---
title: "mixup: Beyond Empirical Risk Minimization — Zhang 2017"
description: "Deep networks trained under Empirical Risk Minimization (ERM) can memorize their training sets, even with random labels, and react unpredictably to…"
authors: ["Hongyi Zhang", "Moustapha Cisse", "Yann N. Dauphin", "David Lopez-Paz"]
year: 2017
venue: "arXiv:1710.09412"
source: "https://arxiv.org/abs/1710.09412"
doi: "10.48550/arxiv.1710.09412"
arxiv: "1710.09412"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhang-2017-mixup-empirical-risk-minimization/"
---
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# mixup: Beyond Empirical Risk Minimization

**Authors:** Hongyi Zhang, Moustapha Cisse, [Yann N. Dauphin](https://md.research.elamur.ai/free/en/authors/yann-n-dauphin/), [David Lopez-Paz](https://md.research.elamur.ai/free/en/authors/david-lopez-paz/) · **Year:** 2017 · **Venue:** arXiv:1710.09412 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1710.09412) · [PDF](https://arxiv.org/pdf/1710.09412) · [DOI 10.48550/arxiv.1710.09412](https://doi.org/10.48550/arxiv.1710.09412) · [arXiv 1710.09412](https://arxiv.org/abs/1710.09412) · [OpenAlex](https://openalex.org/W2765407302)

**Citations:** 4485 citations (openalex-snapshot · 2026-10-14) · [318](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
Deep networks trained under Empirical Risk Minimization (ERM) can memorize their training sets, even with random labels, and react unpredictably to inputs slightly outside the training distribution, such as adversarial examples. Standard data augmentation helps, but it depends on the dataset, needs expert-designed transformations, and never relates examples from different classes. The authors propose mixup, a data-agnostic form of Vicinal Risk Minimization. Each virtual training sample is a weighted blend of two random training inputs, and its target is the same blend of their one-hot labels. The mixing weight λ is drawn from Beta(α, α). This pushes the model toward linear behaviour between training points. It takes only a few lines of code and adds almost no compute. Experiments cover ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI tabular data. mixup consistently lowers error for state-of-the-art architectures. It also reduces memorization of corrupted labels, improves adversarial robustness and stabilizes GAN training. Its simplicity and generality make it a broadly applicable regularizer.

## Key points
- **Method:** λ ~ Beta(α, α), and ERM is recovered as α → 0. α = 0.2 was used for ResNet and α = 0.4 for ResNeXt on ImageNet-2012.
- **ImageNet-2012, 200 epochs:** top-1 error fell from 23.6 to 22.1 for ResNet-50 and from 21.3 to 20.1 for ResNeXt-101 32*4d.
- **CIFAR test error:** DenseNet-BC-190 dropped from 3.7 to 2.7 on CIFAR-10 and from 19.0 to 16.8 on CIFAR-100. PreAct ResNet-18 dropped from 25.6 to 21.1 on CIFAR-100.
- **Design choices:**
  - Mixing three or more examples (Dirichlet weights) gave no extra gain.
  - Mixing only same-label pairs lost the benefit.
  - Shuffling a single minibatch worked as well as using two data loaders.
- **Code:** CIFAR-10 replication code is available at github.com/facebookresearch/mixup-cifar10 (PyTorch).

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [Other](https://md.research.elamur.ai/free/en/shelves/other/)

## Cited by

Cited by

318 papers of our library cite it (of the 140673 whose bibliographies we read); 11 of them have a page here, 307 not yet.

- [Good-Enough Compositional Data Augmentation](https://md.research.elamur.ai/free/en/papers/andreas-2020-good-enough-compositional-data-augmentation/)
- [A Survey of Data Augmentation Approaches for NLP](https://md.research.elamur.ai/free/en/papers/feng-2021-survey-data-augmentation-approaches-nlp/)
- [Bias and Fairness in Large Language Models: A Survey](https://md.research.elamur.ai/free/en/papers/gallegos-2023-bias-fairness-large-language-models/)
- [Masked Autoencoders Are Scalable Vision Learners](https://md.research.elamur.ai/free/en/papers/he-2021-masked-autoencoders-scalable-vision-learners/)
- [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://md.research.elamur.ai/free/en/papers/kim-2021-vilt-vision-language-transformer-convolution/)
- [ERNIE 3.0: Large-scale Knowledge Enhanced Pre-training for Language Understanding and Generation](https://md.research.elamur.ai/free/en/papers/sun-2021-ernie-3-0-large/)
- [Training data-efficient image transformers & distillation through attention](https://md.research.elamur.ai/free/en/papers/touvron-2020-training-data-efficient-image-transformers/)
- [OFA: Unifying Architectures, Tasks, and Modalities Through a Simple Sequence-to-Sequence Learning Framework](https://md.research.elamur.ai/free/en/papers/wang-2022-ofa-unifying-architectures-tasks-modalities/)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://md.research.elamur.ai/free/en/papers/wortsman-2022-model-soups-averaging-weights-multiple/)
- [Unsupervised Data Augmentation for Consistency Training](https://md.research.elamur.ai/free/en/papers/xie-2019-unsupervised-data-augmentation-consistency-training/)
- [GPT3Mix: Leveraging Large-scale Language Models for Text Augmentation](https://md.research.elamur.ai/free/en/papers/yoo-2021-gpt3mix-leveraging-large-scale-language/)

## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{zhang2017mixup,
  title = {{mixup: Beyond Empirical Risk Minimization}},
  author = {Zhang, Hongyi and Cisse, Moustapha and Dauphin, Yann N. and Lopez-Paz, David},
  year = {2017},
  doi = {10.48550/arxiv.1710.09412},
  eprint = {1710.09412},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1710.09412}
}
```

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