Related papers: Rewriting Abstract Structures: Materialization Exp…
We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…
Abstractive text summarization aims at compressing the information of a long source document into a rephrased, condensed summary. Despite advances in modeling techniques, abstractive summarization models still suffer from several key…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…
This paper describes a first step towards the definition of an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the…
Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single…
Causal abstraction provides a theoretical foundation for mechanistic interpretability, the field concerned with providing intelligible algorithms that are faithful simplifications of the known, but opaque low-level details of black box AI…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
Extractive summarization is a task of highlighting the most important parts of the text. We introduce a new approach to extractive summarization task using hidden clustering structure of the text. Experimental results on CNN/DailyMail…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H^1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about…
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
In this article is analyzed technology of automatic text abstracting and annotation. The role of annotation in automatic search and classification for different scientific articles is described. The algorithm of summarization of natural…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
We present a new and powerful algebraic framework for graph rewriting, based on drags, a class of graphs enjoying a novel composition operator. Graphs are embellished with roots and sprouts, which can be wired together to form edges. Drags…