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Our work on how LLMs store relations selected as NeurIPS Spotlight paper
Our paper The Structure of Relation Decoding Linear Operators in Large Language Models by Miranda Anna Christ, Adrián Csiszárik, Gergely Becsó, and Dániel Varga was accepted at the NeurIPS 2025 conference as a Spotlight paper (~3% of submissions).
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Patient Pathway Mission
Leveraging Hungary’s healthcare data assets for prevention, prediction, and decision support.
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Dániel Varga

Solving a Conjecture of Erdős

Blog Post
October 6, 2023
posts
Sets of points with the property that no two elements of the set are one unit distance apart are called unit-distance avoiding sets. If a point is in the unit-distance avoiding set, then the unit circle drawn around it does not intersect the set, but there is no restriction regarding the interior and the exterior of this circle. When searching for unit-distance avoiding sets with high densities, the following construction naturally comes to mind: an open disc with a unit diameter is unit-distance avoiding, as all distances between its two points are less than 1.
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October 6, 2023

The density of planar sets avoiding unit distances

Publication
October 6, 2023
publications
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470.
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October 6, 2023

Lemmas: Generation, Selection, Application

Publication
September 14, 2023
publications
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search.
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September 14, 2023

Rényi Institute researchers confirm more than 50-year-old conjecture of Paul Erdős

Announcement
August 8, 2023
announcements
What fraction of the plane can be colored so that two colored points cannot be exactly a unit distance away from each other? This geometric question was formulated by Leo Moser in the early 1960s. According to a conjecture of Paul Erdős, this fraction must be less than ¼. The currently best lower bound of 0.2293 is given by a construction by Hallard Croft dating back to 1967. Several research groups have published partial results on the problem, gradually strengthening the initial upper density estimate of 0.
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August 8, 2023
The Team
The AI group at the institute brings together experts with backgrounds in both industry and academia. We place equal emphasis on theoretical foundations, thorough experimentation, and practical applications. Our close collaboration ensures a continuous exchange of knowledge between scientific research and applied projects.
All Theory Applications Former members
Balázs Szegedy
Mathematical Theory
Attila Börcs, PhD
NLP, Modeling, MLOps
Adrián Csiszárik
Representation Learning, Foundations
Győző Csóka
NLP, MLOps
Domonkos Czifra
NLP, Foundations
Botond Forrai
Modeling
Péter Kőrösi-Szabó
Modeling
Gábor Kovács
NLP, Modeling
Judit Laki, MD PhD
Healthcare
Márton Muntag
Time Series, NLP, Modeling
Dávid Terjék
Generalization, Mathematical Theory
Dániel Varga
Foundations, Computer aided proofs
Pál Zsámboki
Reinforcement Learning, Geometric Deep Learning
Zsolt Zombori
Formal Reasoning
Péter Ágoston
Combinatory, Geometry
Beatrix Mária Benkő
Representation Learning
Jakab Buda
NLP
Diego González Sánchez
Generalization, Mathematical Theory
Melinda F. Kiss
Representation Learning
Ákos Matszangosz
Topology, Foundations
Alex Olár
Foundations
Gergely Papp
Modeling
Open Positions
The Rényi AI group is actively recruiting both theorists and practitioners.
Machine Learning Engineer
Announcement: July 1, 2025
Deadline: rolling
applications
Rényi Institute is seeking Machine Learning Engineers to join our AI Research & Development team. Preferred Qualifications: • MLOps experience (especially in cloud environments) • Industry experience working on ML solutions
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Research Scientist
Announcement: July 1, 2025
Deadline: rolling
theory, applications
Rényi Institute is seeking Research Scientists to join our AI Research & Development team. You will have the privilege to work at a renowned academic institute and do what you love: do research and publish in the field of machine learning / deep learning.
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All Positions
Rényi AI - Building bridges between mathematics and artificial intelligence.