# Unlearning as Distribution Restoration: A Controlled Counterfactual Study, a Validated Selective Screen, and the Limits of Oracle-Free Certification

arXiv: https://arxiv.org/abs/2607.19442 · HTML: https://mlsanity.com/paper/2607.19442/

## 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 26 of its 27 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Memory-Based Model Editing at Scale](https://mlsanity.com/paper/2206.06520/) (2022)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Machine Unlearning of Pre-trained Large Language Models](https://mlsanity.com/paper/2402.15159/) (2024)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [OpenUnlearning: Accelerating LLM Unlearning via Unified Benchmarking of Methods and Metrics](https://mlsanity.com/paper/2506.12618/) (2025)
- [Revisiting Who's Harry Potter: Towards Targeted Unlearning from a Causal Intervention Perspective](https://mlsanity.com/paper/2407.16997/) (2024)
- [Does Unlearning Truly Unlearn? A Black Box Evaluation of LLM Unlearning Methods](https://mlsanity.com/paper/2411.12103/) (2024)

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

- [Certified Mechanistic Edits: Behavioral Guarantees for Skill Removal and Preservation](https://mlsanity.com/paper/2610.03502/) (2026)

## Abstract (arXiv)

Machine unlearning is commonly evaluated by matching a retrained oracle on trained probes. In a controlled nonce-fact testbed with a matched retraining reference, we find this criterion can favor methods that retain held-out knowledge: candidates it rates adequate score held-out forget facts -2.82 nats below the never-learned level (cluster CI [-3.16,-2.48]). We recast unlearning as restoration to the matched reference and audit oracle-free screens and certificate-style criteria across 45 model-seed cells spanning five open architecture families. The reference itself falsifies an absolute retain/round-trip certificate: the injected model, which retains the retain set by construction, fails the fixed retain threshold in 41/45 cells and its own round trip in 31/45, and the reference fully certifies in only 1/45. A base-anchored held-out screen remains strong as a selective necessary test: on a sealed challenge suite it rejects the injected model in 45/45 cells, accepts the reference in 44/45, and partially detects entity-routing suppression (35/45); it is a necessary test with measured sensitivity, not a sufficiency certificate. A damage-relative recalibration anchored to the reference's own operating point certifies a small subset in 15/45 cells; where it does not abstain, its picks lie within retraining noise (0.80 nats) on the axes it optimizes, while the common trained-probe criterion sits 5.17 nats away (a supporting comparison, not a head-to-head benchmark). A fixed-magnitude logit-suppression attack defeats the full forward battery in 12/45 cells, so forward-only certification is not sound; our method is an empirical selective test for methods-as-produced. An identifiability theorem delimits which facts admit an oracle-free forget threshold at all, with TOFU as the predicted boundary case.