# Semantic Equivariant Mixup

arXiv: https://arxiv.org/abs/2308.06451 · HTML: https://mlsanity.com/paper/2308.06451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 57 references that are in the map.
- First posted on arXiv 12 Aug 2023.

## Builds on (most cited first, 30 of 42)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Puzzle Mix: Exploiting Saliency and Local Statistics for Optimal Mixup](https://mlsanity.com/paper/2009.06962/) (2020)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Do CIFAR-10 Classifiers Generalize to CIFAR-10?](https://mlsanity.com/paper/1806.00451/) (2018)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [SaliencyMix: A Saliency Guided Data Augmentation Strategy for Better Regularization](https://mlsanity.com/paper/2006.01791/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Equivariant Contrastive Learning](https://mlsanity.com/paper/2111.00899/) (2021)

## Abstract (arXiv)

Mixup is a well-established data augmentation technique, which can extend the training distribution and regularize the neural networks by creating ''mixed'' samples based on the label-equivariance assumption, i.e., a proportional mixup of the input data results in the corresponding labels being mixed in the same proportion. However, previous mixup variants may fail to exploit the label-independent information in mixed samples during training, which usually contains richer semantic information. To further release the power of mixup, we first improve the previous label-equivariance assumption by the semantic-equivariance assumption, which states that the proportional mixup of the input data should lead to the corresponding representation being mixed in the same proportion. Then a generic mixup regularization at the representation level is proposed, which can further regularize the model with the semantic information in mixed samples. At a high level, the proposed semantic equivariant mixup (sem) encourages the structure of the input data to be preserved in the representation space, i.e., the change of input will result in the obtained representation information changing in the same way. Different from previous mixup variants, which tend to over-focus on the label-related information, the proposed method aims to preserve richer semantic information in the input with semantic-equivariance assumption, thereby improving the robustness of the model against distribution shifts. We conduct extensive empirical studies and qualitative analyzes to demonstrate the effectiveness of our proposed method. The code of the manuscript is in the supplement.