相关论文: The Geometry of Polynomial Group Convolutional Neu…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere, up to rescaling the filters. By leveraging on tools from…
Hypercomplex neural networks have proven to reduce the overall number of parameters while ensuring valuable performance by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to…
We propose, implement, and compare with competitors a new architecture of equivariant neural networks based on geometric (Clifford) algebras: Generalized Lipschitz Group Equivariant Neural Networks (GLGENN). These networks are equivariant…
This paper presents a novel framework for graded neural networks (GNNs) built over graded vector spaces $\V_\w^n$, extending classical neural architectures by incorporating algebraic grading. Leveraging a coordinate-wise grading structure…
Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
This paper reviews graph convolutional neural networks (GCNNs) through the lens of edge-variant graph filters. The edge-variant graph filter is a finite order, linear, and local recursion that allows each node, in each iteration, to weigh…
$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…
We study the expressivity and learning process for polynomial neural networks (PNNs) with monomial activation functions. The weights of the network parametrize the neuromanifold. In this paper, we study certain neuromanifolds using tools…
Modern Convolutional Neural Network (CNN) architectures, despite their superiority in solving various problems, are generally too large to be deployed on resource constrained edge devices. In this paper, we reduce memory usage and…
Nowadays the development of new functional materials/chemical compounds using machine learning (ML) techniques is a hot topic and includes several crucial steps, one of which is the choice of chemical structure representation. Classical…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms…
Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this…
A fast and accurate predictive tool for polymer properties is demanding and will pave the way to iterative inverse design. In this work, we apply graph convolutional neural networks (GCNN) to predict the dielectric constant and energy…
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…