Related papers: Geometric Scattering on Manifolds
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…
Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
The concept of sharpness has been successfully applied to traditional architectures like MLPs and CNNs to predict their generalization. For transformers, however, recent work reported weak correlation between flatness and generalization. We…
In this work we propose a neural network based image descriptor suitable for image patch matching, which is an important task in many computer vision applications. Our approach is influenced by recent success of deep convolutional neural…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
This study explores the potential of graph neural networks (GNNs) to enhance semantic segmentation across diverse image modalities. We evaluate the effectiveness of a novel GNN-based U-Net architecture on three distinct datasets: PascalVOC,…
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the…
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
In recent years, with the rapid development of computer information technology, the development of artificial intelligence has been accelerating. The traditional geometry recognition technology is relatively backward and the recognition…
An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning.…
Deep learning models have been widely applied for fast MRI. The majority of existing deep learning models, e.g., convolutional neural networks, work on data with Euclidean or regular grids structures. However, high-dimensional features…
Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their…
We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in…