Certified Pixel-Level Unlearning extends the standard (epsilon, delta)-indistinguishability framework of certified approximate unlearning from classification to dense prediction tasks. Rather than requiring indistinguishability over the entire model parameter space or global output distribution, it projects the guarantee onto the conditional probability space of pixel-wise predictions.
Formally, for two masks Y^(r1) (coarse) and Y^(r2) (fine) with r1 < r2, an unlearning operator U is pixel-level (epsilon, delta)-certified if for every pixel (i,j), true label y, and predicted class k:
P(Y_hat_ij = k | Y_ij = y) ⇐ e^epsilon * P(Y_ij^(r2) = k | Y_ij = y) + delta
and vice versa, where Y_hat := U[Y^(r1)] is the unlearned mask. This definition is derived from the Weak Unlearning framework of Nguyen et al. (2025), which relaxes indistinguishability from parameter space to observation space, then further restricted to conditional slices Y_ij = y to enforce structural validity and prevent vacuous solutions (e.g., random permutations that preserve marginals but destroy utility).
Key Details
- Derived by projecting standard certified approximate unlearning (Sekhari et al., 2021) onto pixel-wise conditional distributions
- Adopts the Weak Unlearning relaxation: indistinguishability in output space rather than parameter space
- Restricted to conditional slices to ensure the unlearned model mimics the ideal fine-mask model for the correct semantic class
- Connects directly to gradient clipping and model clipping algorithms from Koloskova et al. (2025), which provide (epsilon, delta)-certified guarantees applicable at the pixel level via the unlearning isomorphism