Certified machine unlearning can be achieved via noise injection leading to differential privacy guarantees, where noise is calibrated to worst-case sensitivity. Such conservative calibration often results in performance degradation, limiting practical applicability. In this work, we investigate an alternative approach based on adaptive per-instance noise calibration tailored to the individual contribution of each data point to the learned solution. This raises the following challenge: how can one establish formal unlearning guarantees when the mechanism depends on the specific point to be removed? To define individual data point sensitivities in noisy gradient dynamics, we consider the use of per-instance differential privacy. For ridge regression trained via Langevin dynamics, we derive high-probability per-instance sensitivity bounds, yielding certified unlearning with substantially less noise injection. We corroborate our theoretical findings through experiments in linear settings and provide further empirical evidence on the relevance of the approach in deep learning settings.

翻译：认证机器遗忘可通过噪声注入实现差分隐私保证，其中噪声根据最坏情况敏感度进行校准。这种保守的校准方式通常会导致性能下降，限制了实际应用。在本研究中，我们探索一种基于自适应单实例噪声校准的替代方案，该方案根据每个数据点对学习解的个体贡献进行定制化调整。这引出了以下挑战：当机制依赖于待删除的具体数据点时，如何建立形式化的遗忘保证？为定义噪声梯度动态中的个体数据点敏感度，我们考虑采用单实例差分隐私。针对通过朗之万动态训练的岭回归，我们推导出高概率的单实例敏感度边界，从而以显著更少的噪声注入实现认证遗忘。我们通过线性场景的实验验证了理论发现，并进一步提供了该方法在深度学习场景中相关性的实证证据。