Bounding Retraining Equivalence and the Deletion Floor in Materials Machine Unlearning
Can Polat, Mustafa Kurban, Erchin Serpedin, Hasan Kurban
cs.LG
Sep 28, 2026 · v1
cond-mat.mtrl-sci quant-ph
TL;DR
The accompanying repository includes Lean 4 formalizations of the bounded-loss transfer theorem and its sharpness, the retained-neighbor bounds, the ridge identities, and leave-one-out stability.
Abstract
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 $\approx 8\times$ 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.
Problem
In materials machine learning, closely related retained structures can keep a deleted record predictable after retraining. This makes post-deletion prediction error an ambiguous metric for machine unlearning.
Approach
The authors define the deletion floor as the expected target loss under a specified retraining procedure. Under (ε,δ) retraining equivalence they prove a sharp interval bounding an update's target loss around that floor. A conditional neighbor bound ties a low floor to retained fit, prediction regularity and label agreement, and an exact ridge identity separates residual fit from deletion-induced prediction change. Key results are formalized in Lean 4 and evaluated on synthetic redundancy sweeps and Materials Project data.
Results
Median normalized retraining loss drops about 8× when one retained relative remains after deletion. In the paired Materials Project study, the lower-floor regime shows larger prediction change on more than 50% of shared requests. Comparisons with approximate updates separate deliberate target suppression from preserved model utility.
| Procedure | Target loss / floor | Test MSE ratio |
|---|
| Retrain (reference) | 1.000 | 1.000 |
| No update | 0.932 | 1.000 |
| SCRUB-style regression | 1.141 | 1.001 |
| NegGrad+ | 1.645 | 1.013 |
| Gradient ascent | 3.081 | 1.083 |
Target loss relative to the retraining floor and test MSE ratio for unlearning procedures (excerpt)