Related papers: CliffordNet: All You Need is Geometric Algebra

This work presents FG-Net, a general deep learning framework for large-scale point clouds understanding without voxelizations, which achieves accurate and real-time performance with a single NVIDIA GTX 1080 GPU. First, a novel noise and…

Protein inverse folding, the task of predicting amino acid sequences for desired structures, is pivotal for de novo protein design. However, existing GNN-based methods typically suffer from restricted receptive fields that miss long-range…

We present a deep learning framework for accurate visual correspondences and demonstrate its effectiveness for both geometric and semantic matching, spanning across rigid motions to intra-class shape or appearance variations. In contrast to…

Dense 3D shape correspondence remains a central challenge in computer vision and graphics as many deep learning approaches still rely on intermediate geometric features or handcrafted descriptors, limiting their effectiveness under…

Cross-View Geo-Localization (CVGL) involves determining the localization of drone images by retrieving the most similar GPS-tagged satellite images. However, the imaging gaps between platforms are often significant and the variations in…

The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…

We have developed a convolutional neural network (CNN) to reconstruct the shape of irregular rough particles from their interferometric images. The CNN is based on a UNET architecture with residual block modules. The database has been…

Low-latency, resource-efficient neural network inference on FPGAs is essential for applications demanding real-time capability and low power. Lookup table (LUT)-based neural networks are a common solution, combining strong representational…

The rapid advancement of object detection architectures has positioned single stage detectors as the dominant solution for real-time visual perception. A primary source of computational overhead in these models lies in the deep backbone…

These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…

The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data.…

3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep…

Convolutional neural networks (CNNs) have demonstrated their capability to solve different kind of problems in a very huge number of applications. However, CNNs are limited for their computational and storage requirements. These limitations…

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer…

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…

This study introduces geometric algebra to decompose credit system relationships into their projective (correlation-like) and rotational (feedback-spiral) components. We represent economic states as multi-vectors in Clifford algebra, where…

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on…

A well-known challenge in applying deep-learning methods to omnidirectional images is spherical distortion. In dense regression tasks such as depth estimation, where structural details are required, using a vanilla CNN layer on the…

Deep learning-based super-resolution (SR) techniques have generally achieved excellent performance in the computer vision field. Recently, it has been proven that three-dimensional (3D) SR for medical volumetric data delivers better visual…

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…