Large language models (LLMs) exhibit unprecedented natural language generation and many text-based problem-solving capabilities. Indeed, in many language-based tasks, for example routine coding, these artificial intelligence models have reduced, or even eliminated, the need for human input. But rather than replacing human cognitive effort, LLMs may instead serve as cognitive tools to extend human abilities, particularly when they are engaged in a task requiring open-ended conceptual exploration and creative ideation. However, we are yet to understand how these models may enhance such generative human cognitive abilities in human--AI interactions. In this study, we explore and evaluate the ability of LLMs to follow and enhance human mental trajectories during semantic memory search. To test this, we use the semantic fluency task (SFT), a classic cognitive paradigm requiring generative semantic memory retrieval that has long served to characterize convergent and divergent thinking in humans. We demonstrate that an LLM's abilities to track and predict human memory trajectories in this task exceed those of other humans.

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