Summary

This paper addresses a fundamental limitation of existing approximate unlearning methods: they rely on assumptions (e.g., stability of SGD, small forget sets) that are often violated in practice, leading to poor empirical performance. The authors argue that the definition of “forgetting” is application-dependent and propose the first framework to study unlearning across three distinct scenarios: Removing Biases (RB), where maximal forget error is desired; Resolving Confusion (RC), where mislabelled data must be unlearned; and User Privacy (UP), where the model must defend against Membership Inference Attacks.

The central methodological contribution is SCRUB (SCalable Remembering and Unlearning unBound), a novel teacher-student formulation where the original model serves as a “teacher” and the student model selectively obeys it — matching the teacher on retained data while diverging on forget data. This is achieved through a contrastive-style min-max objective that simultaneously minimizes KL divergence between student and teacher on the retain set while maximizing it on the forget set, combined with standard cross-entropy loss on retained data. The approach is termed “unbounded” because it does not rely on the limiting assumptions (small forget sets, model closeness to optimum) that constrain prior certified methods.

The paper also contributes NegGrad+, an improved variant of gradient ascent-based unlearning that balances forget and retain objectives, and introduces the first adaptation of the LiRA (Likelihood Ratio Attack) Membership Inference Attack to the unlearning evaluation setting. Through comprehensive experiments on CIFAR-10 and Lacuna-10 with ResNet-18 and All-CNN architectures, SCRUB is shown to be by far the most consistent top performer across all three application scenarios and both model utility metrics.

Key Contributions

  • Application-dependent unlearning evaluation: first paper to study unlearning across three distinct application scenarios (RB, RC, UP), each with tailored forgetting definitions and metrics
  • SCRUB algorithm: teacher-student framework with contrastive min-max objective that consistently achieves high forget quality without damaging model utility across all applications
  • SCRUB+R (SCRUB with Rewind): extension that selects the training checkpoint where forget set error is “just high enough” by calibrating against a validation set, greatly improving defense against Membership Inference Attacks
  • NegGrad+: improved gradient ascent baseline that balances retain and forget losses with a tunable weight parameter beta
  • LiRA for unlearning: first adaptation of the state-of-the-art LiRA Membership Inference Attack to evaluate unlearning quality in the privacy setting
  • Scalability: SCRUB does not require storing the entire training dataset and scales to class-level and selective unlearning without the quadratic cost of NTK-based methods

Methodology

SCRUB’s training objective (Equation 3):

min_{w^u} alpha/N_r * sum_{x_r in D_r} d(x_r; w^u) + gamma/N_r * sum_{(x_r, y_r) in D_r} l(f(x_r; w^u), y_r) - 1/N_f * sum_{x_f in D_f} d(x_f; w^u)

where d(x; w^u) = D_KL(p(f(x; w^o)) || p(f(x; w^u))) is the KL divergence between teacher and student outputs. Training alternates between max-steps (gradient ascent on forget set) and min-steps (gradient descent on retain set), inspired by GAN training. Additional min-steps at the end guard against utility loss.

For the rewinding procedure (SCRUB+R), a validation set matching the forget set distribution is created, and the checkpoint closest to the validation set error is selected, ensuring forget error is neither too high (MIA vulnerability) nor too low (incomplete forgetting).

Key Findings

  • Prior approximate unlearning methods (NTK, Fisher Forgetting) often perform poorly because they violate assumptions about model closeness to optimal solutions and forget set size
  • Finetuning retains utility but fails to forget; EU-k forgets well for UP but is inconsistent for RB
  • SCRUB is the only method consistently ranked as a top performer across all metrics and all application scenarios
  • NegGrad+ is a strong baseline when tuned properly, outperforming prior work in several settings
  • The rewinding procedure substantially improves SCRUB’s defense against LiRA MIA, making it comparable to the Retrain oracle
  • Bad-T (teacher-student with an incompetent teacher) forgets effectively but damages model utility

Important References

Atomic Notes


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