Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy

Eleanor Quint

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arXiv · 2605.01632

Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy

Eleanor Quint

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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.

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Eleanor Quint. 2026-05-02. Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy. https://arxiv.org/abs/2605.01632

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