205 citations · 615 across the 51 of their papers we have counts for
39 papers · 1 filter
Holographic functions and neural networks
Balazs Szegedy
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where . We introduce and compare three ways of saying that such a function has bounded complexity. The first…
Star observations in bounded-degree graphs
Balazs Szegedy
Similarity metrics are central in the theory of large networks and graph limits. For bounded-degree graphs, the Benjamini--Schramm metric records the distribution of rooted neighbo…
Spectral algorithms in higher-order Fourier analysis
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for…
On the inverse theorem for Gowers norms in abelian groups of bounded torsion
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
In recent work, Jamneshan, Shalom and Tao proved an inverse theorem for the Gowers -norm on finite abelian groups of fixed torsion , where the final correlating harmoni…
Free nilspaces, double-coset nilspaces, and Gowers norms
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
Compact finite-rank nilspaces have become central in the nilspace approach to higher-order Fourier analysis, notably through their role in a general form of the inverse theorem for…
A refinement of Cauchy-Schwarz complexity
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
We introduce a notion of complexity for systems of linear forms, called sequential Cauchy-Schwarz complexity, which is parametrized by two positive integers and refines th…
Random homomorphisms into the orthogonality graph
Dávid Kunszenti-Kovács, László Lovász, Balázs Szegedy
Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequen…
Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds
Pablo Candela, Balázs Szegedy
We prove a general form of the regularity theorem for uniformity norms, and deduce an inverse theorem for these norms which holds for a class of compact nilspaces including all com…
Action convergence of operators and graphs
Agnes Backhausz, Balazs Szegedy
We present a new approach to graph limit theory which unifies and generalizes the two most well developed directions, namely dense graph limits (even the more general limits)…
On Sidorenko's conjecture for determinants and Gaussian Markov random fields
Péter Csikvári, Balázs Szegedy
We study a class of determinant inequalities that are closely related to Sidorenko's famous conjecture (Also conjectured by Erd\H os and Simonovits in a different form). Our main r…
Measures on the square as sparse graph limits
Dávid Kunszenti-Kovács, László Lovász, Balázs Szegedy
We study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional "factors". We show that limits of convergent…
A continuous model for systems of complexity 2 on simple abelian groups
Pablo Candela, Balázs Szegedy
It is known that if is a sufficiently large prime then for every function there exists a continuous function on the circle su…
Sparse graph limits, entropy maximization and transitive graphs
Balazs Szegedy
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is…
Limits of functions on groups
Balazs Szegedy
Our goal is to develop a limit approach for a class of problems in additive combinatorics that is analogous to the limit theory of dense graph sequences. We introduce metric, conve…
On linear configurations in subsets of compact abelian groups, and invariant measurable hypergraphs
Pablo Candela, Balázs Szegedy, Lluís Vena
We prove an arithmetic removal result for all compact abelian groups, generalizing a finitary removal result of Král', Serra and the third author. To this end, we consider infinite…
The automorphism group of a graphon
László Lovász, Balázs Szegedy
We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we…
Multigraph limits, unbounded kernels, and Banach space decorated graphs
Dávid Kunszenti-Kovács, László Lovász, Balázs Szegedy
We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional ana…
An information theoretic approach to Sidorenko's conjecture
Balazs Szegedy
We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and i…
Graph properties, graph limits and entropy
Hamed Hatami, Svante Janson, Balázs Szegedy
We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary class…
Limits of local-global convergent graph sequences
Hamed Hatami, László Lovász, Balázs Szegedy
The colored neighborhood metric for sparse graphs was introduced by Bollobás and Riordan. The corresponding convergence notion refines a convergence notion introduced by Benjamini…
On higher order Fourier analysis
Balazs Szegedy
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformit…
Structure of finite nilspaces and inverse theorems for the Gowers norms in bounded exponent groups
Balazs Szegedy
A result of the author shows that the behavior of Gowers norms on bounded exponent abelian groups is connected to finite nilspaces. Motivated by this, we investigate the structure…
Gowers norms, regularization and limits of functions on abelian groups
Balazs Szegedy
For every natural number k we prove a decomposition theorem for bounded measurable functions on compact abelian groups into a structured part, a quasi random part and a small error…
The graph theoretic moment problem
László Lovász, Balázs Szegedy
We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences wher…