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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…
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…
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…
Data-sparse settings such as robotic manipulation, molecular physics, and galaxy morphology classification are some of the hardest domains for deep learning. For these problems, equivariant networks can help improve modeling across…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…
Numerous invariant (or equivariant) neural networks have succeeded in handling invariant data such as point clouds and graphs. However, a generalization theory for the neural networks has not been well developed, because several essential…
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…
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…
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…
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…
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…
Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
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…
Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same…
The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…