Graphon Theory

Latest papers

10 papers1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Implicit Neural Representations for Variational Problems on Graphons
Oct 23, 2026Taeyoung Kim, Jineon Baek, Joonkyung Lee +1Graphon Theory Large Deviation Principles
School of Computing, KAIST · School of Computational Sciences, KIAS · June E Huh Center for Mathematical Challenges, KIAS
A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators
Oct 1, 2026Wooseong Choi, Italo'Ivo Lima Dias Pinto, Chen Sun +3Graphon Theory Graph Generation
Department of Biomedical Engineering University of Southern California Los Angeles, CA 90089 · Department of Electrical Engineering University of Southern California Los Angeles, CA 90089 · AWS AI Santa Clara, CA 95050
Attention Graphons: A Graph Limit Perspective on Graph Transformers
Sep 28, 2026Caio F. Deberaldini Netto, Moshe Eliasof, Luana RuizGraphon Theory Transformer Attention
Johns Hopkins University Baltimore, MD · University of Cambridge Cambridge, UK
DiPhon: Diffusion on Graphons for Scalable Graph Generation
Jul 8, 2026Sergio Rozada, Yiming Qin, Manuel Madeira +2Graphon Theory Graph Generation
King Juan Carlos University · EPFL, Lausanne, Switzerland · University of Pennsylvania
Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence
Jun 25, 2026Mingsong Yan, Zhida Wang, Sui TangGraphon Theory OOD Generalization
Department of Mathematics, University of California, Santa Barbara, CA.
A Topological Characterization of Graph Neural Networks via Stochastic Block Model Embeddings on the n-Sphere
May 29, 2026Gopal AnantharamanGraphon Theory Graph Neural Networks
KnotTheory.ai Inc. · Dept. of Mathematics, Emporia State University
When Do Graph Foundation Models Transfer? A Data-Centric Theory
May 28, 2026Jiajun Zhu, Ying Chen, Peihao Wang +4Graph Positional Encoding Graphon Theory
University of Texas at Austin · Arizona State University · Georgia Institute of Technology
Intensity Dot Product Graphs
Apr 9, 2026Giulio Valentino Dalla Riva, Matteo Dalla RivaGraphon Theory Latent Variable Models
Baffelan OU, Noumea, New Caledonia · Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università di Padova, Vicenza, Italy
A Note on Graphon-Signal Analysis of Graph Neural Networks
Aug 25, 2025Levi Rauchwerger, Ron LevieGraphon Theory Graph Neural Networks
Graphons of Line Graphs
Sep 3, 2024Sevvandi Kandanaarachchi, Cheng Soon OngGraphon Theory

Oct 23, 2026J/K move · Enter open · S save

Implicit Neural Representations for Variational Problems on Graphons

Taeyoung Kim, Jineon Baek, Joonkyung Lee, Hongseok Yang

School of Computing, KAIST · School of Computational Sciences, KIAS · June E Huh Center for Mathematical Challenges, KIAS

Graphon Theory Large Deviation Principles Implicit Neural Representations

Open paper AskPDF arXiv

We propose a neural exploratory framework for variational problems over graphons, i.e., symmetric measurable functions

[0,1]^2 \to [0,1]

, that arise as limits of dense graph sequences. Such problems are central to two parts of the mathematical literature: extremal graph theory, which studies graph parameter optimisation under given restrictions, often for those graphs with a large number of vertices, and the large deviation theory of dense random graphs, which characterises the structure of rare events through constrained graphon optimisation. We represent graphons by implicit neural networks and optimise graphon objectives by gradient descent. Our design combines three ingredients: a multi-scale sinusoidal residual architecture biased toward sharp, step-like graphons; an embedded solver that enforces a single empirical density constraint and is differentiated by implicit differentiation; and symmetry-aware Monte Carlo estimators. On generalised Turán problems that previously required substantial human effort, our framework rediscovers known optimal graphons without human intervention. Applied to open instances, it produces candidate optima, including a previously unreported family of extremal structures. Applied to the variational problems from the large deviation theory of Erdős--Rényi random graphs, the framework produces new candidate optimal graphons across both upper- and lower-tail regimes for multiple pattern graphs; for the case of the triangle graph and the upper-tail regime, these candidates improve upon the best-known reference construction of Lubetzky and Zhao. The structures found by our framework have also led to new theorems on the optimal graphons for both families of problems.