Related papers: Using Multiple Vector Channels Improves E(n)-Equiv…

In recent years, graph neural networks (GNNs) combined with variants of recurrent neural networks (RNNs) have reached state-of-the-art performance in spatiotemporal forecasting tasks. This is particularly the case for traffic forecasting,…

With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with $\mathsf{SO}(3)$-equivariant layers have been developed to cope with data that are samples of signals on the sphere $S^2$. One can implicitly…

Currently there exists rather promising new trend in machine leaning (ML) based on the relationship between neural networks (NN) and Gaussian processes (GP), including many related subtopics, e.g., signal propagation in NNs, theoretical…

In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…

It is well established that graph neural networks (GNNs) can be interpreted and designed from the perspective of optimization objective. With this clear optimization objective, the deduced GNNs architecture has sound theoretical foundation,…

We devise a new type of feedforward neural network. It is equivariant with respect to the unitary group $U(n)$. The input and output can be vectors in $\mathbb{C}^n$ with arbitrary dimension $n$. No convolution layer is required in our…

Objective: A novel structure based on channel-wise attention mechanism is presented in this paper. Embedding with the proposed structure, an efficient classification model that accepts multi-lead electrocardiogram (ECG) as input is…

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter…

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

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…

Recent work in the multi-agent domain has shown the promise of Graph Neural Networks (GNNs) to learn complex coordination strategies. However, most current approaches use minor variants of a Graph Convolutional Network (GCN), which applies…

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…

Graph Neural Networks (GNNs) have been widely applied in the semi-supervised node classification task, where a key point lies in how to sufficiently leverage the limited but valuable label information. Most of the classical GNNs solely use…

Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials…

Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…

Deep convolutional neural network has made huge revolution and shown its superior performance on computer vision tasks such as classification and segmentation. Recent years, researches devote much effort to scaling down size of network…

Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…

Group-equivariant convolutional neural networks (G-CNN) heavily rely on parameter sharing to increase CNN's data efficiency and performance. However, the parameter-sharing strategy greatly increases the computational burden for each added…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of…