Related papers: Rewriting Graphically with Symmetric Traced Monoid…

A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G, there exists a unique smallest Helly graph H(G) into which G…

Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…

We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels…

Graph neural networks (GNNs) have gained significant attention in recent years for their ability to process data that may be represented as graphs. This has prompted several studies to explore their representational capability based on the…

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…

We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…

In this article, we establish a mathematical framework that utilizes concepts from graph theory to formalize the parity transformation, an encoding strategy for compiling optimization problems on quantum devices. We introduce the…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented…

Can we model Non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The Non-Euclidean property have posed a long term challenge in graph modeling. Despite recent graph neural networks and…

A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and…

We present Multimodal OCR (MOCR), a document parsing paradigm that jointly parses text and graphics into unified textual representations. Unlike conventional OCR systems that focus on text recognition and leave graphical regions as cropped…

The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the…

The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…

It is known that every monoidal bicategory has an associated braided monoidal category of scalars. In this thesis we show that every monoidal bicategory, which is closed both monoidally and compositionally, can be enriched over the monoidal…

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations:…

Multi-graph learning is crucial for extracting meaningful signals from collections of heterogeneous graphs. However, effectively integrating information across graphs with differing topologies, scales, and semantics, often in the absence of…

We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…