Related papers: Exploiting Learned Symmetries in Group Equivariant…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in many computer vision tasks over the years. However, this comes at the cost of heavy computation and memory intensive network designs, suggesting potential…
Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…
This paper introduces versatile filters to construct efficient convolutional neural networks that are widely used in various visual recognition tasks. Considering the demands of efficient deep learning techniques running on cost-effective…
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…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
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 CNNs (G-CNNs) have shown promising efficacy in various tasks, owing to their ability to capture hierarchical features in an equivariant manner. However, their equivariance is fixed to the symmetry of the whole group,…
Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input…
Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…
Graph Convolutional Networks (GCNs) have become a pivotal method in machine learning for modeling functions over graphs. Despite their widespread success across various applications, their statistical properties (e.g., consistency,…
In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group $G$. We then leverage this theory in the context of deep neural networks with group symmetries in order to obtain novel…
Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…
Graph Convolution Network (GCN) has attracted significant attention and become the most popular method for learning graph representations. In recent years, many efforts have been focused on integrating GCN into the recommender tasks and…
Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…
Typical convolutional neural networks (CNNs) have several millions of parameters and require a large amount of annotated data to train them. In medical applications where training data is hard to come by, these sophisticated machine…
We present the group equivariant conditional neural process (EquivCNP), a meta-learning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in…
Building large models with parameter sharing accounts for most of the success of deep convolutional neural networks (CNNs). In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance…
Symmetry, where certain features remain invariant under geometric transformations, can often serve as a powerful prior in designing convolutional neural networks (CNNs). While conventional CNNs inherently support translational equivariance,…
In this paper, we aim at improving the computational efficiency of graph convolutional networks (GCNs) for learning on point clouds. The basic graph convolution that is typically composed of a $K$-nearest neighbor (KNN) search and a…