GenCtrl -- A Formal Controllability Toolkit for Generative Models
Emily Cheng, Carmen Amo Alonso, Federico Danieli, Arno Blaas, Luca Zappella, Pau Rodriguez, Xavier Suau

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…
Peer Reviews
Decision·ICLR 2026 Poster
This paper proposes a control-theoretic framework to analyze and estimate the controllability and reachability of generative models (LLMs, T2IMs) viewed as black-box dynamical systems. The method provides PAC-style probabilistic guarantees for estimating controllable sets using Monte Carlo sampling, under minimal assumptions. Strengths: 1.Theoretical originality – Introduces a formal and model-agnostic definition of controllability for generative systems, offering a new lens to study model behav
Conceptual Level: Ambiguity of Controllability Definition The core concept of the paper, controllability, lacks a clear physical and semantic interpretation in the context of generative models. In classical control theory, controllability implies the existence of a set of inputs capable of steering the system from any initial state to any desired final state. However, for LLMs or T2I models: The boundaries of the state space X and input space U are semantically unclear; Prompts or noise vectors
1. The central idea of shifting focus from how to control models to if they can be controlled is a valuable and novel contribution. It brings a much-needed layer of formal scrutiny to a field dominated by empirical trial-and-error. 2. The paper is well-written, and the authors do an admirable job of introducing concepts from control theory and adapting them to the context of generative models, particularly with their discussion of the discrete bottleneck.
1. The paper claims its framework can assess any control mechanism, including finetuning and representation engineering. Yet, the experiments are confined exclusively to prompting, arguably the weakest and least reliable form of control. 2. The framework is not scalable to complex, high-dimensional control problems. The sample complexity scales with the number of discretized output bins, N. For any realistic task involving the control of multiple attributes simultaneously (e.g., style, tone, an
1) The formalization of dialogue-as-control is clear and rigorous. 2) The paper provides PAC-style, distribution-free bounds, avoiding intractable verification of global smoothness, thus suits black-box examinations well. 3) The proposed algorithms are simple and easy to follow. 4) The eventually alerting conclusion reveals the fragility of controllability in LLMs to the community, which could be of higher impacts.
1) Please correct me if I misunderstood this: how about when N -> \infty? In practice this is easy due to the dimensionality curse, and thus the total demanded sampling number by THM1 can explode to some extent. 2) The role of the readout h is a little bit less clearly demonstrated. In my understanding, isn't it the case that its calibration can be very hard in practice when considering the general case? I would appreciate if the authors can provide guidance for me to better understand how this
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Taxonomy
TopicsMultimodal Machine Learning Applications · Topic Modeling · Speech and dialogue systems
