# Adversarial Mixing Policy for Relaxing Locally Linear Constraints in Mixup

arXiv: https://arxiv.org/abs/2109.07177 · HTML: https://mlsanity.com/paper/2109.07177/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [EDA: Easy Data Augmentation Techniques for Boosting Performance on Text Classification Tasks](https://mlsanity.com/paper/1901.11196/) (2019)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [Adversarial Training Methods for Semi-Supervised Text Classification](https://mlsanity.com/paper/1605.07725/) (2016)
- [Adversarial Domain Adaptation with Domain Mixup](https://mlsanity.com/paper/1912.01805/) (2019)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [Augmenting Data with Mixup for Sentence Classification: An Empirical Study](https://mlsanity.com/paper/1905.08941/) (2019)
- [Adversarial Vertex Mixup: Toward Better Adversarially Robust Generalization](https://mlsanity.com/paper/2003.02484/) (2020)
- [Data augmentation instead of explicit regularization](https://mlsanity.com/paper/1806.03852/) (2018)
- [Distributional Smoothing with Virtual Adversarial Training](https://mlsanity.com/paper/1507.00677/) (2015)
- [Mixup Inference: Better Exploiting Mixup to Defend Adversarial Attacks](https://mlsanity.com/paper/1909.11515/) (2019)
- [SeqMix: Augmenting Active Sequence Labeling via Sequence Mixup](https://mlsanity.com/paper/2010.02322/) (2020)
- [Fine-grained Sentiment Classification using BERT](https://mlsanity.com/paper/1910.03474/) (2019)
- [Virtual Mixup Training for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1905.04215/) (2019)
- [MetaMixUp: Learning Adaptive Interpolation Policy of MixUp with Meta-Learning](https://mlsanity.com/paper/1908.10059/) (2019)
- [Mixup-Transformer: Dynamic Data Augmentation for NLP Tasks](https://mlsanity.com/paper/2010.02394/) (2020)
- [MixUp as Directional Adversarial Training](https://mlsanity.com/paper/1906.06875/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainability](https://mlsanity.com/paper/2212.10888/) (2022)
- [A Survey on Mixup Augmentations and Beyond](https://mlsanity.com/paper/2409.05202/) (2024)
- [Enlightenment Period Improving DNN Performance](https://mlsanity.com/paper/2504.01737/) (2025)

## Abstract (arXiv)

Mixup is a recent regularizer for current deep classification networks. Through training a neural network on convex combinations of pairs of examples and their labels, it imposes locally linear constraints on the model's input space. However, such strict linear constraints often lead to under-fitting which degrades the effects of regularization. Noticeably, this issue is getting more serious when the resource is extremely limited. To address these issues, we propose the Adversarial Mixing Policy (AMP), organized in a min-max-rand formulation, to relax the Locally Linear Constraints in Mixup. Specifically, AMP adds a small adversarial perturbation to the mixing coefficients rather than the examples. Thus, slight non-linearity is injected in-between the synthetic examples and synthetic labels. By training on these data, the deep networks are further regularized, and thus achieve a lower predictive error rate. Experiments on five text classification benchmarks and five backbone models have empirically shown that our methods reduce the error rate over Mixup variants in a significant margin (up to 31.3%), especially in low-resource conditions (up to 17.5%).