# DC4L: Distribution Shift Recovery via Data-Driven Control for Deep Learning Models

arXiv: https://arxiv.org/abs/2302.10341 · HTML: https://mlsanity.com/paper/2302.10341/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Learning Enriched Features for Real Image Restoration and Enhancement](https://mlsanity.com/paper/2003.06792/) (2020)
- [Puzzle Mix: Exploiting Saliency and Local Statistics for Optimal Mixup](https://mlsanity.com/paper/2009.06962/) (2020)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Test-Time Training with Masked Autoencoders](https://mlsanity.com/paper/2209.07522/) (2022)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Learning Enriched Features for Fast Image Restoration and Enhancement](https://mlsanity.com/paper/2205.01649/) (2022)
- [Deep Image Deblurring: A Survey](https://mlsanity.com/paper/2201.10700/) (2022)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [Test-Time Adaptation to Distribution Shift by Confidence Maximization and Input Transformation](https://mlsanity.com/paper/2106.14999/) (2021)
- [Greedy Policy Search: A Simple Baseline for Learnable Test-Time Augmentation](https://mlsanity.com/paper/2002.09103/) (2020)
- [Learning Loss for Test-Time Augmentation](https://mlsanity.com/paper/2010.11422/) (2020)
- [Why do classifier accuracies show linear trends under distribution shift?](https://mlsanity.com/paper/2012.15483/) (2020)

## Built on by (most cited first, 7 of 7)

- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [IBCL: Zero-shot Model Generation under Stability-Plasticity Trade-offs](https://mlsanity.com/paper/2305.14782/) (2023)
- [Imprecise Markov Semigroups and their Ergodicity](https://mlsanity.com/paper/2405.00081/) (2024)
- [AR-Pro: Counterfactual Explanations for Anomaly Repair with Formal Properties](https://mlsanity.com/paper/2410.24178/) (2024)
- [Lights out: training RL agents robust to temporary blindness](https://mlsanity.com/paper/2312.02665/) (2023)
- [Optimal Transport for ε-Contaminated Credal Sets: To the Memory of Sayan Mukherjee](https://mlsanity.com/paper/2410.03267/) (2024)
- [Monitor and Recover: A Paradigm for Future Research on Distribution Shift in Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2504.13484/) (2025)

## Abstract (arXiv)

Deep neural networks have repeatedly been shown to be non-robust to the uncertainties of the real world, even to naturally occurring ones. A vast majority of current approaches have focused on data-augmentation methods to expand the range of perturbations that the classifier is exposed to while training. A relatively unexplored avenue that is equally promising involves sanitizing an image as a preprocessing step, depending on the nature of perturbation. In this paper, we propose to use control for learned models to recover from distribution shifts online. Specifically, our method applies a sequence of semantic-preserving transformations to bring the shifted data closer in distribution to the training set, as measured by the Wasserstein distance. Our approach is to 1) formulate the problem of distribution shift recovery as a Markov decision process, which we solve using reinforcement learning, 2) identify a minimum condition on the data for our method to be applied, which we check online using a binary classifier, and 3) employ dimensionality reduction through orthonormal projection to aid in our estimates of the Wasserstein distance. We provide theoretical evidence that orthonormal projection preserves characteristics of the data at the distributional level. We apply our distribution shift recovery approach to the ImageNet-C benchmark for distribution shifts, demonstrating an improvement in average accuracy of up to 14.21% across a variety of state-of-the-art ImageNet classifiers. We further show that our method generalizes to composites of shifts from the ImageNet-C benchmark, achieving improvements in average accuracy of up to 9.81%. Finally, we test our method on CIFAR-100-C and report improvements of up to 8.25%.