Related papers: IGraph/M: graph theory and network analysis for Ma…
Solving arithmetic tasks is a simple and fundamental skill, yet modern Large Language Models (LLMs) have great difficulty with them. We introduce the Integrated Gated Calculator (IGC), a module that enables LLMs to perform arithmetic by…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
With the advent of end-to-end deep learning approaches in machine translation, interest in word alignments initially decreased; however, they have again become a focus of research more recently. Alignments are useful for typological…
Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets…
Large language models (LLMs) exhibit strong semantic understanding, yet struggle when user instructions involve ambiguous or conceptually misaligned terms. We propose the Language Graph Model (LGM) to enhance conceptual clarity by…
Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are `graphs' - structures containing objects…
Machine learning techniques have recently been adopted in various applications in medicine, biology, chemistry, and material engineering. An important task is to predict the properties of molecules, which serves as the main subroutine in…
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…
Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the…
Graph mining is an important area in data mining and machine learning that involves extracting valuable information from graph-structured data. In recent years, significant progress has been made in this field through the development of…
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
Large Language Models (LLMs) face significant limitations when applied to large-scale graphs, struggling with context constraints and inflexible reasoning. We present GraphChain, a framework that enables LLMs to analyze complex graphs…
Large Language Models (LLMs) have shown remarkable capabilities in processing various data structures, including graphs. While previous research has focused on developing textual encoding methods for graph representation, the emergence of…
This paper introduces the recent work of Nebula Graph, an open-source, distributed, scalable, and native graph database. We present a system design trade-off and a comprehensive overview of Nebula Graph internals, including graph data…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
This paper shows an application of Bloom and Esik's iteration algebras to model graph data in a graph database query language. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional…
The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
This paper presents a Matlab toolbox to perform basic image processing and visualization tasks, particularly designed for medical image processing. The functionalities available are similar to basic functions found in other non-Matlab…