Related papers: An Ontology-Based Approach to Optimizing Geometry …
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
While classical planning languages make the closed-domain and closed-world assumption, there have been various approaches to extend those with DL reasoning, which is then interpreted under the usual open-world semantics. Current approaches…
Large Language Models (LLMs) have been extensively adopted in Knowledge Graph Completion (KGC), showcasing significant research advancements. However, as black-box models driven by deep neural architectures, current LLM-based KGC methods…
The paper describes the architecture of the intelligence system for automated design of ontological knowledge bases of domain areas and the software model of the management GUI (Graphical User Interface) subsystem
One area of physics education research has focused on the nature of ontologies (mental categorizations of concepts, substances and processes), and how they might be used to gain insight into student thinking when learning classical physics.…
Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…
Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…
We propose an ontology-grounded approach to Knowledge Graph (KG) construction using Large Language Models (LLMs) on a knowledge base. An ontology is authored by generating Competency Questions (CQ) on knowledge base to discover knowledge…
Task-oriented grasping (TOG) is more challenging than simple object grasping because it requires precise identification of object parts and careful selection of grasping areas to ensure effective and robust manipulation. While recent…
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…
The literature on machine teaching, machine education, and curriculum design for machines is in its infancy with sparse papers on the topic primarily focusing on data and model engineering factors to improve machine learning. In this paper,…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
The terms 'semantics' and 'ontology' are increasingly appearing together with 'explanation', not only in the scientific literature, but also in organizational communication. However, all of these terms are also being significantly…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
Understanding intelligence is a central pursuit in neuroscience, cognitive science, and artificial intelligence. Intelligence encompasses learning, problem-solving, creativity, and even consciousness. Recent advancements in geometric…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
Organizing a large-scale knowledge graph into a typed property graph requires structural decisions -- which entities become nodes, which properties become edges, and what schema governs these choices. Existing approaches embed these…