arXiv:2602.14553v1 Announce Type: cross Abstract: Despite legal mandates for the right to be forgotten, AI operators routinely fail to comply with data deletion requests. While machine unlearning (MU) provides a technical solution to remove personal data's influence from trained models, ensuring compliance remains challenging due to the fundamental gap between MU's technical feasibility and regulatory implementation. In this paper, we introduce the first economic framework for auditing MU compliance, by integrating certified unlearning theory with regulatory enforcement. We first characterize MU's inherent verification uncertainty using a hypothesis-testing interpretation of certified unlearning to derive the auditor's detection capability, and then propose a game-theoretic model to capture the strategic interactions between the auditor and the operator. A key technical challenge arises from MU-specific nonlinearities inherent in the model utility and the detection probability, which create complex strategic couplings that traditional auditing frameworks do not address and that also preclude closed-form solutions. We address this by transforming the complex bivariate nonlinear fixed-point problem into a tractable univariate auxiliary problem, enabling us to decouple the system and establish the equilibrium existence, uniqueness, and structural properties without relying on explicit solutions. Counterintuitively, our analysis reveals that the auditor can optimally reduce the inspection intensity as deletion requests increase, since the operator's weakened unlearning makes non-compliance easier to detect. This is consistent with recent auditing reductions in China despite growing deletion requests. Moreover, we prove that although undisclosed auditing offers informational advantages for the auditor, it paradoxically reduces the regulatory cost-effectiveness relative to disclosed auditing.

arXiv:2506.08672v2 Announce Type: replace-cross Abstract: Rule-based reasoning is acknowledged as one of the fundamental problems of reasoning. While recent studies show that large reasoning models (LRMs) have remarkable reasoning capabilities enhanced by reinforcement learning (RL), real applications still face severe challenges due to variations in rule formats, types, and complexity. To mitigate this issue, we introduce RuleReasoner, an effective method for rule-based reasoning via a wide collection of curated tasks and a novel domain-aware dynamic sampling approach in RL. Specifically, RuleReasoner resamples each training batch by updating the domain weights based on historical rewards. This facilitates domain balance and active learning schedules for RL, obviating static mix-training engineered by human. Evaluations on in-distribution (ID) and out-of-distribution (OOD) benchmarks reveal that RuleReasoner outperforms frontier LRMs by a significant margin ($\Delta$4.1% on eight ID tasks and $\Delta$10.4% on three OOD tasks over OpenAI-o1). Notably, our approach also exhibits higher computational efficiency compared to prior methods.