A Variational Framework for LLM Generator-Regulator Games

2026/06/16 by Quanyan Zhu · 1 voice
Mathematics · Computer Science · #stat.OT #cs.AI #cs.IT

paper · pdf

Abstract

This paper develops a variational framework for regulated language generation. Starting from autoregressive token sampling, we derive the induced distribution over complete messages and relate it to an entropy-regularized Gibbs law. Regulation is modeled as an optimal discriminator whose convex-dual value is an f-divergence, and the generator-regulator interaction is formulated as a saddle-point problem. The framework applies to moderation, censorship, AI deception detection, compliance auditing, phishing defense, and manipulation control, where regulation concerns a distribution over possible messages rather than a single output. The equilibrium clarifies the tradeoff among utility, entropy, regulatory alignment, and finite-length detectability. Two finite-vocabulary case studies, censorship filtering and phishing defense, illustrate how the theory can be evaluated through utility, entropy, divergence, receiver-side scores, and detection probability.

Citations

• Game-Theoretic Foundations for Cyber Resilience Against Deceptive Information Attacks in Intelligent Transportation Systems
• Foundations of Cyber Resilience: The Confluence of Game, Control, and Learning Theories
• Language Models are Few-Shot Learners
• Security of Distributed Machine Learning: A Game-Theoretic Approach to Design Secure DSVM
• Game Theory for Cyber Deception: A Tutorial
• A Game-Theoretic Foundation of Deception: Knowledge Acquisition and Fundamental Limits
• Game Theory Meets Network Security: A Tutorial at ACM CCS
• Modeling and Analysis of Leaky Deception using Signaling Games with Evidence
• A Game-Theoretic Taxonomy and Survey of Defensive Deception for Cybersecurity and Privacy
• Attention Is All You Need
• f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization
• How Censorship in China Allows Government Criticism but Silences Collective Expression
• On general minimax theorems
• Zur Theorie der Gesellschaftsspiele

Discussions

• Quanyan Zhu: A Variational Framework for LLM Generator-Regulator Games https://arxiv.org/abs/2606.18424 https://arxiv.org/pdf/2606.18424 https://arxiv.org/html/2606.18424 [bsky, 0 points, 0 comments]

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