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Form and Function: Machine Unlearning as a Problem of Misaligned States
[Submitted on 17 May 2026] · 2026-05-19 · via cs.LG updates on arXiv.org

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Abstract: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.

Submission history

From: Kennon Stewart [view email]
[v1] Sun, 17 May 2026 18:34:14 UTC (908 KB)

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