  Generative Artificial Intelligence systems have been developed for image,
code, story, and game generation with the goal of facilitating human
creativity. Recent work on neural generative systems has emphasized one
particular means of interacting with AI systems: the user provides a
specification, usually in the form of prompts, and the AI system generates the
content. However, there are other configurations of human and AI coordination,
such as co-creativity (CC) in which both human and AI systems can contribute to
content creation, and mixed-initiative (MI) in which both human and AI systems
can initiate content changes. In this paper, we define a hypothetical human-AI
configuration design space consisting of different means for humans and AI
systems to communicate creative intent to each other. We conduct a human
participant study with 185 participants to understand how users want to
interact with differently configured MI-CC systems. We find out that MI-CC
systems with more extensive coverage of the design space are rated higher or on
par on a variety of creative and goal-completion metrics, demonstrating that
wider coverage of the design space can improve user experience and achievement
when using the system; Preference varies greatly between expertise groups,
suggesting the development of adaptive, personalized MI-CC systems;
Participants identified new design space dimensions including scrutability --
the ability to poke and prod at models -- and explainability.
