GenCtrl - A Formal Controllability Toolkit for Generative Models

2026-01-09

arXiv.org

AI Summary

Current generative models lack theoretical guarantees for fine-grained controllability, making it difficult to assess their actual control capabilities in human–AI interaction. This work formulates interaction as a control process and, for the first time, establishes a distribution-agnostic controllability framework applicable to any black-box nonlinear generative model, relying solely on output boundedness. Building on control theory, the authors propose an algorithm to estimate controllable sets and derive probably approximately correct (PAC)-style error bounds. Experiments on both language and text-to-image models reveal that model controllability is highly sensitive to experimental settings and remarkably fragile, thereby validating the proposed framework and underscoring the necessity of systematic controllability analysis.

Technology Category

• Natural Language Processing: Generation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

As generative models become ubiquitous, there is a critical need for fine-grained control over the generation process. Yet, while controlled generation methods from prompting to fine-tuning proliferate, a fundamental question remains unanswered: are these models truly controllable in the first place? In this work, we provide a theoretical framework to formally answer this question. Framing human-model interaction as a control process, we propose a novel algorithm to estimate the controllable sets of models in a dialogue setting. Notably, we provide formal guarantees on the estimation error as a function of sample complexity: we derive probably-approximately correct bounds for controllable set estimates that are distribution-free, employ no assumptions except for output boundedness, and work for any black-box nonlinear control system (i.e., any generative model). We empirically demonstrate the theoretical framework on different tasks in controlling dialogue processes, for both language models and text-to-image generation. Our results show that model controllability is surprisingly fragile and highly dependent on the experimental setting. This highlights the need for rigorous controllability analysis, shifting the focus from simply attempting control to first understanding its fundamental limits.

Problem

• controllability
• generative models
• control theory
• dialogue systems
• black-box control

Innovation

• controllability
• generative models
• formal guarantees
• black-box control
• PAC bounds