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

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…

Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node…

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…

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…

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…

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…

Many machine learning tasks in the natural sciences are precisely equivariant to particular symmetries. Nonetheless, equivariant methods are often not employed, perhaps because training is perceived to be challenging, or the symmetry is…

Image-level weakly supervised semantic segmentation is a challenging problem that has been deeply studied in recent years. Most of advanced solutions exploit class activation map (CAM). However, CAMs can hardly serve as the object mask due…

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with…

We prove an impossibility result, which in the context of function learning says the following: under certain conditions, it is impossible to simultaneously learn symmetries and functions equivariant under them using an ansatz consisting of…

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant…

This paper presents an equivariant filter (EqF) transformation approach for visual--inertial navigation. By establishing analytical links between EqFs with different symmetries, the proposed approach enables systematic consistency design…

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for…

Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…

In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on…

Self-attention mechanism has been widely used for various tasks. It is designed to compute the representation of each position by a weighted sum of the features at all positions. Thus, it can capture long-range relations for computer vision…

This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…

Although equivariant machine learning has proven effective at many tasks, success depends heavily on the assumption that the ground truth function is symmetric over the entire domain matching the symmetry in an equivariant neural network. A…