# MixUp as Directional Adversarial Training

arXiv: https://arxiv.org/abs/1906.06875 · HTML: https://mlsanity.com/paper/1906.06875/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2019.

## Built on by (most cited first, 14 of 14)

- [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)
- [Towards Understanding the Data Dependency of Mixup-style Training](https://mlsanity.com/paper/2110.07647/) (2021)
- [TGDM: Target Guided Dynamic Mixup for Cross-Domain Few-Shot Learning](https://mlsanity.com/paper/2210.05392/) (2022)
- [Over-training with Mixup May Hurt Generalization](https://mlsanity.com/paper/2303.01475/) (2023)
- [Semi-supervised Semantics-guided Adversarial Training for Trajectory Prediction](https://mlsanity.com/paper/2205.14230/) (2022)
- [MixACM: Mixup-Based Robustness Transfer via Distillation of Activated Channel Maps](https://mlsanity.com/paper/2111.05073/) (2021)
- [Interdisciplinary Fairness in Imbalanced Research Proposal Topic Inference: A Hierarchical Transformer-based Method with Selective Interpolation](https://mlsanity.com/paper/2309.01717/) (2023)
- [Adversarially Optimized Mixup for Robust Classification](https://mlsanity.com/paper/2103.11589/) (2021)
- [Midpoint Regularization: from High Uncertainty Training to Conservative Classification](https://mlsanity.com/paper/2106.13913/) (2021)
- [Adversarial Mixing Policy for Relaxing Locally Linear Constraints in Mixup](https://mlsanity.com/paper/2109.07177/) (2021)
- [Hierarchical MixUp Multi-label Classification with Imbalanced Interdisciplinary Research Proposals](https://mlsanity.com/paper/2209.13912/) (2022)
- [A Diversity-Enhanced and Constraints-Relaxed Augmentation for Low-Resource Classification](https://mlsanity.com/paper/2109.11834/) (2021)
- [On the Equivalence of Graph Convolution and Mixup](https://mlsanity.com/paper/2310.00183/) (2023)

## Abstract (arXiv)

In this work, we explain the working mechanism of MixUp in terms of adversarial training. We introduce a new class of adversarial training schemes, which we refer to as directional adversarial training, or DAT. In a nutshell, a DAT scheme perturbs a training example in the direction of another example but keeps its original label as the training target. We prove that MixUp is equivalent to a special subclass of DAT, in that it has the same expected loss function and corresponds to the same optimization problem asymptotically. This understanding not only serves to explain the effectiveness of MixUp, but also reveals a more general family of MixUp schemes, which we call Untied MixUp. We prove that the family of Untied MixUp schemes is equivalent to the entire class of DAT schemes. We establish empirically the existence of Untied Mixup schemes which improve upon MixUp.