We provide counterexamples showing that uniform laws of large numbers do not hold for subdifferentials under natural assumptions. Our results apply to random Lipschitz functions and random convex functions with a finite number of smooth pieces. Consequently, they resolve the questions posed by Shapiro and Xu [J. Math. Anal. Appl., 325(2), 2007] in the negative and highlight the obstacles nonsmoothness poses to uniform results.

AI policymakers are responsible for delivering effective governance mechanisms that can provide safe, aligned and trustworthy AI development. However, the information environment offered to policymakers is characterised by an unnecessarily low Signal-To-Noise Ratio, favouring regulatory capture and creating deep uncertainty and divides on which risks should be prioritised from a governance perspective. We posit that the current publication speeds in AI combined with the lack of strong scientific standards, via weak reproducibility protocols, effectively erodes the power of policymakers to enact meaningful policy and governance protocols. Our paper outlines how AI research could adopt stricter reproducibility guidelines to assist governance endeavours and improve consensus on the AI risk landscape. We evaluate the forthcoming reproducibility crisis within AI research through the lens of crises in other scientific domains; providing a commentary on how adopting preregistration, increased statistical power and negative result publication reproducibility protocols can enable effective AI governance. While we maintain that AI governance must be reactive due to AI's significant societal implications we argue that policymakers and governments must consider reproducibility protocols as a core tool in the governance arsenal and demand higher standards for AI research. Code to replicate data and figures: https://github.com/IFMW01/reproducibility-the-new-frontier-in-ai-governance

This point should be corrected in the introduction).

Thank you for helpful comments and suggestions. We will address the concerns raised by the reviewers. We discuss the difficulty to satisfy Corollary 5 when the problem becomes multiclass in Lines 144-158. This makes it easier to tune the hyperparameters to satisfy the necessary condition as illustrated in Eq. (9) for We checked Eq. (5) in "Learning Confidence for Out-of-Distribution Detection in Neural Networks" Regarding the problem addressed by "On calibration of modern neural

With the rapid advancement of large language model technology, there is growing interest in whether multi-feature approaches can significantly improve AI text detection beyond what single neural models achieve. While intuition suggests that combining semantic, syntactic, and statistical features should provide complementary signals, this assumption has not been rigorously tested with modern LLM-generated text. This paper provides a systematic empirical investigation of multi-hierarchical feature integration for AI text detection, specifically testing whether the computational overhead of combining multiple feature types is justified by performance gains. We implement MHFD (Multi-Hierarchical Feature Detection), integrating DeBERTa-based semantic analysis, syntactic parsing, and statistical probability features through adaptive fusion. Our investigation reveals important negative results: despite theoretical expectations, multi-feature integration provides minimal benefits (0.4-0.5% improvement) while incurring substantial computational costs (4.2x overhead), suggesting that modern neural language models may already capture most relevant detection signals efficiently. Experimental results on multiple benchmark datasets demonstrate that the MHFD method achieves 89.7% accuracy in in-domain detection and maintains 84.2% stable performance in cross-domain detection, showing modest improvements of 0.4-2.6% over existing methods.