# PURGE: Projected Unlearning via Retain-Guided Erasure

arXiv: https://arxiv.org/abs/2606.03808 · HTML: https://mlsanity.com/paper/2606.03808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [Mixed-Privacy Forgetting in Deep Networks](https://mlsanity.com/paper/2012.13431/) (2020)

## Built on by (most cited first, 1 of 1)

- [Published Unlearning Numbers Move Per Checkpoint, and Not Because the Removed Data Survives: An Audit of 263 Released Batch-Normalized Checkpoints](https://mlsanity.com/paper/2609.11490/) (2026)

## Abstract (arXiv)

We propose PURGE, a machine unlearning algorithm built on a simple but an under-exploited observation: continual learning (CL) and machine unlearning (MU) which are fundamentally dual problems. CL tries to learn new tasks without forgetting old ones; MU tries to erase specific data without hurting retained performance representing the same underlying tension in opposite directions. PURGE leverages this duality by adapting gradient projection from A-GEM (Chaudhry et al., 2019) so that every unlearning step is constrained to not increase the retain-set loss. On top of this, it performs multi-layer representation erasure, pushing forget-set activations in intermediate layers towards the retain distribution to remove information from hidden representations rather than just suppressing it at the output. A key design choice is the retain-confusion target: rather than pushing forget outputs toward the uniform distribution, which we found to be surprisingly easy for membership inference attacks to detect, we instead target the model's natural confusion pattern on retain data. This makes the unlearned model hard to distinguish from one retrained from scratch. Two self-regulating stopping criteria (a retain-loss budget and a forget-accuracy target) let the algorithm decide on its own when to stop, removing the need for manual epoch tuning. In experiments on five datasets (CIFAR-10, MNIST, SVHN, STL10, PathMNIST) across 22 class-level forgetting tasks, PURGE consistently keeps retain accuracy above 96% while achieving MIA AUROC close to 0.5 (the ideal), outperforming gradient ascent, KL-uniform, and several published baselines on the privacy-utility frontier.