Abstract
Recursive self-modification is increasingly central in AutoML, neural architecture search, and adaptive optimization, yet no existing framework ensures that such changes are made safely. Godel machines offer a principled safeguard by requiring formal proofs of improvement before rewriting code; however, such proofs are unattainable in stochastic, high-dimensional settings. We introduce the Statistical Godel Machine (SGM), the first statistical safety layer for recursive edits. SGM replaces proof-based requirements with statistical confidence tests (e-values, Hoeffding bounds), admitting a modification only when superiority is certified at a chosen confidence level, while allocating a global error budget to bound cumulative risk across this http URL also propose Confirm-Triggered Harmonic Spending (CTHS), which indexes spending by confirmation events rather than rounds, concentrating the error budget on promising edits while preserving familywise this http URL across supervised learning, reinforcement learning, and black-box optimization validate this role: SGM certifies genuine gains on CIFAR-100, rejects spurious improvement on ImageNet-100, and demonstrates robustness on RL and optimization this http URL, these results position SGM as foundational infrastructure for continual, risk-aware self-modification in learning this http URL is available at: this https URL.
Abstract (translated)
递归自我修改在自动机器学习（AutoML）、神经架构搜索和自适应优化中变得越来越重要，但现有的框架并不能保证这些更改的安全性。哥德尔机通过要求必须提供改进的正式证明来重新编写代码的方式提供了原则性的安全保护；然而，在随机性和高维度设置下，这样的证明是无法实现的。我们引入了统计哥德尔机器（SGM），这是第一个用于递归编辑的统计安全保障层。SGM用统计置信度测试（e值、Hoeffding界）代替基于证明的要求，并且只有当在选定的信心水平上被认证为更优越时才允许修改，同时分配全局误差预算以限制在整个过程中的累计风险。 我们还提出了确认触发谐波花费（CTHS），它通过确认事件而不是轮次来索引支出，在保留家族级错误率的同时将误差预算集中在有希望的编辑上。在监督学习、强化学习和黑盒优化中验证了SGM的作用：SGM在CIFAR-100数据集上认证了真正的改进，拒绝了ImageNet-100上的虚假改善，并且在RL和优化任务上展示了鲁棒性。 这些结果将SGM定位为持续风险意识自我修改学习的基础架构。更多详细信息，请参阅：https://this https URL.（请注意，最后一个链接应指向实际的论文或资源位置，而非占位符）
URL
https://arxiv.org/abs/2510.10232
