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In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest.…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

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…

This work introduces a novel approach to achieving architecture-agnostic equivariance in deep learning, particularly addressing the limitations of traditional layerwise equivariant architectures and the inefficiencies of the existing…

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to…

Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…

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…

Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly…

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…

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

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…

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…