H2DF: Calibrated Target Bands for Controllable Language-Model Unlearning
Author: Jupiter Yao
Subjects: Computation and Language (cs.CL); Machine Learning (cs.LG)
arXiv: 2610.26864 [cs.CL] — submitted 26 June 2026
Abstract
Gradient ascent (GA) is a simple baseline for language-model unlearning, but it keeps increasing the forget loss even after useful forgetting has already occurred. This unbounded pressure can degrade retained utility and push forgotten examples to abnormally high loss. To address this, we introduce H2DF, a calibrated target-band objective that applies GA-like pressure below a data-dependent lower target and suppresses—or reverses—that pressure once the target region is reached. The targets are estimated from matched non-member examples before training, so the base objective requires only one forget-batch forward/backward pass per optimization step; the reported TOFU variant adds sparse retain replay every tenth step.
We instantiate a one-sided objective for TOFU question answering and a two-sided objective for MUSE-News language modeling. Across three TOFU seeds, H2DF achieves a forget NLL of 1.528 (margin 0.049) and a retain NLL of 1.165 (margin 0.047), matching GradDiff while using retain replay only every tenth step and showing substantially lower variability than GA. On MUSE-News, H2DF improves retention over GA and NPO and is competitive with SimNPO, though it does not dominate it. Ablations show that the upper target reduces overshoot and that validation-based checkpoint selection is important.
Overall, these results support calibrated target bands as a practical mechanism for controlling forgetting strength, while also exposing sensitivity to random seed and calibration quality.
Key Contributions
- Calibrated target-band objective: Applies GA-like pressure only below a data-dependent lower target, then suppresses or reverses it after the target region is reached, preventing unbounded forget-loss growth.
- Efficient training: Targets are estimated from matched non-member examples before training; the base objective needs one forget-batch forward/backward pass per step, with sparse retain replay (every tenth step) in the TOFU variant.
- Task-specific instantiations: A one-sided objective for TOFU question answering and a two-sided objective for MUSE-News language modeling.
- Empirical results: On TOFU, H2DF matches GradDiff with substantially lower variability than GA; on MUSE-News, it improves retention over GA and NPO and is competitive with SimNPO.
- Ablation insights: The upper target reduces overshoot, and validation-based checkpoint selection is important.
Limitations
Performance is sensitive to random seed and calibration quality, and on MUSE-News H2DF is competitive with but does not dominate SimNPO.
Metadata
- Cite as: arXiv:2610.26864 [cs.CL]
- DOI: https://doi.org/10.48550/arXiv.2610.26864
- Submission history: [v1] Fri, 26 Jun 2026 06:51:15 UTC (17 KB)
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