Related papers: Canonical Selection of Colimits
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
In this paper, we justify and make precise an elementary approach that establishes the existence of (co)limits in $\mathbf{Cat}$. This approach, while conceptually evident, has not been made fully explicit or systematically described in the…
Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and…
In this paper, we present an approach to define the semantics for object-oriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates…
Large Language Models (LLMs) exhibit remarkable generative capabilities, enabling the generation of valuable information. Despite these advancements, previous research found that LLMs sometimes struggle with adhering to specific constraints…
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become…
Cross-Language Information Retrieval (CLIR) and machine translation (MT) resources, such as dictionaries and parallel corpora, are scarce and hard to come by for special domains. Besides, these resources are just limited to a few languages,…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Combinatorial optimization (CO) is essential for improving efficiency and performance in engineering applications. As complexity increases with larger problem sizes and more intricate dependencies, identifying the optimal solution become…
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
The idea of product line scoping is to identify the set of features and configurations that a product line should include, i.e., offer for configuration purposes. In this context, a major scoping task is to find a balance between commercial…
Generic Ontology Design Patterns, GODPs, are defined in Generic DOL, an extension of DOL, the Distributed Ontology, Model and Specification Language, and implemented using Heterogeneous Tool Set. Parameters such as classes, properties,…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
We show that any directed colimit of acessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals, any directed colimit of acessible categories and accessible…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Vision-language models (VLMs) such as CLIP have shown promising performance on a variety of recognition tasks using the standard zero-shot classification procedure -- computing similarity between the query image and the embedded words for…
Large language models (LLMs) are empowering decision-making in several applications, including tool or API usage and answering multiple-choice questions (MCQs). However, incorrect outputs pose significant risks in high-stakes domains like…
Understanding the world through models is a fundamental goal of scientific research. While large language model (LLM) based approaches show promise in automating scientific discovery, they often overlook the importance of criticizing…
Detecting objects accurately from a large or open vocabulary necessitates the vision-language alignment on region representations. However, learning such a region-text alignment by obtaining high-quality box annotations with text labels or…