Quantifying and Certifying Unlearning for Large Language Models Without Full Retraining

Large language models are increasingly deployed across mobile and edge environments, where privacy-sensitive and heterogeneous user data raise critical concerns of copyright infringement, data leakage, and regulatory non-compliance. Machine unlearning has thus emerged as an essential capability to remove the influence of specific data without full retraining. However, two key challenges remain open: 1) how to quantify unlearning to enable data valuation without retraining, especially since the massive scale of pretraining makes it infeasible to evaluate the contribution of individual data samples in advance, and 2) how to verify the correctness without retraining to ensure that third-party auditors can efficiently confirm the complete removal of targeted data influence. To address the aforementioned challenges, in this paper, we design a dual-stage machine unlearning framework to quantify the contribution of forgotten data and certify data removal without full retraining, serving as an auditing layer for first-order unlearning methods. Specifically, we design a run-time Shapley value-based unlearned data evaluation mechanism that utilizes a first-order approximation strategy to estimate the marginal contribution of forgotten samples. Moreover, we propose a proof of unlearning mechanism that generates compact, auditable artifacts of the unlearning process to efficiently verify that the targeted data influence has been completely removed. Compared with five state-of-the-art unlearning baselines, our approach achieves effectiveness in data valuation, stronger guarantees of removal correctness, and lower computational overhead.