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This paper analyzes gradient-based machine unlearning, showing that matching forget and retain losses doesn't guarantee that a model's outputs match those of one retrained without the forget data. It derives closed-form expressions for this output gap in linear regression, extends them to nonlinear models via local approximations, and proposes "leverage" diagnostics that could help auditors estimate whether a given forget set is likely to unlearn successfully. For practitioners, the main takeaway is that loss curves alone are an unreliable check on unlearning, though the results rest on linearized approximations whose reach to large deep networks still needs empirical testing.
Loss is Not Behavior: A Unified Output-Space Analysis of Gradient-Based Machine Unlearning
arXiv:2610.38784v1 Announce Type: new Abstract: Gradient-based machine unlearning methods typically ``unlearn'' by optimizing forget and retain losses, but similar losses do not necessarily imply similar output-space behavior. Prior work has shown that high forget loss alone does not certify that unlearning has produced retraining-like output behavior. We therefore ask: when a gradient-based unlearner differs from the model that would have been learned on only the retain data, what structure does the resulting output-space gap have? We derive closed-form expressions for this gap in linear regression, with an extension to nonlinear models via a generalized Gauss-Newton and local linearity approximations. Our analysis puts various gradient-based methods under a unified framework parametrized by geometry, reweighting, and projection. Two leverage matrices emerge that capture the forget-retain entanglement under the retrained model geometry: forget self-leverage and retain cross-leverage. We show both theoretically and empirically that these two leverage matrices drive the impact of the forget residual on the forget and retain outputs, and existing methods account for this geometry only partially. Our framework yields precomputable leverage diagnostics for auditing forget sets to identify what type of gradient-based unlearning is likely to be successful.
Abstract:Gradient-based machine unlearning methods typically ``unlearn'' by optimizing forget and retain losses, but similar losses do not necessarily imply similar output-space behavior. Prior work has shown that high forget loss alone does not certify that unlearning has produced retraining-like output behavior. We therefore ask: when a gradient-based unlearner differs from the model that would have been learned on only the retain data, what structure does the resulting output-space gap have? We derive closed-form expressions for this gap in linear regression, with an extension to nonlinear models via a generalized Gauss-Newton and local linearity approximations. Our analysis puts various gradient-based methods under a unified framework parametrized by geometry, reweighting, and projection. Two leverage matrices emerge that capture the forget-retain entanglement under the retrained model geometry: forget self-leverage and retain cross-leverage. We show both theoretically and empirically that these two leverage matrices drive the impact of the forget residual on the forget and retain outputs, and existing methods account for this geometry only partially. Our framework yields precomputable leverage diagnostics for auditing forget sets to identify what type of gradient-based unlearning is likely to be successful.
Machine Learning (cs.LG)
arXiv:2610.38784 [cs.LG]
(or arXiv:2610.38784v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.38784 Focus to learn more arXiv-issued DOI via DataCite
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