Related papers: Diffeomorphism-Equivariant Neural Networks

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including…

Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

This paper presents a predictive model for estimating regularization parameters of diffeomorphic image registration. We introduce a novel framework that automatically determines the parameters controlling the smoothness of diffeomorphic…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

In many information processing systems, it may be desirable to ensure that any change of the input, whether by shifting or scaling, results in a corresponding change in the system response. While deep neural networks are gradually replacing…

In Reinforcement Learning (RL), Convolutional Neural Networks(CNNs) have been successfully applied as function approximators in Deep Q-Learning algorithms, which seek to learn action-value functions and policies in various environments.…

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to…

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…

Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve…

Recently, equivariant neural networks for policy learning have shown promising improvements in sample efficiency and generalization, however, their wide adoption faces substantial barriers due to implementation complexity. Equivariant…

Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than…

Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…

Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…

Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…

Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an…