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arXiv AI By Xuening Wu, Shenqin Yin, Yanlan Kang, Xinhang Zhang, Qianya Xu, Zeping Chen, Wenqiang Zhang

SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification

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The paper introduces the Statistical Godel Machine (SGM), a framework that replaces formal proof requirements with statistical confidence tests to safely allow recursive self-modification in machine learning systems. SGM uses e-values and Hoeffding bounds to certify improvements at a chosen confidence level while managing a global error budget, and introduces Confirm-Triggered Harmonic Spending (CTHS) to allocate risk more efficiently. Experiments on supervised learning, reinforcement learning, and black-box optimization demonstrate that SGM can certify genuine gains on CIFAR-100, reject false improvements on ImageNet-100, and maintain robustness across benchmarks.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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