Related papers: Categorical Data Structures for Technical Computin…
Our goal is to derive some families of maps, also known as functions, from injective maps and surjective maps; this can be useful in various fields of mathematics. Let A be a small concrete category. We define a functor F, cometic functor,…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve…
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor…
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
We show that the comma category $(\mathcal{F}\downarrow\mathbf{Grp})$ of groups under the free group functor $\mathcal{F}: \mathbf{Set} \to \mathbf{Grp}$ contains the category $\mathbf{Gph}$ of simple graphs as a full coreflective…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
In recent years, several models have improved the capacity to generate synthetic tabular datasets. However, such models focus on synthesizing simple columnar tables and are not useable on real-life data with complex structures. This paper…
Hypergraphs are used to model higher-order interactions amongst agents and there exist many practically relevant instances of hypergraph datasets. To enable efficient processing of hypergraph-structured data, several hypergraph neural…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $f^+:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. A graph…
The paper provides an introduction to the field of Algebraic Set Theory (AST). AST is a flexible categorical framework for studying different kinds of set theories: both classical and constructive, predicative and impredicative. We discuss…
We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint functors between corresponding copresheaf categories. These may…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
Call graphs depict the static, caller-callee relation between "functions" in a program. With most source/target languages supporting functions as the primitive unit of composition, call graphs naturally form the fundamental control flow…
Category Theory is a well-known powerful mathematical modeling language with a wide area of applications in mathematics and computer science, including especially the semantical foundations of topics in software science and development.…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
Graph neural networks (GNNs) are widely believed to excel at node representation learning through trainable neighborhood aggregations. We challenge this view by introducing Fixed Aggregation Features (FAFs), a training-free approach that…