Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy

TL;DR

Perturb-and-Correct (P&C) is a post-hoc method that creates diverse predictors from a single pretrained network by applying hidden layer perturbations and affine corrections, improving out-of-distribution performance.

Contribution

The paper introduces P&C, a novel post-hoc ensemble technique that leverages affine redundancy to enhance epistemic diversity and OOD detection without retraining models.

Findings

P&C achieves a strong ID/OOD tradeoff in dynamics prediction and OOD detection.

It matches or outperforms standard post-hoc baselines using only a single pretrained model.

The method exploits overparameterization to improve model robustness.

Abstract

Models that are 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 subsequent 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 and its first-order sensitivity: the residual is controlled near the calibration distribution by a leverage term, while corrected sensitivity grows as inputs deviate from the calibration geometry. Empirically, P&C achieves a strong ID/OOD tradeoff across MuJoCo dynamics prediction and CIFAR-10 OOD detection, matching or outperforming standard post-hoc baselines while requiring only a single pretrained model. Our findings highlight the potential in further exploiting overparameterization as a strength of deep learning models.