NexusAI: Enabling Design Space Exploration of Ideas through Cognitive Abstraction and Functional Decomposition

Large Language Models (LLMs) offer vast potential for creative ideation; however, their standard interaction paradigm often produces unstructured textual outputs that lead users to prematurely converge on sub-optimal ideas-a phenomenon known as fixation. While recent creativity tools have begun to structure these outputs, they remain compositionally opaque: ideas are organized as monolithic units that cannot be decomposed, abstracted, or recombinable at a sub-idea level. To address this, we propose Cognitive Abstraction (CA), a computational pipeline that transforms raw LLM-generated inspiration into a navigable and transformable design space. We implement this pipeline in NexusAI, a prototype diagramming system that supports (I) decomposition of inspiration into typed functional fragments, (II) multi-level abstraction to externalize mental scaling, and (III) cross-dimensional recombination to spark novel design directions. A within-subject user study (N=14) demonstrates that NexusAI significantly improves design space exploration, reduces cognitive overhead, and facilitates perspective reframing compared to a baseline. Our work contributes: (1) a characterization of "compositional opacity" as a barrier in human-AI co-creation; (2) the CA pipeline for operationalizing creative cognitive primitives at scale; and (3) empirical evidence that structured, multi-level representations can effectively mitigate fixation and support divergent exploration.