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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…

Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…

Equivariance guarantees that a model's predictions capture key symmetries in data. When an image is translated or rotated, an equivariant model's representation of that image will translate or rotate accordingly. The success of…

Adversarial examples reveal critical vulnerabilities in deep neural networks by exploiting their sensitivity to imperceptible input perturbations. While adversarial training remains the predominant defense strategy, it often incurs…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain…

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…

We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…

A current challenge in atomistic machine learning is that of efficiently predicting the response of the electron density under electric fields. We address this challenge with symmetry-adapted kernel functions that are specifically derived…

Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality…

This paper presents an equivariant reinforcement learning framework for quadrotor unmanned aerial vehicles. Successful training of reinforcement learning often requires numerous interactions with the environments, which hinders its…

In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to…

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…

While end-to-end approaches have achieved state-of-the-art performance in many perception tasks, they are not yet able to compete with 3D geometry-based methods in pose estimation. Moreover, absolute pose regression has been shown to be…

It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of…

Recent work in reinforcement learning has leveraged symmetries in the model to improve sample efficiency in training a policy. A commonly used simplifying assumption is that the dynamics and reward both exhibit the same symmetry; however,…

Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…

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…

Multirotors flying in close proximity induce aerodynamic wake effects on each other through propeller downwash. Conventional methods have fallen short of providing adequate 3D force-based models that can be incorporated into robust control…