GenCtrl -- A Formal Controllability Toolkit for Generative Models

TL;DR

This paper introduces a formal framework and algorithm to assess and guarantee the controllability of generative models, revealing that controllability is fragile and context-dependent, thus emphasizing the importance of rigorous analysis.

Contribution

It provides the first theoretical framework with formal guarantees for estimating controllable sets in black-box generative models, applicable across various tasks.

Findings

Controllability of models is highly fragile and context-dependent.

The proposed algorithm offers distribution-free, sample-efficient estimates.

Formal guarantees are derived for controllable set estimation.

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.