Related papers: Equivariant Polynomial Functional Networks
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural…
Conditional Neural Fields (CNFs) are increasingly being leveraged as continuous signal representations, by associating each data-sample with a latent variable that conditions a shared backbone Neural Field (NeF) to reconstruct the sample.…
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…
Automatic tumor segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on convolutional neural networks (CNNs) have achieved the state-of-the-art performance, many…
Equivariant Graph Neural Networks (eGNNs) trained on density-functional theory (DFT) data can potentially perform electronic structure prediction at unprecedented scales, enabling investigation of the electronic properties of materials with…
The nature of heterophilous graphs is significantly different from that of homophilous graphs, which causes difficulties in early graph neural network models and suggests aggregations beyond the 1-hop neighborhood. In this paper, we develop…
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…
Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…
Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide…
Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies,…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
A deeper network structure generally handles more complicated non-linearity and performs more competitively. Nowadays, advanced network designs often contain a large number of repetitive structures (e.g., Transformer). They empower the…
Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…
Message-passing graph neural network interatomic potentials (GNN-IPs), particularly those with equivariant representations such as NequIP, are attracting significant attention due to their data efficiency and high accuracy. However,…
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…
Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional…