforcement Learning Agents in Games
Reinforcement Learning (RL) in games has gained significant momentum in recent years, enabling the creation of different agent behaviors that can transform a player's gaming experience. However, deploying RL agents in production environments presents two key challenges: (1) designing an effective reward function typically requires an RL expert, and (2) when a game's content or mechanics are modified, previously tuned reward weights may no longer be optimal. Towards the latter challenge, we prop…

Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games
Heidi Wolles Lj\'osheim, Dante Kalise, John W. Pearson, Francisco J. Silva
https://arxiv.org/abs/2507.01958

Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference discretization and solve the resulting finite-dimensional optimization problem using the Chambolle--Pock primal--dual algorithm. As this involves computing proximal operators and solving ill-conditioned linear systems at each iteration, we propose a general class of par…

This https://arxiv.org/abs/2409.05547 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Critical Dynamics of Random Surfaces: Time Evolution of Area and Genus
Conformal field theories with central charge $c\le1$ on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the conjecture that these models describe the time evolution of certain social networks that are self-driven to a critical point. This paper focuses on the dynamics of the overall area and the genus of the surface. The time evolution of the area is shown to follow …

Evaluation of LLMs for mathematical problem solving
Ruonan Wang, Runxi Wang, Yunwen Shen, Chengfeng Wu, Qinglin Zhou, Rohitash Chandra
https://arxiv.org/abs/2506.00309

Evaluation of LLMs for mathematical problem solving
Large Language Models (LLMs) have shown impressive performance on a range of educational tasks, but are still understudied for their potential to solve mathematical problems. In this study, we compare three prominent LLMs, including GPT-4o, DeepSeek-V3, and Gemini-2.0, on three mathematics datasets of varying complexities (GSM8K, MATH500, and UNSW datasets). We take a five-dimensional approach based on the Structured Chain-of-Thought (SCoT) framework to assess final answer correctness, step com…