Why Forget-Only Unlearning Needs Memorization

2026-10-07

AI Summary

This study addresses whether machine unlearning is feasible without retaining the original training data, observing that the information discarded during standard training is precisely what enables exact forgetting. By integrating theoretical analysis, learning algorithm modeling, and information-theoretic bound derivations, this work establishes the first memory lower bounds for unlearning algorithms that rely solely on the forget set, while quantifying the precision floor required to match retraining and the necessary memory capacity. It rigorously proves that successful unlearning without retained data demands additional storage of training information, revealing that models must preserve more information than standard training permits. This research bridges a critical theoretical gap in machine unlearning, providing a rigorous foundation for designing inherently forgettable models.

Abstract

Machine unlearning asks for a deletion algorithm whose output is close to retraining from scratch without the selected forget examples. In this work, we study forget-only unlearning, where the deletion algorithm receives only the trained model and the examples to forget, with no retained data or extra training information. We ask whether forget-only unlearning is always possible. We first show that this depends on the learning method: different datasets can produce the same trained model but require very different outputs after the same examples are removed. Using this observation, we derive lower bounds on how accurately unlearning can match retraining and instantiate them for several standard learning algorithms. We then ask what must be true when forget-only unlearning succeeds. To this end, we derive lower bounds on what an algorithm must memorize about the training data to handle arbitrary deletion requests. For simple threshold learners, the required information can be as large as the entire dataset, even though ordinary training keeps only one boundary point. Overall, our results show that information discarded during ordinary learning may be needed later for deletion, so models designed for forget-only unlearning may need to retain more information than standard training does.

Problem

• machine unlearning
• forget-only unlearning
• memorization
• retraining
• lower bounds

Innovation

• Machine Unlearning
• Forget-Only Unlearning
• Memorization Lower Bounds
• Theoretical Analysis