As generative fashions turn out to be ubiquitous, there’s a vital want for fine-grained management over the technology course of. But, whereas managed technology strategies from prompting to fine-tuning proliferate, a basic query stays unanswered: are these fashions actually controllable within the first place? On this work, we offer a theoretical framework to formally reply this query. Framing human-model interplay as a management course of, we suggest a novel algorithm to estimate the controllable units of fashions in a dialogue setting. Notably, we offer formal ensures on the estimation error as a operate of pattern complexity: we derive probably-approximately right bounds for controllable set estimates which are distribution-free, make use of no assumptions aside from output boundedness, and work for any black-box nonlinear management system (i.e., any generative mannequin). We empirically display the theoretical framework on completely different duties in controlling dialogue processes, for each language fashions and text-to-image technology. Our outcomes present that mannequin controllability is surprisingly fragile and extremely depending on the experimental setting. This highlights the necessity for rigorous controllability evaluation, shifting the main target from merely trying management to first understanding its basic limits.<\/p>\n