Machine Unlearning in Low-Dimensional Feature Subspace
Kun Fang, Qinghua Tao, Junxu Liu, Yaxin Xiao, Qingqing Ye, Jian Sun, Haibo Hu

TL;DR
This paper introduces LOFT, a low-dimensional feature subspace method for machine unlearning that efficiently removes data influence with minimal data access and reduced privacy risks.
Contribution
LOFT presents a novel low-dimensional feature subspace approach for machine unlearning, optimizing a small projection matrix to efficiently unlearn data without raw data reaccess.
Findings
LOFT achieves significantly lower computational overhead.
LOFT demonstrates superior unlearning performance.
LOFT works across diverse models and datasets.
Abstract
Machine Unlearning (MU) aims at removing the influence of specific data from a pretrained model while preserving performance on the remaining data. In this work, a novel perspective for MU is presented upon low-dimensional feature subspaces, which gives rise to the potentials of separating the remaining and forgetting data herein. This separability motivates our LOFT, a method that proceeds unlearning in a LOw-dimensional FeaTure subspace from the pretrained model skithrough principal projections, which are optimized to maximally capture the information of the remaining data and meanwhile diminish that of the forgetting data. In training, LOFT simply optimizes a small-size projection matrix flexibly plugged into the pretrained model, and only requires one-shot feature fetching from the pretrained backbone instead of repetitively accessing the raw data. Hence, LOFT mitigates two critical…
Peer Reviews
Decision·Submitted to ICLR 2026
Unlike parameter-space or data-space methods, SUN reinterprets unlearning as a geometric operation in feature space. The subspace-based view of machine unlearning is both elegant and novel. SUN requires only one forward pass to extract features, then computes a projection matrix offline — making it orders of magnitude faster and more lightweight than retraining-based baselines and achieving one-shot unlearning by requiring only feature-level access. The authors evaluate on multiple datasets and
Although SUN eliminates the need for retraining, it still requires a complete forward pass through the remaining dataset to estimate the feature covariance matrices. This may become computationally expensive for very large-scale datasets or repeated unlearning requests. And because of the dependence on the remaining data, I question whether it's reasonable to focus the comparison more on baselines that only use the forget dataset. Besides, the separability assumption (that forgetting and remaini
- Paper is well-organized and easy to follow. - Extending experiments to instance unlearning - Experiments extend to instance unlearning and face and emotion recognition, showing the effectiveness of the proposal under varying image classification tasks. - The proposed method is effective in continual unlearning scenarios.
- I think the analysis of the eigenvalues is incorrect. Having similar eigenvalues does not mean that subspaces collapse and are not separable. Similar eigenvalue information does not imply that principal directions are shared, too. We can not comment on this just by looking at the eigenvalues (corresponding directions matter). Moreover, we know that the penultimate hidden states of the model trained on the full data are separable: we apply a linear transform in the last layer, and the model has
The topic of machine unlearning is very timely and important. If all the hypothesis and observations are true in the paper, then the proposed technique could serve as a good method for machine unlearning. It's great that the authors tried to apply SUN at different layers.
The paper is entirely built upon the observation and hypothesis that exists a low-dimensional feature subspace, where the features of forgetting and remaining datasets are easy to be separated. There is no justification for why this assumption makes sense. On a related note, why is it a good idea to fix g after pretraining? After pretraining, g(.) might be too restrictive and the separation may not be possible to do depending on the problem. The paper lacks any theoretical guarantees for the
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Taxonomy
TopicsAdvanced Neural Network Applications · Stochastic Gradient Optimization Techniques · Machine Learning and Data Classification
