Related papers: Any-dimensional equivariant neural networks

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

The task of shape space learning involves mapping a train set of shapes to and from a latent representation space with good generalization properties. Often, real-world collections of shapes have symmetries, which can be defined as…

Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…

Self-supervised learning (SSL) methods have achieved remarkable success in learning image representations allowing invariances in them - but therefore discarding transformation information that some computer vision tasks actually require.…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…

This paper proposes a method to construct pretext tasks for self-supervised learning on group equivariant neural networks. Group equivariant neural networks are the models whose structure is restricted to commute with the transformations on…

While end-to-end approaches have achieved state-of-the-art performance in many perception tasks, they are not yet able to compete with 3D geometry-based methods in pose estimation. Moreover, absolute pose regression has been shown to be…

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Many problems in computer vision and machine learning can be cast as learning on hypergraphs that represent higher-order relations. Recent approaches for hypergraph learning extend graph neural networks based on message passing, which is…

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…

In this work we investigate how to achieve equivariance to input transformations in deep networks, purely from data, without being given a model of those transformations. Convolutional Neural Networks (CNNs), for example, are equivariant to…