Related papers: Toward a Functional Geometric Algebra for Natural …
Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our geometric (Clifford)…
Implicit spatial relations and deep semantic structures encoded in object attributes are crucial for procedural planning in embodied AI systems. However, existing approaches often over rely on the reasoning capabilities of vision language…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
Any natural language can be considered as a tool for producing large databases (consisting of texts, written, or discursive). This tool for its description in turn requires other large databases (dictionaries, grammars etc.). Nowadays, the…
Graph embedding methods such as Graph Neural Networks (GNNs) and Graph Transformers have contributed to the development of graph reasoning algorithms for various tasks on knowledge graphs. However, the lack of interpretability and…
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…
Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…
Most current work in NLP utilizes deep learning, which requires a lot of training data and computational power. This paper investigates the strengths of Genetic Algorithms (GAs) for extractive summarization, as we hypothesized that GAs…
Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…
Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…
Neural Architecture Representation Learning aims to transform network models into feature representations for predicting network attributes, playing a crucial role in deploying and designing networks for real-world applications. Recently,…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
The paper relates two variants of semantic models for natural language, logical functional models and compositional distributional vector space models, by transferring the logic and reasoning from the logical to the distributional models.…
Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation…
In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
This work presents the introduction of UniSG^GA, a novel integrated scenegraph structure, that to incorporates behavior and geometry data on a 3D scene. It is specifically designed to seamlessly integrate Graph Neural Networks (GNNs) and…