相关论文: CliffordNet: All You Need is Geometric Algebra

The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…

During 3D reconstruction, it is often the case that people cannot scan each individual object from all views, resulting in missing geometry in the captured scan. This missing geometry can be fundamentally limiting for many applications,…

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance,…

Multi-scale deep CNN architecture [1, 2, 3] successfully captures both fine and coarse level image descriptors for visual similarity task, but they come up with expensive memory overhead and latency. In this paper, we propose a competing…

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is…

The recent proposal (M Planat and M Kibler, Preprint 0807.3650 [quantph]) of representing Clifford quantum gates in terms of unitary reflections is revisited. In this essay, the geometry of a Clifford group G is expressed as a BN-pair, i.e.…

Nucleus segmentation is a challenging task due to the crowded distribution and blurry boundaries of nuclei. Recent approaches represent nuclei by means of polygons to differentiate between touching and overlapping nuclei and have…

The hybrid architecture of convolutional neural networks (CNNs) and Transformer are very popular for medical image segmentation. However, it suffers from two challenges. First, although a CNNs branch can capture the local image features…

As a critical cue for understanding human intention, human gaze provides a key signal for Human-Computer Interaction(HCI) applications. Appearance-based gaze estimation, which directly regresses the gaze vector from eye images, has made…

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs) in deep learning. KANs have already been integrated into various architectures, such as convolutional neural networks,…

We discuss a Clifford algebra framework for discrete symmetry groups (such as reflection, Coxeter, conformal and modular groups), leading to a surprising number of new results. Clifford algebras allow for a particularly simple description…

Feature pyramids have become ubiquitous in multi-scale computer vision tasks such as object detection. Given their importance, a computer vision network can be divided into three parts: a backbone (generating a feature pyramid), a neck…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

U-Net has become a cornerstone in various visual applications such as image segmentation and diffusion probability models. While numerous innovative designs and improvements have been introduced by incorporating transformers or MLPs, the…

This work presents and analyzes three convolutional neural network (CNN) models for efficient pixelwise classification of images. When using convolutional neural networks to classify single pixels in patches of a whole image, a lot of…

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and…

In the realm of deep learning, the Kolmogorov-Arnold Network (KAN) has emerged as a potential alternative to multilayer projections (MLPs). However, its applicability to vision tasks has not been extensively validated. In our study, we…

Object detection is one of the most fundamental yet challenging research topics in the domain of computer vision. Recently, the study on this topic in aerial images has made tremendous progress. However, complex background and worse imaging…