A Variational Framework for LLM Generator-Regulator Games

2026-06-16

AI Summary

This work addresses the need for compliance in language model–generated content—particularly in applications such as content moderation and deception detection—by proposing a variational framework that regulates message distributions. It formalizes, for the first time, the interaction between a generator and a regulator as a saddle-point optimization problem. The framework models generated messages via an entropy-regularized Gibbs distribution and encodes regulatory objectives using f-divergences. Leveraging convex duality theory, it reveals fundamental trade-offs among utility, entropy, regulatory alignment, and finite-length detectability. Empirical validation on content moderation and phishing defense tasks demonstrates the method’s efficacy, with multidimensional metrics quantifying its controllability and performance.

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.

Problem

• regulated language generation
• generator-regulator games
• distributional control
• AI content moderation
• message-level regulation

Innovation

• variational framework
• generator-regulator game
• entropy-regularized Gibbs distribution
• f-divergence
• regulated language generation