# Meta-Learning Symmetries by Reparameterization

**Authors:** Allan Zhou, Tom Knowles, Chelsea Finn  
**arXiv:** [2007.02933](https://arxiv.org/abs/2007.02933)  
**Date:** 2020-07-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2007.02933v1/

## Key points

- Paper introduces a general approach for learning equivariances from data in deep learning architectures
- Equivariance refers to maintaining structure and parameters under certain transformations
- Traditionally, manual construction of architectures with known symmetries was required for equivariance
- Authors propose a method that can automatically learn and encode equivariances into networks without prior knowledge or custom architectures
- Method involves learning parameter sharing patterns from data to encode equivariance-inducing parameter sharing
- Experiments demonstrate the ability to learn a variety of equivariances from symmetries present in the data
- Experiment code and pre-trained models are provided on GitHub for further research and experimentation

## Summary

The paper titled "Meta-Learning Symmetries by Reparameterization" introduces a general approach for learning equivariances from data in deep learning architectures. Equivariance refers to the property of a model being able to maintain its structure and parameters under certain transformations, such as shifts or rotations. This property is crucial for improving generalization and parameter conservation. Traditionally, practitioners had to manually construct architectures with known symmetries of the task in order to achieve equivariance. However, this approach requires prior knowledge of the task's symmetries and custom task-specific architectures. The authors aim to overcome these limitations by proposing a method that can automatically learn and encode equivariances into networks without any prior knowledge of the symmetries or custom architectures. The proposed method involves learning parameter sharing patterns from data to encode equivariance-inducing parameter sharing. It can provably encode such parameter sharing for any finite group of symmetry transformations. Through experiments, the authors demonstrate that their method can automatically learn a variety of equivariances from symmetries present in the data. To facilitate further research and experimentation, the authors provide their experiment code and pre-trained models on GitHub. In summary, this paper presents a novel approach for learning equivariances from data in deep learning architectures which eliminates the need for prior knowledge of task symmetries or custom architectures. The proposed method enables automation by encoding equivariance-inducing parameter sharing patterns which can be used to effectively learn various equivariances from data symmetries thereby enhancing generalization and parameter conservation in deep learning models.