SILO: Tight PAC-Bayes Generalization Guarantees for Large Language Model Judges

Abstract

Large language model (LLM) judges are increasingly used to monitor the outputs of LLM-based AI agents, yet formal guarantees on the reliability of these judges remain largely absent, limiting confidence in their use for safety-critical oversight. In this talk, I will consider certifying such judges and formalize their risk over safety classifications of prompt–response pairs drawn from a deployed generator LLM. I will present a PAC-Bayes framework for this setting, refining existing compression-based methodology with tighter bounds, coding, and compression schemes, and show that parameter-efficient fine-tuning can yield non-vacuous and even tight certificates for oversight model judges without holding out data for validation. I will show that across five guardrail models and four benchmarking datasets, certificate tightness is governed more by adaptation complexity than by base model scale. I will then introduce a novel LLM adaptation method that shares a single quantization scale across layers and achieves the tightest certificates with minimal degradation in predictive performance, and discuss how far quantization can be pushed before functional distortion outweighs the resulting gains in certificate tightness. Together, these results provide a practical route for certifying oversight model judges while providing insight into how the complexity of targeted safety adaptations affects generalization.

Bio

Tim G. J. Rudner is an Assistant Professor of Statistics and Computer Science at the University of Toronto, a Canada CIFAR AI Chair and Faculty Member at the Vector Institute for Artificial Intelligence, and the Chief Scientist at Vijil. He is also a Junior Research Fellow of Trinity College at the University of Cambridge, an Associate Member of the Department of Computer Science at the University of Oxford, a Faculty Affiliate at the Oxford Martin AI Governance Initiative, a Faculty Associate at Harvard University’s Berkman Klein Center for Internet and Society, a Faculty Affiliate at the Schwartz Reisman Institute for Technology and Society, and an AI Fellow at Georgetown University’s Center for Security and Emerging Technology. His research interests span probabilistic machine learning, AI safety, and AI governance. Before joining the University of Toronto, he was an Assistant Professor and Faculty Fellow at New York University. Tim holds a PhD in Computer Science from the University of Oxford, where he was a Qualcomm Innovation Fellow and a Rhodes Scholar