# Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy

arXiv: https://arxiv.org/abs/2605.01632 · HTML: https://mlsanity.com/paper/2605.01632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Masksembles for Uncertainty Estimation](https://mlsanity.com/paper/2012.08334/) (2020)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [Adversarial vulnerability for any classifier](https://mlsanity.com/paper/1802.08686/) (2018)
- [Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks](https://mlsanity.com/paper/2102.12567/) (2021)

## Abstract (arXiv)

Models that are nearly indistinguishable on in-distribution data can behave very differently under distribution shift. We introduce Perturb-and-Correct (P&C), a post-hoc method for constructing epistemically diverse predictors from a single pretrained network. P&C applies random hidden-layer perturbations with a least-squares correction in the following affine layer, producing predictors that agree on calibration data while remaining free to disagree away from it. We analyze this mechanism through the post-correction residual that remains in the activation of the layer corrected using calibration data, yielding a leverage-based preservation bound and a covariance interpretation of ensemble disagreement. Empirically, P&C achieves a strong ID/OOD tradeoff across MuJoCo dynamics prediction and CIFAR-10 OOD detection, and scales to a pretrained ViT-B/16 on ImageNet-1K. In matched comparisons with Deep Ensembles, P&C substantially reduces construction and storage cost. Our findings highlight the potential in further exploiting overparameterization as a strength of deep learning models.