# Form and Function: Machine Unlearning as a Problem of Misaligned States

arXiv: https://arxiv.org/abs/2605.17590 · HTML: https://mlsanity.com/paper/2605.17590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 17 May 2026.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Algorithms that Approximate Data Removal: New Results and Limitations](https://mlsanity.com/paper/2209.12269/) (2022)
- [Threats, Attacks, and Defenses in Machine Unlearning: A Survey](https://mlsanity.com/paper/2403.13682/) (2024)
- [Reconstruction Attacks on Machine Unlearning: Simple Models are Vulnerable](https://mlsanity.com/paper/2405.20272/) (2024)
- [Machine Unlearning Doesn't Do What You Think: Lessons for Generative AI Policy and Research](https://mlsanity.com/paper/2412.06966/) (2024)
- [Shape of Memory: a Geometric Analysis of Machine Unlearning in Second-Order Optimizers](https://mlsanity.com/paper/2604.23046/) (2026)

## Abstract (arXiv)

We formulate machine unlearning for online L-BFGS as a counterfactual state-alignment problem. Given an actual event stream and a deletion-edited counterfactual stream, the target of unlearning is the optimizer state that would have arisen had the deleted samples never been processed. We introduce state-aware metrics that separately measure parameter error, memory-operator error, combined state error, and update-direction error. The memory metric compares the inverse-Hessian actions induced by the o-L-BFGS memory, rather than treating curvature pairs as of finite influence. Under convexity assumptions, we derive a recursive bound on counterfactual state deviation. We then evaluate a state-aware benchmark of deletion interventions, including memory-only and parameter-only corrections, against an counterfactual oracle model. These results show that unlearning for online L-BFGS is not merely a parameter-correction problem: it requires alignment with a realizable counterfactual optimizer state.