Learning Layer-wise Equivariances Automatically using Gradients
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Date
2024-07
Publication Type
Conference Paper
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yes
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Abstract
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 can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients. Learning symmetry and associated weight connectivity structures from scratch is difficult for two reasons. First, it requires efficient and flexible parameterisations of layer-wise equivariances. Secondly, symmetries act as constraints and are therefore not encouraged by training losses measuring data fit. To overcome these challenges, we improve parameterisations of soft equivariance and learn the amount of equivariance in layers by optimising the marginal likelihood, estimated using differentiable Laplace approximations. The objective balances data fit and model complexity enabling layer-wise symmetry discovery in deep networks. We demonstrate the ability to automatically learn layer-wise equivariances on image classification tasks, achieving equivalent or improved performance over baselines with hard-coded symmetry.
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published
Book title
Advances in Neural Information Processing Systems 36
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Pages / Article No.
28365 - 28377
Publisher
Curran
Event
37th Annual Conference on Neural Information Processing Systems (NeurIPS 2023)
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09568 - Rätsch, Gunnar / Rätsch, Gunnar
Notes
Spotlight poster presented on December 13, 2023.
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Related publications and datasets
Is supplemented by: https://github.com/tychovdo/ellaIs new version of: https://openreview.net/forum?id=bNIHdyunFCIs new version of: 10.48550/arXiv.2310.06131