# Restore Translation Using Equivariant Neural Networks

arXiv: https://arxiv.org/abs/2306.16938 · HTML: https://mlsanity.com/paper/2306.16938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 29 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Exploring the Landscape of Spatial Robustness](https://mlsanity.com/paper/1712.02779/) (2017)
- [Pooling Methods in Deep Neural Networks, a Review](https://mlsanity.com/paper/2009.07485/) (2020)
- [Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1411.6369/) (2014)
- [Learning Covariant Feature Detectors](https://mlsanity.com/paper/1605.01224/) (2016)
- [Warped Convolutions: Efficient Invariance to Spatial Transformations](https://mlsanity.com/paper/1609.04382/) (2016)
- [Scale Steerable Filters for Locally Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1906.03861/) (2019)
- [Scale equivariance in CNNs with vector fields](https://mlsanity.com/paper/1807.11783/) (2018)
- [Transform-Invariant Convolutional Neural Networks for Image Classification and Search](https://mlsanity.com/paper/1912.01447/) (2019)

## Abstract (arXiv)

Invariance to spatial transformations such as translations and rotations is a desirable property and a basic design principle for classification neural networks. However, the commonly used convolutional neural networks (CNNs) are actually very sensitive to even small translations. There exist vast works to achieve exact or approximate transformation invariance by designing transformation-invariant models or assessing the transformations. These works usually make changes to the standard CNNs and harm the performance on standard datasets. In this paper, rather than modifying the classifier, we propose a pre-classifier restorer to recover translated (or even rotated) inputs to the original ones which will be fed into any classifier for the same dataset. The restorer is based on a theoretical result which gives a sufficient and necessary condition for an affine operator to be translational equivariant on a tensor space.