让机器遗忘数据，关键是让优化器状态对齐删除后的假设状态。
Form and Function: Machine Unlearning as a Problem of Misaligned States
- 将遗忘问题建模为优化器状态的反事实对齐，而非单纯参数修正。
- 提出四种状态感知指标，精准衡量参数、记忆、更新方向等误差。
- 证明在凸条件下状态偏差有递归上界，适合研究在线学习的隐私保护。
我们将在线L-BFGS中的机器遗忘问题建模为反事实状态对齐问题。给定真实事件流与删除样本后的反事实流，遗忘的目标是恢复若未处理被删样本时应产生的优化器状态。我们引入状态感知度量，分别评估参数误差、记忆算子误差、联合状态误差和更新方向误差。其中记忆度量关注o-L-BFGS记忆所诱导的逆海森作用，而非将曲率对视为有限影响。在凸性假设下，我们推导出反事实状态偏差的递归上界。进一步，我们在一个状态感知基准上评估多种删除干预策略（仅修正记忆或仅修正参数），并与反事实最优模型对比。结果表明，线上L-BFGS的遗忘不仅是参数修正问题，更需与可实现的反事实优化器状态对齐。
原文摘要 · Abstract (English)
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.
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