Ascent Fails to Forget

2025-09-30

AI Summary

Unconstrained machine unlearning methods based on gradient ascent often fail due to statistical dependencies between the forget set and retain set—sometimes degrading model performance below that of the original model—challenging the implicit assumption that these sets can be optimized independently. Method: Through theoretical analysis and empirical evaluation across logistic regression and neural networks, we demonstrate that even weak statistical correlations distort the optimization trajectory, causing unlearning to deviate from the ideal retraining path. We further propose an alternating gradient descent–ascent framework and validate the universality of this phenomenon under both stochastic and deterministic forgetting settings. Contribution/Results: This work provides the first systematic characterization of how statistical dependence undermines unconstrained unlearning, revealing a fundamental failure mode. It delivers critical theoretical insights and empirical benchmarks for designing robust unlearning algorithms, highlighting the necessity of explicitly modeling or mitigating inter-set dependencies in unlearning design.

Technology Category

• Machine Learning: Other Foundations of Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Contrary to common belief, we show that gradient ascent-based unconstrained optimization methods frequently fail to perform machine unlearning, a phenomenon we attribute to the inherent statistical dependence between the forget and retain data sets. This dependence, which can manifest itself even as simple correlations, undermines the misconception that these sets can be independently manipulated during unlearning. We provide empirical and theoretical evidence showing these methods often fail precisely due to this overlooked relationship. For random forget sets, this dependence means that degrading forget set metrics (which, for a retrained model, should mirror test set metrics) inevitably harms overall test performance. Going beyond random sets, we consider logistic regression as an instructive example where a critical failure mode emerges: inter-set dependence causes gradient descent-ascent iterations to progressively diverge from the ideal retrained model. Strikingly, these methods can converge to solutions that are not only far from the retrained ideal but are potentially even further from it than the original model itself, rendering the unlearning process actively detrimental. A toy example further illustrates how this dependence can trap models in inferior local minima, inescapable via finetuning. Our findings highlight that the presence of such statistical dependencies, even when manifest only as correlations, can be sufficient for ascent-based unlearning to fail. Our theoretical insights are corroborated by experiments on complex neural networks, demonstrating that these methods do not perform as expected in practice due to this unaddressed statistical interplay.

Problem

• Gradient ascent methods fail at machine unlearning due to data dependencies
• Statistical dependence between forget and retain datasets undermines unlearning effectiveness
• Unlearning process can degrade model performance beyond original state

Innovation

• Gradient ascent fails machine unlearning
• Statistical dependence causes divergence from retraining
• Correlations trap models in inferior local minima