Machine learning has been heavily researched and widely used in many disciplines.
However, achieving high accuracy requires a large amount of data that is sometimes …

One of the main challenges in machine vision relates to the problem of obtaining robust
representation of visual features that remain unaffected by geometric transformations. This …

Modern neural networks use building blocks such as convolutions that are equivariant to
arbitrary 2 D translations. However, these vanilla blocks are not equivariant to arbitrary 3 D …

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs)
on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these …

Incorporating symmetry as an inductive bias into neural network architecture has led to
improvements in generalization, data efficiency, and physical consistency in dynamics …

Recent work has shown deep learning can accelerate the prediction of physical dynamics
relative to numerical solvers. However, limited physical accuracy and an inability to …

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially
attributed to their built-in property of translation equivariance. However, CNNs do not have …

Modeling complex physical dynamics is a fundamental task in science and engineering.
Traditional physics-based models are sample efficient, and interpretable but often rely on …

Motivated by the vast success of deep convolutional networks, there is a great interest in
generalizing convolutions to non-Euclidean manifolds. A major complication in comparison …

In computer vision, models must be able to adapt to changes in image resolution to
effectively carry out tasks such as image segmentation; This is known as scale-equivariance …