Related papers: Graphical Symplectic Algebra
We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the…
Diagrammatic sets are presheaves on a rich category of shapes, whose definition is motivated by combinatorial topology and higher-dimensional diagram rewriting. These shapes include representatives of oriented simplices, cubes, and positive…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…
We introduce AutoGraph, a scalable autoregressive model for attributed graph generation using decoder-only transformers. By flattening graphs into random sequences of tokens through a reversible process, AutoGraph enables modeling graphs as…
In applications, quantities of interest are often modelled in equilibrium or an equilibrium solution is sought. The presence of confounding makes causal inference in this setting challenging. We provide interpretable graphical models for…
Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…
Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
Semantic parsing is the task of producing a structured meaning representation for natural language utterances or questions. Recent research has pointed out that the commonly-used sequence-to-sequence (seq2seq) semantic parsers struggle to…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
Asymptotic expansions of Gaussian integrals may often be interpreted as generating functions for certain combinatorial objects (graphs with additional data). In this article we discuss a general approach to all such cases using colored…
Semantic parses are directed acyclic graphs (DAGs), so semantic parsing should be modeled as graph prediction. But predicting graphs presents difficult technical challenges, so it is simpler and more common to predict the linearized graphs…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…