# Confounder-Free Continual Learning via Recursive Feature Normalization

arXiv: https://arxiv.org/abs/2507.09031 · HTML: https://mlsanity.com/paper/2507.09031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 76 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Hidden Stratification Causes Clinically Meaningful Failures in Machine Learning for Medical Imaging](https://mlsanity.com/paper/1909.12475/) (2019)
- [CheXclusion: Fairness gaps in deep chest X-ray classifiers](https://mlsanity.com/paper/2003.00827/) (2020)
- [Ethical Machine Learning in Health Care](https://mlsanity.com/paper/2009.10576/) (2020)
- [EnD: Entangling and Disentangling deep representations for bias correction](https://mlsanity.com/paper/2103.02023/) (2021)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [On the Global Optima of Kernelized Adversarial Representation Learning](https://mlsanity.com/paper/1910.07423/) (2019)
- [Metadata Normalization](https://mlsanity.com/paper/2104.09052/) (2021)
- [BiasPruner: Debiased Continual Learning for Medical Image Classification](https://mlsanity.com/paper/2407.08609/) (2024)
- [A Penalty Approach for Normalizing Feature Distributions to Build Confounder-Free Models](https://mlsanity.com/paper/2207.04607/) (2022)
- [Representation Learning with Statistical Independence to Mitigate Bias](https://mlsanity.com/paper/1910.03676/) (2019)
- [Projection-wise Disentangling for Fair and Interpretable Representation Learning: Application to 3D Facial Shape Analysis](https://mlsanity.com/paper/2106.13734/) (2021)
- [RegBN: Batch Normalization of Multimodal Data with Regularization](https://mlsanity.com/paper/2310.00641/) (2023)
- [Combining Counterfactuals With Shapley Values To Explain Image Models](https://mlsanity.com/paper/2206.07087/) (2022)
- [Bridging the Generalization Gap: Training Robust Models on Confounded Biological Data](https://mlsanity.com/paper/1812.04778/) (2018)
- [Measuring the effects of confounders in medical supervised classification problems: the Confounding Index (CI)](https://mlsanity.com/paper/1905.08871/) (2019)

## Abstract (arXiv)

Confounders are extraneous variables that affect both the input and the target, resulting in spurious correlations and biased predictions. There are recent advances in dealing with or removing confounders in traditional models, such as metadata normalization (MDN), where the distribution of the learned features is adjusted based on the study confounders. However, in the context of continual learning, where a model learns continuously from new data over time without forgetting, learning feature representations that are invariant to confounders remains a significant challenge. To remove their influence from intermediate feature representations, we introduce the Recursive MDN (R-MDN) layer, which can be integrated into any deep learning architecture, including vision transformers, and at any model stage. R-MDN performs statistical regression via the recursive least squares algorithm to maintain and continually update an internal model state with respect to changing distributions of data and confounding variables. Our experiments demonstrate that R-MDN promotes equitable predictions across population groups, both within static learning and across different stages of continual learning, by reducing catastrophic forgetting caused by confounder effects changing over time.