Related papers: Solving Tree Problems with Category Theory
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Recently, there is an increasing interest in understanding the performance of AI systems in solving math problems. A multitude of tests have been performed, with mixed conclusions. In this paper we discuss an experiment we have made in the…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple…
Code generation, defined as automatically writing a piece of code to solve a given problem for which an evaluation function exists, is a classic hard AI problem. Its general form, writing code using a general language used by human…
The rapid expansion of Artificial Intelligence (AI) technologies has introduced both significant advancements and challenges, with diversity and inclusion (D&I) emerging as a critical concern. Addressing D&I in AI is essential to reduce…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
As artificial intelligence (AI) becomes more powerful and widespread, the AI alignment problem - how to ensure that AI systems pursue the goals that we want them to pursue - has garnered growing attention. This article distinguishes two…
In colored range counting (CRC), the input is a set of points where each point is assigned a ``color'' (or a ``category'') and the goal is to store them in a data structure such that the number of distinct categories inside a given query…
This paper investigates one of the most fundamental computer vision problems: image segmentation. We propose a supervised hierarchical approach to object-independent image segmentation. Starting with over-segmenting superpixels, we use a…
Solutions relying on artificial intelligence are devised to predict data patterns and answer questions that are clearly defined, involve an enumerable set of solutions, clear rules, and inherently binary decision mechanisms. Yet, as they…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
Large Language Models (LLMs) are being integrated into professional domains, yet their limitations in such high-stakes fields as law remain poorly understood. In response, this paper introduces examples of critical challenges to the…
When used in high-stakes settings, AI systems are expected to produce decisions that are transparent, interpretable and auditable, a requirement increasingly expected by regulations. Decision trees such as CART provide clear and verifiable…
Human-level AI will have significant impacts on human society. However, estimates for the realization time are debatable. To arrive at human-level AI, artificial general intelligence (AGI), as opposed to AI systems that are specialized for…
New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for…
The paper discusses the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary knowledge with commonsense reasoning. No existing AI systems can solve these reliably. We…