# Preventing Manifold Intrusion with Locality: Local Mixup

arXiv: https://arxiv.org/abs/2201.04368 · HTML: https://mlsanity.com/paper/2201.04368/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 12 Jan 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [A Baseline for Few-Shot Image Classification](https://mlsanity.com/paper/1909.02729/) (2019)
- [Puzzle Mix: Exploiting Saliency and Local Statistics for Optimal Mixup](https://mlsanity.com/paper/2009.06962/) (2020)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [Remix: Rebalanced Mixup](https://mlsanity.com/paper/2007.03943/) (2020)
- [Charting the Right Manifold: Manifold Mixup for Few-shot Learning](https://mlsanity.com/paper/1907.12087/) (2019)
- [On Mixup Regularization](https://mlsanity.com/paper/2006.06049/) (2020)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [MixMo: Mixing Multiple Inputs for Multiple Outputs via Deep Subnetworks](https://mlsanity.com/paper/2103.06132/) (2021)
- [CIFAR-10: KNN-based Ensemble of Classifiers](https://mlsanity.com/paper/1611.04905/) (2016)
- [k-Mixup Regularization for Deep Learning via Optimal Transport](https://mlsanity.com/paper/2106.02933/) (2021)
- [Enhancing Mixup-based Semi-Supervised Learning with Explicit Lipschitz Regularization](https://mlsanity.com/paper/2009.11416/) (2020)

## Built on by (most cited first, 11 of 11)

- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [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)
- [IPMix: Label-Preserving Data Augmentation Method for Training Robust Classifiers](https://mlsanity.com/paper/2310.04780/) (2023)
- [Anchor Data Augmentation](https://mlsanity.com/paper/2311.06965/) (2023)
- [Augment on Manifold: Mixup Regularization with UMAP](https://mlsanity.com/paper/2312.13141/) (2023)
- [SoftEdge: Regularizing Graph Classification with Random Soft Edges](https://mlsanity.com/paper/2204.10390/) (2022)
- [A Generalized Theory of Mixup for Structure-Preserving Synthetic Data](https://mlsanity.com/paper/2503.02645/) (2025)
- [SaVe-TAG: LLM-based Interpolation for Long-Tailed Text-Attributed Graphs](https://mlsanity.com/paper/2410.16882/) (2024)
- [LH-Mix: Local Hierarchy Correlation Guided Mixup over Hierarchical Prompt Tuning](https://mlsanity.com/paper/2412.16963/) (2024)
- [ID-MixGCL: Identity Mixup for Graph Contrastive Learning](https://mlsanity.com/paper/2304.10045/) (2023)

## Abstract (arXiv)

Mixup is a data-dependent regularization technique that consists in linearly interpolating input samples and associated outputs. It has been shown to improve accuracy when used to train on standard machine learning datasets. However, authors have pointed out that Mixup can produce out-of-distribution virtual samples and even contradictions in the augmented training set, potentially resulting in adversarial effects. In this paper, we introduce Local Mixup in which distant input samples are weighted down when computing the loss. In constrained settings we demonstrate that Local Mixup can create a trade-off between bias and variance, with the extreme cases reducing to vanilla training and classical Mixup. Using standardized computer vision benchmarks , we also show that Local Mixup can improve test accuracy.