# MixUp as Locally Linear Out-Of-Manifold Regularization

arXiv: https://arxiv.org/abs/1809.02499 · HTML: https://mlsanity.com/paper/1809.02499/

## Key facts

- Cited by 158 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2018.

## Built on by (most cited first, 30 of 158)

- [Unbiased Teacher for Semi-Supervised Object Detection](https://mlsanity.com/paper/2102.09480/) (2021)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Co-Mixup: Saliency Guided Joint Mixup with Supermodular Diversity](https://mlsanity.com/paper/2102.03065/) (2021)
- [Mix3D: Out-of-Context Data Augmentation for 3D Scenes](https://mlsanity.com/paper/2110.02210/) (2021)
- [Open Domain Generalization with Domain-Augmented Meta-Learning](https://mlsanity.com/paper/2104.03620/) (2021)
- [SynFace: Face Recognition with Synthetic Data](https://mlsanity.com/paper/2108.07960/) (2021)
- [Amplitude-Phase Recombination: Rethinking Robustness of Convolutional Neural Networks in Frequency Domain](https://mlsanity.com/paper/2108.08487/) (2021)
- [PointCutMix: Regularization Strategy for Point Cloud Classification](https://mlsanity.com/paper/2101.01461/) (2021)
- [Unbiased Teacher v2: Semi-supervised Object Detection for Anchor-free and Anchor-based Detectors](https://mlsanity.com/paper/2206.09500/) (2022)
- [Mixture Outlier Exposure: Towards Out-of-Distribution Detection in Fine-grained Environments](https://mlsanity.com/paper/2106.03917/) (2021)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [SODA10M: A Large-Scale 2D Self/Semi-Supervised Object Detection Dataset for Autonomous Driving](https://mlsanity.com/paper/2106.11118/) (2021)
- [Qimera: Data-free Quantization with Synthetic Boundary Supporting Samples](https://mlsanity.com/paper/2111.02625/) (2021)
- [AlignMixup: Improving Representations By Interpolating Aligned Features](https://mlsanity.com/paper/2103.15375/) (2021)
- [MixMo: Mixing Multiple Inputs for Multiple Outputs via Deep Subnetworks](https://mlsanity.com/paper/2103.06132/) (2021)
- [On the Calibration of Pre-trained Language Models using Mixup Guided by Area Under the Margin and Saliency](https://mlsanity.com/paper/2203.07559/) (2022)
- [A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainability](https://mlsanity.com/paper/2212.10888/) (2022)
- [Graph Transplant: Node Saliency-Guided Graph Mixup with Local Structure Preservation](https://mlsanity.com/paper/2111.05639/) (2021)
- [CUDA: Curriculum of Data Augmentation for Long-Tailed Recognition](https://mlsanity.com/paper/2302.05499/) (2023)
- [Defending Against Image Corruptions Through Adversarial Augmentations](https://mlsanity.com/paper/2104.01086/) (2021)
- [Survey: Image Mixing and Deleting for Data Augmentation](https://mlsanity.com/paper/2106.07085/) (2021)
- [Exploring Color Invariance through Image-Level Ensemble Learning](https://mlsanity.com/paper/2401.10512/) (2024)
- [Medical Image Segmentation with Limited Supervision: A Review of Deep Network Models](https://mlsanity.com/paper/2103.00429/) (2021)
- [Balanced Product of Calibrated Experts for Long-Tailed Recognition](https://mlsanity.com/paper/2206.05260/) (2022)
- [A Survey on Mixup Augmentations and Beyond](https://mlsanity.com/paper/2409.05202/) (2024)
- [Salient Objects in Clutter](https://mlsanity.com/paper/2105.03053/) (2021)
- [Towards Understanding the Data Dependency of Mixup-style Training](https://mlsanity.com/paper/2110.07647/) (2021)
- [RankMixup: Ranking-Based Mixup Training for Network Calibration](https://mlsanity.com/paper/2308.11990/) (2023)
- [A Ranking Game for Imitation Learning](https://mlsanity.com/paper/2202.03481/) (2022)

## Abstract (arXiv)

MixUp is a recently proposed data-augmentation scheme, which linearly interpolates a random pair of training examples and correspondingly the one-hot representations of their labels. Training deep neural networks with such additional data is shown capable of significantly improving the predictive accuracy of the current art. The power of MixUp, however, is primarily established empirically and its working and effectiveness have not been explained in any depth. In this paper, we develop an understanding for MixUp as a form of "out-of-manifold regularization", which imposes certain "local linearity" constraints on the model's input space beyond the data manifold. This analysis enables us to identify a limitation of MixUp, which we call "manifold intrusion". In a nutshell, manifold intrusion in MixUp is a form of under-fitting resulting from conflicts between the synthetic labels of the mixed-up examples and the labels of original training data. Such a phenomenon usually happens when the parameters controlling the generation of mixing policies are not sufficiently fine-tuned on the training data. To address this issue, we propose a novel adaptive version of MixUp, where the mixing policies are automatically learned from the data using an additional network and objective function designed to avoid manifold intrusion. The proposed regularizer, AdaMixUp, is empirically evaluated on several benchmark datasets. Extensive experiments demonstrate that AdaMixUp improves upon MixUp when applied to the current art of deep classification models.