Related papers: The Cost of Compositionality: A High-Performance I…
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to…
We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
Finite-state transducers (FSTs) are frequently used in speech recognition. Transducer composition is an essential operation for combining different sources of information at different granularities. However, composition is also one of the…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
In this paper we report a new promising idea on the design and manufacturing of ply composite structures, tailored to exhibit maximum stiffness under given weight constraints and loading conditions. It is based on the idea behind an…
Annotating large collections of textual data can be time consuming and expensive. That is why the ability to train models with limited annotation budgets is of great importance. In this context, it has been shown that under tight annotation…
The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…
Well-designed queuing systems form the backbone of modern communications, distributed computing, and content delivery architectures. Designs balancing infrastructure costs and user experience indices require tools from teletraffic theory…
Graphs provide a unified representation of semantic content and relational structure, making them a natural fit for domains such as molecular modeling, citation networks, and social graphs. Meanwhile, large language models (LLMs) have…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. As well as being relevant in computer science, mathematical analysis…