# Bounding Retraining Equivalence and the Deletion Floor in Materials Machine Unlearning

arXiv: https://arxiv.org/abs/2609.35635 · HTML: https://mlsanity.com/paper/2609.35635/

## 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 12 of its 22 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [What makes unlearning hard and what to do about it](https://mlsanity.com/paper/2406.01257/) (2024)
- [Inexact Unlearning Needs More Careful Evaluations to Avoid a False Sense of Privacy](https://mlsanity.com/paper/2403.01218/) (2024)
- [Are we making progress in unlearning? Findings from the first NeurIPS unlearning competition](https://mlsanity.com/paper/2406.09073/) (2024)
- [Evaluating Deep Unlearning in Large Language Models](https://mlsanity.com/paper/2410.15153/) (2024)
- [Machine Unlearning under Retain-Forget Entanglement](https://mlsanity.com/paper/2603.26569/) (2026)
- [Data Duplication: A Novel Multi-Purpose Attack Paradigm in Machine Unlearning](https://mlsanity.com/paper/2501.16663/) (2025)
- [Distributional Machine Unlearning via Selective Data Removal](https://mlsanity.com/paper/2507.15112/) (2025)
- [Is your algorithm unlearning or untraining?](https://mlsanity.com/paper/2604.07962/) (2026)

## Abstract (arXiv)

In materials machine learning, closely related retained structures can sustain accurate property predictions even after removing a specific record, rendering post-deletion prediction error an ambiguous metric for machine unlearning. To resolve this ambiguity, we define the deletion floor as the expected target loss under a specified retraining procedure at the deleted request. Standard indistinguishability constraints yield a sharp interval bounding an update's target loss around this baseline reference. Theoretically, a conditional neighbor bound links a low deletion floor directly to retained fit, prediction regularity, and local label agreement, while an exact ridge identity isolates residual fit from the prediction change induced by record deletion. Empirically, controlled redundancy sweeps show an ≈ 8× drop in median normalized retraining loss when one retained relative remains after deletion. Across two distinct fitting regimes in a paired Materials Project study, the lower-floor regime also exhibits a larger prediction change on more than 50% of the shared requests. Systematic comparisons against approximate updates and the original model decouple deliberate target suppression from preserved overall model utility. Consequently, request-level unlearning evaluations should report reference loss, prediction change, and retained utility together, interpreting post-deletion accuracy against what retraining itself leaves behind.