# Offset equivariant networks and their applications

arXiv: https://arxiv.org/abs/2207.00292 · HTML: https://mlsanity.com/paper/2207.00292/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Deep Image Harmonization](https://mlsanity.com/paper/1703.00069/) (2017)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Deep Multi-View Enhancement Hashing for Image Retrieval](https://mlsanity.com/paper/2002.00169/) (2020)
- [Color Constancy Using CNNs](https://mlsanity.com/paper/1504.04548/) (2015)
- [Depth image denoising using nuclear norm and learning graph model](https://mlsanity.com/paper/2008.03741/) (2020)
- [Approaching the Computational Color Constancy as a Classification Problem through Deep Learning](https://mlsanity.com/paper/1608.07951/) (2016)
- [Color Cerberus](https://mlsanity.com/paper/1907.06483/) (2019)

## Built on by (most cited first, 6 of 6)

- [Color Equivariant Convolutional Networks](https://mlsanity.com/paper/2310.19368/) (2023)
- [Loss it right: Euclidean and Riemannian Metrics in Learning-based Visual Odometry](https://mlsanity.com/paper/2401.05396/) (2023)
- [Monocular visual simultaneous localization and mapping: (r)evolution from geometry to deep learning-based pipelines](https://mlsanity.com/paper/2503.02955/) (2025)
- [DUET: 2D Structured and Approximately Equivariant Representations](https://mlsanity.com/paper/2306.16058/) (2023)
- [Normalize Filters! Classical Wisdom for Deep Vision](https://mlsanity.com/paper/2506.04401/) (2025)
- [Log NeRF: Comparing Spaces for Learning Radiance Fields](https://mlsanity.com/paper/2512.09375/) (2025)

## Abstract (arXiv)

In this paper we present a framework for the design and implementation of offset equivariant networks, that is, neural networks that preserve in their output uniform increments in the input. In a suitable color space this kind of networks achieves equivariance with respect to the photometric transformations that characterize changes in the lighting conditions. We verified the framework on three different problems: image recognition, illuminant estimation, and image inpainting. Our experiments show that the performance of offset equivariant networks are comparable to those in the state of the art on regular data. Differently from conventional networks, however, equivariant networks do behave consistently well when the color of the illuminant changes.