Related papers: Diffeomorphism-Equivariant Neural Networks
In many machine learning tasks, known symmetries can be used as an inductive bias to improve model performance. In this paper, we consider learning group equivariance through training with data augmentation. We summarize results from a…
Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…
Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…
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…
In this paper we propose a Deep Learning architecture to approximate diffeomorphisms diffeotopic to the identity. We consider a control system of the form $\dot x = \sum_{i=1}^lF_i(x)u_i$, with linear dependence in the controls, and we use…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
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…
Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
Equivariant and invariant machine learning models exploit symmetries and structural patterns in data to improve sample efficiency. While empirical studies suggest that data-driven methods such as regularization and data augmentation can…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Deep belief networks are used extensively for unsupervised stochastic learning on large datasets. Compared to other deep learning approaches their layer-by-layer learning makes them highly scalable. Unfortunately, the principles by which…
Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are…
Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely…
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…
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…
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,…
Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…