Related papers: Group Equivariant Stand-Alone Self-Attention For V…

Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the…

In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…

Applying Global Self-attention (GSA) mechanism over features has achieved remarkable success on Convolutional Neural Networks (CNNs). However, it is not clear if Graph Convolutional Networks (GCNs) can similarly benefit from such a…

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…

We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…

This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…

This research introduces the Theory of Partial Symmetry Enforced Attention Decomposition (PSEAD), a new and rigorous group-theoretic framework designed to seamlessly integrate local symmetry awareness into the core architecture of…

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…

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,…

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…

Self-attention mechanisms, especially multi-head self-attention (MSA), have achieved great success in many fields such as computer vision and natural language processing. However, many existing vision transformer (ViT) works simply inherent…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

Attention mechanism has gained great success in vision recognition. Many works are devoted to improving the effectiveness of attention mechanism, which finely design the structure of the attention operator. These works need lots of…

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-attention (SA) network has shown profound value in image captioning. In this paper, we improve SA from two aspects to promote the performance of image captioning. First, we propose Normalized Self-Attention (NSA), a reparameterization…

Shift equivariance is a fundamental principle that governs how we perceive the world - our recognition of an object remains invariant with respect to shifts. Transformers have gained immense popularity due to their effectiveness in both…

This paper deals with the design of globally exponentially stable invariant observers on the Special Euclidian group SE(3). First, we propose a generic hybrid observer scheme (depending on a generic potential function) evolving on…

There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…

Group equivariance is a strong inductive bias useful in a wide range of deep learning tasks. However, constructing efficient equivariant networks for general groups and domains is difficult. Recent work by Finzi et al. (2021) directly…