Related papers: CliffordNet: All You Need is Geometric Algebra

Recently, the rapid advancement of multimodal domains has driven a data-centric paradigm shift in graph ML, transitioning from text-attributed to multimodal-attributed graphs. This advancement significantly enhances data representation and…

This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…

Deep convolutional networks have become the mainstream in computer vision applications. Although CNNs have been successful in many computer vision tasks, it is not free from drawbacks. The performance of CNN is dramatically degraded by…

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…

Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph…

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs…

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no…

A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and significant performance improvements on a variety of tasks,…

I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is…

As key models in geometric deep learning, graph neural networks have demonstrated enormous power in molecular data analysis. Recently, a specially-designed learning scheme, known as Kolmogorov-Arnold Network (KAN), shows unique potential…

In this work we introduce a convolutional neural network (CNN) that jointly handles low-, mid-, and high-level vision tasks in a unified architecture that is trained end-to-end. Such a universal network can act like a `swiss knife' for…

This paper presents an experimental study of Kolmogorov-Arnold Networks (KANs) applied to computer vision tasks, particularly image classification. KANs introduce learnable activation functions on edges, offering flexible non-linear…

The Convolutional Neural Network (CNN) has been successfully applied in many fields during recent decades; however it lacks the ability to utilize prior domain knowledge when dealing with many realistic problems. We present a framework…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

In this paper, we present Convolutional Kolmogorov-Arnold Networks, a novel architecture that integrates the learnable spline-based activation functions of Kolmogorov-Arnold Networks (KANs) into convolutional layers. By replacing…

Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state…

Recent salient object detection (SOD) models predominantly rely on heavyweight backbones, incurring substantial computational cost and hindering their practical application in various real-world settings, particularly on edge devices. This…

Manufacturability assessment is a critical step in bridging the persistent gap between design and production. While artificial intelligence (AI) has been widely applied to this task, most existing frameworks rely on geometry-driven methods…

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional…

The emergence of Kolmogorov-Arnold Networks (KANs) has sparked significant interest and debate within the scientific community. This paper explores the application of KANs in the domain of computer vision (CV). We examine the convolutional…