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Recent 2D-to-3D human pose estimation works tend to utilize the graph structure formed by the topology of the human skeleton. However, we argue that this skeletal topology is too sparse to reflect the body structure and suffer from serious…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

Recently, graph Convolutional Neural Networks (graph CNNs) have been widely used for graph data representation and semi-supervised learning tasks. However, existing graph CNNs generally use a fixed graph which may be not optimal for…

In this paper we study the spontaneous development of symmetries in the early layers of a Convolutional Neural Network (CNN) during learning on natural images. Our architecture is built in such a way to mimic the early stages of biological…

How humans understand and recognize the actions of others is a complex neuroscientific problem that involves a combination of cognitive mechanisms and neural networks. Research has shown that humans have brain areas that recognize actions…

Graph convolutional networks (GCNs) aim at extending deep learning to arbitrary irregular domains, namely graphs. Their success is highly dependent on how the topology of input graphs is defined and most of the existing GCN architectures…

Graph Convolutional Networks (GCNs) have recently been shown to be quite successful in modeling graph-structured data. However, the primary focus has been on handling simple undirected graphs. Multi-relational graphs are a more general and…

In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We…

The objective of image manipulation detection is to identify and locate the manipulated regions in the images. Recent approaches mostly adopt the sophisticated Convolutional Neural Networks (CNNs) to capture the tampering artifacts left in…

Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the…

In the context of machine learning for graphs, many researchers have empirically observed that Deep Graph Networks (DGNs) perform favourably on node classification tasks when the graph structure is homophilic (\ie adjacent nodes are…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

Heterogeneous graph neural network has unleashed great potential on graph representation learning and shown superior performance on downstream tasks such as node classification and clustering. Existing heterogeneous graph learning networks…

Manifold Learning occupies a vital role in the field of nonlinear dimensionality reduction and its ideas also serve for other relevant methods. Graph-based methods such as Graph Convolutional Networks (GCN) show ideas in common with…

We study algebraic neural networks (AlgNNs) with commutative algebras which unify diverse architectures such as Euclidean convolutional neural networks, graph neural networks, and group neural networks under the umbrella of algebraic signal…

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…

Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…

In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper etale Lie groupoid is studied. We compute the Hochschild cohomology of the convolution algebra and express it…

Recent work suggests that changing Convolutional Neural Network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively…

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…