Joint Lyapunov Certificates for K-Agent Generative AI Governance: Stochastic Stability, Emergent Ensemble Risk, and Zero-Knowledge Governance Attestation
2026-08-10 • Cryptography and Security
Cryptography and Security
AI summaryⓘ
The authors study how to safely manage multiple AI models that adapt and learn together. They found that analyzing each model separately doesn't guarantee the whole group behaves well, so they developed a new method called the Joint Lyapunov Proof (JLP) to check the combined system's stability without exposing private model details. Their work includes mathematical tools to find when these systems become unstable and a way to securely verify ongoing safety at each update. They tested their theory with simulated AI models to confirm their results.
Model Risk ManagementLyapunov StabilityMeta-learningJoint Lyapunov ProofMean-square StabilityNoise-Floor TheoremZero-knowledge AttestationSuccinct Non-Interactive Argument of Knowledge (SNARK)Multi-agent SystemsSoftmax Function
Authors
Sriram Nagaraj
Abstract
We develop a rigorous mathematical framework for the governance of systems of K self-adapting generative AI models under the principles of Model Risk Management (MRM). When multiple models share a meta-learning coupling through an interaction matrix, the per-agent Lyapunov analysis that underpins standard MRM is provably insufficient: individual agents can each satisfy their declared stability bounds while the joint system is in a regime of emergent ensemble-level drift. We formalize this gap through the Joint Lyapunov Proof (JLP)---a cryptographic and stochastic protocol that attests, without revealing proprietary weights, that the aggregate dynamics satisfy MRM Ongoing Monitoring standard at every validation epoch. Our main contributions are the following. We give a complete characterization of the infinitesimal generator of the joint quadratic Lyapunov function. We derive the exact critical coupling threshold above which the system loses mean-square stability. We prove a Noise-Floor Theorem and identify the correct target for zero-knowledge attestation. A per-epoch Succinct Non-Interactive Argument of Knowledge (SNARK) on the live weights is derived. All theoretical claims are validated against five numerical studies using a multi-agent softmax system.