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The Strengths and Limitations of Equivariant Neural Networks

The Strengths and Limitations of Equivariant Neural Networks

Deep learning has had transformative impacts in many fields in recent years, yet there remain serious challenges to future progress: deep models require vast datasets to train, can fail to generalize under surprisingly small changes in domain, and lack trustworthiness; moreover, we lack guarantees and fundamental understanding of their characteristics. Incorporating symmetry constraints into neural networks using representation theoretic methods has resulted in models called equivariant neural networks (ENN) which have gone far in addressing these challenges. I will discuss several recent success stories using ENNs for dynamics applications, such as trajectory prediction for autonomous vehicles, ocean currents, and robotics. However, there are also limits to the effectiveness of the current generation of ENNs. In many applications where symmetry is only approximate or does apply across the entire input distribution, equivariance may not be the correct inductive bias to aid learning and may even hurt model performance. I will discuss recent work theoretically characterizing errors that can result from mismatched symmetry biases which can be used for model selection. I will also suggest different methods for relaxing symmetry constraints so that approximately equivariant models can still be used in these situations.

## Department of Mathematics and Statistics