Easy to Learn, Yet Hard to Forget: Towards Robust Unlearning Under Bias

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.

Machine unlearning poses challenges in removing mislabeled, contaminated, or problematic data from a pretrained model. Current unlearning approaches and evaluation metrics are solely focused on model predictions, which limits insight into the model's true underlying data characteristics. To address this issue, we introduce a new metric called relearning convergence delay, which captures both changes in weight space and prediction space, providing a more comprehensive assessment of the model's understanding of the forgotten dataset. This metric can be used to assess the risk of forgotten data being recovered from the unlearned model. Based on this, we propose the Influence Eliminating Unlearning framework, which removes the influence of the forgetting set by degrading its performance and incorporates weight decay and injecting noise into the model's weights, while maintaining accuracy on the retaining set. Extensive experiments show that our method outperforms existing metrics and our proposed relearning convergence delay metric, approaching ideal unlearning performance. We provide theoretical guarantees, including exponential convergence and upper bounds, as well as empirical evidence of strong retention and resistance to relearning in both classification and generative unlearning tasks.

Machine unlearning enables models to selectively forget training data, driven by privacy regulations such as GDPR and CCPA. However, its fairness implications remain underexplored: when a model forgets a demographic group, does it neutralize that concept or redistribute it to correlated groups, potentially amplifying bias? We investigate this bias redistribution phenomenon on CelebA using CLIP models (ViT/B-32, ViT-L/14, ViT-B/16) under a zero-shot classification setting across intersectional groups defined by age and gender. We evaluate three unlearning methods, Prompt Erasure, Prompt Reweighting, and Refusal Vector using per-group accuracy shifts, demographic parity gaps, and a redistribution score. Our results show that unlearning does not eliminate bias but redistributes it primarily along gender rather than age boundaries. In particular, removing the dominant Young Female group consistently transfers performance to Old Female across all model scales, revealing a gender-dominant structure in CLIP's embedding space. While the Refusal Vector method reduces redistribution, it fails to achieve complete forgetting and significantly degrades retained performance. These findings highlight a fundamental limitation of current unlearning methods: without accounting for embedding geometry, they risk amplifying bias in retained groups.