The Geometry of Creative Variability: How Credal Sets Expose Calibration Gaps in Language Models (2025)

Abstract: Understanding uncertainty in large language models remains a fundamental challenge, particularly in creative tasks where multiple valid outputs exist. We present a geometric framework using credal sets—convex hulls of probability distributions—to quantify and decompose uncertainty in neural text generation, calibrated against human creative variation. Analyzing 500 creative writing prompts from the dataset with 10 unique human continuations each, we evaluate four language models across five decoding strategies, generating 100,000 stories. Our credal set analysis reveals substantial gaps in capturing human creative variation, with the best model-human calibration reaching only 0.434 (Gemma-2B with temperature 0.7). We decompose total uncertainty into epistemic and aleatoric components, finding that the choice of decoding strategy contributes 39.4% to 72.0% of total epistemic uncertainty. Model scale shows weak correlation with calibration quality and no significant difference exists between base and instruction-tuned models in calibration quality. Our geometric framework provides actionable insights for improving generation systems for human-AI creative alignment. We release our complete experimental framework at https://github.com/EstebanGarces/uncertainHuman .

## introduction the deployment of large language models in creative and open-ended applications demands not merely generating plausible text, but understanding and calibrating the uncertainty inherent in these generations. while uncertainty quantification has been extensively studied in discriminative tasks @xcite @xcite , the challenge becomes substantially more complex in generative settings where no single ground truth exists and prompt: "the last person on earth sits alone. there is a knock on the door." human continuations: current approaches to uncertainty quantification in language models predominantly focus on tokenlevel probabilities or computationally expensive ensemble methods @xcite . these methods, while valuable, fail to capture the semantic, lexical, and syntactic-level uncertainty that determines whether a model appropriately captures the breadth of human creative expression. more fundamentally, existing frameworks lack principled methods for distinguishing between aleatoric uncertainty-the irreducible variation inherent in creative tasks-and epistemic uncertainty arising from model limitations. this distinction proves crucial for both improving model design and establishing appropriate deployment boundaries. in this work, we address these limitations through a novel framework that leverages human variation as a natural calibration target for model uncertainty. our key insight is that multiple human responses to the same creative prompt provide a direct empirical measure of aleatoric uncertainty. by representing both human and model variation as credal sets-convex hulls of probability distributions over textual characteristics-we can geometrically analyze whether models exhibit appropriate uncertainty: high variation when humans disagree, and convergent outputs when humans reach consensus. this credal set approach offers several theoretical and practical advantages over existing methods. theoretically, it provides a rigorous framework for uncertainty decomposition that respects the inherently distributional nature of creative variation. each prompt induces its own distribution over possible continuations, and the collection of these distributions across many prompts forms a credal set that fully characterizes the uncertainty landscape. practically, this framework enables direct comparison between human and the model's uncertainty through geometric measures such as overlap coefficients, hausdorff distance @xcite , and volume ratios. our empirical investigation analyzes 500 carefully selected prompts from the writingprompts dataset, each accompanied by 10 verified unique human continuations totaling 5,000 human-written stories. we evaluate four language models-gpt2-xl @xcite , gemma-2b @xcite , mistral-7b-instruct-v0.2 @xcite , and llama-3.1-8b-instruct @xcite )-generating 10 samples per configuration across five decoding strategies, yielding 100,000 model-generated stories. through comprehensive analysis of semantic, lexical, and syntactic diversity, we construct and compare credal sets that reveal systematic patterns in how models capture or fail to capture human-like variation. ## related work uncertainty quantification in language models has emerged as a critical research area, particularly as these models are deployed in high-stakes applications. we organize our discussion around three main themes: theoretical frameworks for uncertainty decomposition, practical estimation methods, and uncertainty-aware generation strategies. ## conclusion this work establishes credal sets as a rigorous framework for uncertainty quantification in openended text generation, enabling principled geometric comparison between human and model variation patterns. through comprehensive analysis of 100,000 generated stories calibrated against 5,000 human-written stories, we demonstrate substantial gaps in how current language models capture human creative variation, with the best calibration reaching only 0.434 (gemma-2b with temperature 0.7) and overlap coefficients at most 0.033. our decomposition reveals that epistemic uncertainty from decoding strategy choice contributes 39.4-72.0% of total uncertainty across models, with base models showing higher sensitivity to configuration choices. the weak correlation between model scale and calibration (ρ = 0.400, @xmath0.600) and lack of significant difference between base and instruction-tuned models (@xmath1.486) challenge common assumptions about model development priorities. the credal set framework provides actionable insights for deploying language models in creative contexts and establishes quantitative benchmarks for evaluating progress toward human-ai creative alignment. as language models increasingly engage in open-ended generation tasks, our findings highlight the critical importance of decoding strategy selection and the need for architectural or training innovations specifically targeting uncertainty calibration.