arXiv subjects

Mateusz Topolewski

Publications and source records attributed to Mateusz Topolewski.

5 recordsLinked to original sources

arXiv2026

Putnam-like dataset summary: LLMs as mathematical competition contestants

In this paper we summarize the results of the Putnam-like benchmark published by Google DeepMind. This dataset consists of 96 original problems in the spirit of the Putnam Competition and 576 solutions generated by LLMs. We analyze the performance of models on this set of problems to verify their ability to solve problems from mathematical contests. We find that top models, particularly Gemini 2.5 Pro, achieve high scores, demonstrating strong mathematical reasoning capabilities, although their performance was lower on problems from the 2024 Putnam competition. The analysis highlights distinct behavioral patterns among models, including bimodal scoring distributions and challenges in providing fully rigorous justifications.

cs.LG↗

arXiv2021

Long-term series forecasting with Query Selector -- efficient model of sparse attention

Various modifications of TRANSFORMER were recently used to solve time-series forecasting problem. We propose Query Selector - an efficient, deterministic algorithm for sparse attention matrix. Experiments show it achieves state-of-the art results on ETT, Helpdesk and BPI'12 datasets.

cs.LG↗

arXiv2018

Reflected BSDEs with general filtration and two completely separated barriers

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we assume that there are càdlàg processes of class D that are completely separated. We prove the existence and uniqueness of solutions for integrable final condition and integrable monotone generator. An application to zero-sum Dynkin game is given.

math.PR↗

arXiv2018

Systems of BSDEs with oblique reflection and related optimal switching problems

We consider systems of backward stochastic differential equations with càdlàg upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces with a filtration satisfying merely the usual assumptions of right continuity and completeness. We assume that the pair $(H(U),U)$ satisfies a Mokobodzki--type condition. We prove the existence of a solution for integrable terminal conditions and integrable quasi--monotone generators. Applications to the optimal switching problem are given.

math.PR↗

arXiv2015

Cadlag Skorokhod problem driven by a maximal monotone operator

The article deals with existence and uniqueness of the solution of the following differential equation (a càdlàg Skorokhod problem) driven by a maximal monotone operator and with singular input generated by the càdlàg function $m$: \[ \left\{ \begin{array} [c]{l} dx_{t}+A\left( x_{t}\right) \left( dt\right) +dk_{t}^{d}\ni dm_{t} \,,~t\geq0,\\ x_{0}=m_{0}, \end{array} \right. \] where $k^{d}$ is a pure jump function. The jumps outside of the constrained domain $\overline{\mathrm{D}(A)}$ are counteracted through the generalized projection $Π$, by taking $x_{t}=Π(x_{t-}+Δm_{t})$, whenever $x_{t-}+Δm_{t}\notin\overline {\mathrm{D}(A)}\,$. Approximations of the solution based on discretization and Yosida penalization are considered.

math.DS↗