# Automatic Data Augmentation via Invariance-Constrained Learning

arXiv: https://arxiv.org/abs/2209.15031 · HTML: https://mlsanity.com/paper/2209.15031/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 89 references that are in the map.
- First posted on arXiv 29 Sep 2022.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Fast AutoAugment](https://mlsanity.com/paper/1905.00397/) (2019)
- [TrivialAugment: Tuning-free Yet State-of-the-Art Data Augmentation](https://mlsanity.com/paper/2103.10158/) (2021)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Population Based Augmentation: Efficient Learning of Augmentation Policy Schedules](https://mlsanity.com/paper/1905.05393/) (2019)
- [Adversarial AutoAugment](https://mlsanity.com/paper/1912.11188/) (2019)
- [Model-Based Domain Generalization](https://mlsanity.com/paper/2102.11436/) (2021)
- [Faster AutoAugment: Learning Augmentation Strategies using Backpropagation](https://mlsanity.com/paper/1911.06987/) (2019)
- [Towards Principled Disentanglement for Domain Generalization](https://mlsanity.com/paper/2111.13839/) (2021)
- [On the Benefits of Invariance in Neural Networks](https://mlsanity.com/paper/2005.00178/) (2020)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Meta-Learning Symmetries by Reparameterization](https://mlsanity.com/paper/2007.02933/) (2020)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [Semantic Adversarial Attacks: Parametric Transformations That Fool Deep Classifiers](https://mlsanity.com/paper/1904.08489/) (2019)
- [DADA: Differentiable Automatic Data Augmentation](https://mlsanity.com/paper/2003.03780/) (2020)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)

## Built on by (most cited first, 17 of 17)

- [Fourier-basis Functions to Bridge Augmentation Gap: Rethinking Frequency Augmentation in Image Classification](https://mlsanity.com/paper/2403.01944/) (2024)
- [Resilient Constrained Learning](https://mlsanity.com/paper/2306.02426/) (2023)
- [Balancing Act: Constraining Disparate Impact in Sparse Models](https://mlsanity.com/paper/2310.20673/) (2023)
- [Data Optimization in Deep Learning: A Survey](https://mlsanity.com/paper/2310.16499/) (2023)
- [Position: Adopt Constraints Over Fixed Penalties in Deep Learning](https://mlsanity.com/paper/2505.20628/) (2025)
- [Sample-aware RandAugment: Search-free Automatic Data Augmentation for Effective Image Recognition](https://mlsanity.com/paper/2508.08004/) (2025)
- [Competitive Distillation: A Simple Learning Strategy for Improving Visual Classification](https://mlsanity.com/paper/2506.23285/) (2025)
- [Solving Differential Equations with Constrained Learning](https://mlsanity.com/paper/2410.22796/) (2024)
- [Learning Tree-Structured Composition of Data Augmentation](https://mlsanity.com/paper/2408.14381/) (2024)
- [Optimizing Data Augmentation through Bayesian Model Selection](https://mlsanity.com/paper/2505.21813/) (2025)
- [Dual Optimistic Ascent (PI Control) is the Augmented Lagrangian Method in Disguise](https://mlsanity.com/paper/2509.22500/) (2025)
- [RA-Det: Towards Universal Detection of AI-Generated Images via Robustness Asymmetry](https://mlsanity.com/paper/2603.01544/) (2026)
- [Sparse Data Augmentation for Optimization with Provable Guarantees](https://mlsanity.com/paper/2609.08133/) (2026)
- [Approximate Nullspace Augmented Finetuning for Robust Vision Transformers](https://mlsanity.com/paper/2403.10476/) (2024)
- [The geometry of invariant learning: an information-theoretic analysis of data augmentation and generalization](https://mlsanity.com/paper/2602.14423/) (2026)
- [Ctrl-A: Control-Driven Online Data Augmentation](https://mlsanity.com/paper/2603.21819/) (2026)
- [Waggle: Learning One Anonymous Local Law for Self-Organizing LLM Swarms](https://mlsanity.com/paper/2609.34136/) (2026)

## Abstract (arXiv)

Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and computationally intensive. Data augmentation, on the other hand, induces these symmetries during training by applying multiple transformations to the input data. Despite its ubiquity, its effectiveness depends on the choices of which transformations to apply, when to do so, and how often. In fact, there is both empirical and theoretical evidence that the indiscriminate use of data augmentation can introduce biases that outweigh its benefits. This work tackles these issues by automatically adapting the data augmentation while solving the learning task. To do so, it formulates data augmentation as an invariance-constrained learning problem and leverages Monte Carlo Markov Chain (MCMC) sampling to solve it. The result is a practical algorithm that not only does away with a priori searches for augmentation distributions, but also dynamically controls if and when data augmentation is applied. Our experiments illustrate the performance of this method, which achieves state-of-the-art results in automatic data augmentation benchmarks for CIFAR datasets. Furthermore, this approach can be used to gather insights on the actual symmetries underlying a learning task.