Tootfinder

Benchmarking Foundation Models with Retrieval-Augmented Generation in Olympic-Level Physics Problem Solving
Shunfeng Zheng, Yudi Zhang, Meng Fang, Zihan Zhang, Zhitan Wu, Mykola Pechenizkiy, Ling Chen
https://arxiv.org/abs/2510.00919

Benchmarking Foundation Models with Retrieval-Augmented Generation in Olympic-Level Physics Problem Solving
Retrieval-augmented generation (RAG) with foundation models has achieved strong performance across diverse tasks, but their capacity for expert-level reasoning-such as solving Olympiad-level physics problems-remains largely unexplored. Inspired by the way students prepare for competitions by reviewing past problems, we investigate the potential of RAG to enhance physics reasoning in foundation models. We introduce PhoPile, a high-quality multimodal dataset specifically designed for Olympiad-lev…

On the complex moment problem as a dynamic inverse problem for a discrete system
A. S. Mikhaylov, V. S. Mikhaylov
https://arxiv.org/abs/2509.02443 https://…

On the complex moment problem as a dynamic inverse problem for a discrete system
We consider the complex moment problem, that is the problem of constructing a positive Borel measure on $\mathbb{C}$ from a given set of moments. We relate this problem to the dynamic inverse problem for the discrete system associated with the complex Jacobi matrix. We show how the characterization of dynamic inverse data in solving the inverse problem provides sufficient conditions for solving the complex moment problem.

Measurement-Guided Consistency Model Sampling for Inverse Problems
Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Sajjad Amini
https://arxiv.org/abs/2510.02208 https://

Measurement-Guided Consistency Model Sampling for Inverse Problems
Diffusion models have become powerful generative priors for solving inverse imaging problems, but their reliance on slow multi-step sampling limits practical deployment. Consistency models address this bottleneck by enabling high-quality generation in a single or only a few steps, yet their direct adaptation to inverse problems is underexplored. In this paper, we present a modified consistency sampling approach tailored for inverse problem reconstruction: the sampler's stochasticity is guided b…

A first-order method for constrained nonconvex--nonconcave minimax problems under a local Kurdyka-{\L}ojasiewicz condition
Zhaosong Lu, Xiangyuan Wang
https://arxiv.org/abs/2510.01168

A first-order method for constrained nonconvex--nonconcave minimax problems under a local Kurdyka-Łojasiewicz condition
We study a class of constrained nonconvex--nonconcave minimax problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax problem satisfies a local Kurdyka-Łojasiewicz (KL) condition, we show that the maximal function of the original problem enjoys a local Hölder smoothness property. We also propose a sequential convex programming (SCP) method for solving constrained optimization problems and establis…

Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
Kunal Vyas, Fengping Jin, Hans De Raedt, Kristel Michielsen
https://arxiv.org/abs/2510.02141

Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum algorithms for solving such many-body problems. The focus of our current work is on the one-dimensional model which is integrable, meaning that there exist analytical results for determining its ground state. In particular, we demonstrate how to perform a gate-ba…

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
Lefu Cai, Zhixin Liu, Minghui Song, Xianchao Wang
https://arxiv.org/abs/2510.00597

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE constraints have been widely used to deal with this problem. However, such approaches typically require repeated iterations and solving the forward problem at each iteration, which leads to a heavy computational cost. To address this issue, we first reformulate …

Syntactic Blind Spots: How Misalignment Leads to LLMs Mathematical Errors
Dane Williamson, Yangfeng Ji, Matthew Dwyer
https://arxiv.org/abs/2510.01831 https://

Syntactic Blind Spots: How Misalignment Leads to LLMs Mathematical Errors
Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities but frequently fail on problems that deviate syntactically from their training distribution. We identify a systematic failure mode, syntactic blind spots, in which models misapply familiar reasoning strategies to problems that are semantically straightforward but phrased in unfamiliar ways. These errors are not due to gaps in mathematical competence, but rather reflect a brittle coupling between surface form …

Optimization by Directional Attacks: Solving Problems with Neural Network Surrogates
Pierre-Yves Bouchet, Thibaut Vidal
https://arxiv.org/abs/2510.01461 https://

Optimization by Directional Attacks: Solving Problems with Neural Network Surrogates
This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize $f(Φ(x))$ subject to $c(Φ(x)) \leq 0$, with $f$ smooth, $c$ general and non-stringent, and $Φ$ an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of dir…

Probing quantum advantage for solving the Fermi-Hubbard model with entropy benchmarking
Pauline Besserve, Ra\'ul Garc\'ia-Patr\'on
https://arxiv.org/abs/2510.00930 h…

Probing quantum advantage for solving the Fermi-Hubbard model with entropy benchmarking
We developed a practical quantum advantage benchmarking framework that connects the accumulation of entropy in a quantum processing unit and the degradation of the solution to a target optimization problem. The benchmark is based on approximating from below the Gibbs states boundary in the energy-entropy space for the application of interest. We believe the proposed benchmarking technique creates a powerful bridge between hardware benchmarking and application benchmarking, while remaining hardw…

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
Xiaokai Chang, Junfeng Yang, Jianchao Bai, Jianxiong Cao
https://arxiv.org/abs/2510.00437

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
The primal-dual splitting algorithm (PDSA) by Chambolle and Pock is efficient for solving structured convex optimization problems. It adopts an extrapolation step and achieves convergence under certain step size condition. Chang and Yang recently proposed a modified PDSA for bilinear saddle point problems, integrating a convex combination step to enable convergence with extended step sizes. In this paper, we focus on composite monotone inclusion problems (CMIPs), a generalization of convex opti…