Is Imagination Derived from Hallucination? A Cross-Taxonomy Evaluation of Imagination and Hallucination in Large Language Models

Hallucination is a central limitation of large language models (LLMs), and substantial effort has been devoted to understanding and mitigating it. Towards this, Kalai and Vempala (STOC 2024) introduced a probabilistic framework formalizing calibration and hallucination, and showed that, with high probability, calibrated LLMs hallucinate roughly at the rate of the "missing mass", a measure of how incomplete the training data is relative to its source. This raises two fundamental questions: (i) what property of a calibrated LLM makes hallucinations unavoidable? and (ii) can hallucinations be avoided by giving up calibration? We answer these questions by introducing a simpler property we call innovation that measures the tendency of a model to produce outputs outside the training data. We show that innovation is implied by the condition for hallucination identified by Kalai and Vempala, and, further, that it is an almost characterization of hallucination: hallucination implies innovation, and conversely, innovation implies hallucination with high probability. We also provide lower bounds on the hallucination rate based on the "innovation rate", and by relating innovation rate back to missing mass, we obtain new hallucination rate lower bounds based on missing mass that extend the results of Kalai and Vempala.

Measuring the creativity of large language models (LLMs) is essential for designing methods that can improve creativity and for enhancing our scientific understanding of this ability. To accomplish this, it has become common in recent years to administer tests of human creativity to LLMs. Although these tests provide a convenient and fully automated way to score "creativity," their validity as measures of machine creativity has not been established, and these tests already have limited validity as predictors of human creativity. To address this problem, we conduct the first large-scale, systematic study assessing the effectiveness of human creativity tests for predicting the creative achievement of LLMs across three target constructs: creative writing, divergent thinking, and scientific ideation. We find that the Divergent Association Task (DAT) and the Conditional DAT are the best predictors of creative writing and divergent thinking, respectively, but that test effectiveness varies significantly by construct, and no single test predicts all constructs well. Moreover, contrary to popular belief, no existing test reliably predicts scientific ideation ability. Motivated by this problem, we introduce the Divergent Remote Association Test (DRAT), a vocabulary-space test that assesses both convergent and divergent thinking in a single instrument. The DRAT is the first and only creativity test for LLMs that is a significant predictor of scientific ideation ability, demonstrating robustness across major design choices. Furthermore, the performance gain of the DRAT is not recoverable from any linear combination of the Divergent Association Task and the Remote Associates Test, indicating that assessing divergent and convergent thinking in the same test is essential to reliably predicting scientific ideation ability.

Despite the growing use of large language models (LLMs) as creativity evaluators, evidence of their alignment with human evaluations remains mixed, raising the question of when and why their judgments converge with or diverge from those of humans. Across three studies and six widely used LLMs, we addressed this gap by identifying the standards underlying LLM creativity evaluation and examining their downstream implications. Study 1 showed that LLMs generally relied on a narrower subset of human creativity evaluation standards. Convergence with human standards was strongest in the novelty dimension, whereas divergence was clearest in the contextual dimension, which captures social, market, and reputational information. Moreover, each LLM exhibited distinct, model-specific standards that varied substantially in breadth. These differences in evaluation standards were reflected in actual creativity judgments. Study 2 (N = 1,103 ideas) showed that LLM evaluations were moderately correlated with human evaluations, and individual LLMs with broader standards better distinguished ideas humans judged as more versus less creative. Study 3 (N = 1,195 participants) showed that LLMs were less sensitive to contextual information: such information significantly altered human creativity ratings but left LLM ratings largely unchanged. Together, our findings help explain the mixed evidence on LLM-human alignment, showing that alignment depends on the evidence a judgment demands and the standards each model applies. Selecting an LLM evaluator is therefore a consequential decision: different models, applying different standards, recognise different ideas as creative.