Related papers: Colored props for large scale graphical reasoning

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…

Pretrained Large Language Models (LLMs) have demonstrated various reasoning capabilities through language-based prompts alone, particularly in unstructured task settings (tasks purely based on language semantics). However, LLMs often…

This paper is intended to provide concrete examples of concepts discussed elsewhere in this volume, especially splittings of groups and non-positively curved cube complexes but also other things. The idea of the construction (configuration…

Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…

While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…

The use of symbolic knowledge representation and reasoning as a way to resolve the lack of transparency of machine learning classifiers is a research area that lately attracts many researchers. In this work, we use knowledge graphs as the…

We use the framework of "props" to study electrical circuits, signal-flow diagrams, and bond graphs. A prop is a strict symmetric monoidal category where the objects are natural numbers, with the tensor product of objects given by addition.…

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…

We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…

A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs…

Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges…

Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…

This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…

Polymorphism in programming languages enables code reuse. Here, we show that polymorphism has broad applicability far beyond computations for technical computing: parallelism in distributed computing, presentation of visualizations of…

Large-scale Vision-Language Models, such as CLIP, learn powerful image-text representations that have found numerous applications, from zero-shot classification to text-to-image generation. Despite that, their capabilities for solving novel…

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings…

Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…

With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced…