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：认证式机器遗忘可以通过引入噪声来实现，从而获得差分隐私保证，其中噪声的校准基于最坏情况下的敏感性。这种保守的校准常导致性能下降，限制了实际应用。本研究探索了一种替代方法，即基于自适应每实例噪声校准，该噪声根据每个数据点对学习解的个体贡献进行调整。这引发了以下挑战：当机制依赖于待移除的具体数据点时，如何建立形式化的遗忘保证？为了定义嘈杂梯度动力学中单个数据点的敏感性，我们考虑使用每实例差分隐私。对于通过朗之万动力学训练的岭回归，我们推导出高概率的每实例敏感性边界，从而在显著减少噪声注入的情况下实现认证遗忘。我们通过线性环境下的实验验证了理论发现，并在深度学习环境中提供了进一步的实证证据，证明了该方法的有效性。