Related papers: CliffordNet: All You Need is Geometric Algebra

In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be…

Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…

Microbial Fuel Cells (MFCs) offer a promising pathway for sustainable energy generation by converting organic matter into electricity through microbial processes. A key factor influencing MFC performance is the anode structure, where design…

Convolutional neural network (CNN) slides a kernel over the whole image to produce an output map. This kernel scheme reduces the number of parameters with respect to a fully connected neural network (NN). While CNN has proven to be an…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Depth completion is a key task in autonomous driving, aiming to complete sparse LiDAR depth measurements into high-quality dense depth maps through image guidance. However, existing methods usually treat depth maps as an additional channel…

Kolmogorov-Arnold Networks (KANs) have recently demonstrated promising potential in scientific machine learning, partly due to their capacity for grid adaptation during training. However, existing adaptation strategies rely solely on input…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

In this paper we combine methods from projective geometry, Klein's model, and Clifford algebra. We develop a Clifford algebra whose Pin group is a double cover of the group of regular projective transformations. The Clifford algebra we use…

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby increasing expressivity and accuracy while also resulting in a multiplicative increase in parameters and memory. We propose…

Convolutional neural networks (CNNs) trained on object recognition achieve high task performance but continue to exhibit vulnerability under a range of visual perturbations and out-of-domain images, when compared with biological vision.…

Deep convolutional neural networks (CNN) brought revolution without any doubt to various challenging tasks, mainly in computer vision. However, their model designing still requires attention to reduce number of learnable parameters, with no…

The field of geometric deep learning has had a profound impact on the development of innovative and powerful graph neural network architectures. Disciplines such as computer vision and computational biology have benefited significantly from…

Reconstructing the detailed geometric structure of a face from a given image is a key to many computer vision and graphics applications, such as motion capture and reenactment. The reconstruction task is challenging as human faces vary…

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…

Recent semantic segmentation research has increasingly moved toward stronger context modeling, dense attention, and transformer-based architectures. Although these models achieve impressive performance, classical CNN-based segmentation…

In this paper, we introduce Wav-KAN, an innovative neural network architecture that leverages the Wavelet Kolmogorov-Arnold Networks (Wav-KAN) framework to enhance interpretability and performance. Traditional multilayer perceptrons (MLPs)…

Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures are not well suited. Our goal in this paper is to…

The small receptive field and capacity of minimal neural networks limit their performance when using them to be the backbone of detectors. In this work, we find that the appearance feature of a generic face is discriminative enough for a…

Despite the success of convolution- and attention-based models in vision tasks, their rigid receptive fields and complex architectures limit their ability to model irregular spatial patterns and hinder interpretability, therefore posing…