Related papers: Matrix Graph Grammars
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
In recent years, large language models (LLMs) have emerged as promising candidates for graph tasks. Many studies leverage natural language to describe graphs and apply LLMs for reasoning, yet most focus narrowly on performance benchmarks…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…
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…
We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…
Grammatic is a tool for grammar definition and manipulation aimed to improve modularity and reuse of grammars and related development artifacts. It is independent from parsing technology and any other details of target system…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…
The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…
Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…
Graphs, as a relational data structure, have been widely used for various application scenarios, like molecule design and recommender systems. Recently, large language models (LLMs) are reorganizing in the AI community for their expected…
This report is a survey of the relationships between various state-of-the-art neural network architectures and formal languages as, for example, structured by the Chomsky Language Hierarchy. Of particular interest are the abilities of a…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…