The Geometry of Creative Variability: How Credal Sets Expose Calibration Gaps in Language Models
Introduces a geometric credal set framework to quantify and decompose uncertainty in language models, analyzing 500 prompts with only 0.434 calibration at best.
Key Findings
Methodology
This paper proposes a geometric framework based on credal sets—convex hulls of probability distributions—to quantify uncertainty in neural text generation. By analyzing 500 prompts with 10 human continuations each, the authors construct human credal sets representing natural creative variation. They evaluate four language models across five decoding strategies, generating 100,000 stories. Using metrics like Hausdorff distance and overlap coefficients, they compare model and human credal sets to assess calibration. The total uncertainty is decomposed into epistemic (model-related) and aleatoric (inherent) components, revealing that decoding strategies contribute 39.4%-72% to epistemic uncertainty. The framework provides a geometric, interpretable measure of how well models capture human-like diversity.
Key Results
- The best model-human calibration achieved is 0.434 (Gemma-2B, temperature 0.7), indicating significant gaps in modeling human creative variation.
- Model size shows weak correlation with calibration (Spearman ρ=0.400, p=0.600), and no significant difference exists between base and instruction-tuned models in calibration quality.
- Decoding strategy choice accounts for 39.4%-72% of epistemic uncertainty, emphasizing the importance of strategy tuning for diversity control.
Significance
This work advances the understanding of uncertainty in generative models by providing a geometric, distribution-aware approach. It highlights the limitations of current models in capturing the full scope of human creative variation, guiding future improvements in model design and decoding strategies. The credal set framework offers a rigorous, interpretable way to quantify and compare model calibration, fostering more reliable and diverse content generation. Its implications span from theoretical insights into model uncertainty to practical tools for enhancing human-AI creative alignment, addressing longstanding challenges in AI-generated content quality and trustworthiness.
Technical Contribution
The paper introduces a novel geometric approach using credal sets—convex hulls of diversity vectors—to quantify uncertainty. It systematically decomposes total uncertainty into epistemic and aleatoric parts, based on diversity metrics across semantic, lexical, and syntactic dimensions. The framework employs set operations and distance metrics like Hausdorff distance and overlap coefficients for calibration assessment. It also analyzes the impact of decoding strategies and model scale on uncertainty, providing a comprehensive, interpretable toolkit for uncertainty quantification in open-ended text generation. This approach bridges distributional uncertainty with geometric intuition, enabling precise calibration diagnostics.
Novelty
This is the first application of credal sets to open-ended text generation, offering a distributional, geometric perspective on uncertainty. Unlike traditional probabilistic measures, credal sets capture the full range of plausible distributions, allowing for a nuanced analysis of diversity and calibration. The integration of multiple diversity metrics and the decomposition into epistemic and aleatoric components represent a significant methodological innovation, providing deeper insights into model behavior in creative tasks. This approach addresses a critical gap in the literature, where most prior work focused on token-level probabilities or ensemble methods.
Limitations
- The geometric calibration metrics primarily reflect diversity overlap and do not directly measure semantic coherence or content quality, which are subjective and context-dependent.
- The analysis is limited to a specific dataset and set of models; broader validation across tasks and architectures is needed.
- Constructing credal sets depends on human-generated samples, which may introduce bias or sampling variance, affecting robustness.
Future Work
Future research could incorporate semantic similarity measures into credal set construction, enabling richer uncertainty modeling. Extending the framework to multi-modal and multi-task scenarios will test its generality. Developing dynamic credal sets that adapt during generation could improve real-time calibration. Additionally, integrating user preferences and feedback may refine diversity control, making models more aligned with human expectations. Exploring automated methods for credal set optimization and visualization will further enhance practical usability.
AI Executive Summary
In the rapidly evolving field of natural language generation, understanding and calibrating model uncertainty remains a fundamental challenge. While large language models such as GPT-3 and beyond have demonstrated remarkable capabilities, their outputs often lack a transparent measure of confidence, especially in creative tasks where multiple valid responses exist. Traditional uncertainty quantification methods, focusing on token probabilities or ensemble approaches, fall short in capturing the semantic, lexical, and syntactic diversity inherent in human expression.
This paper introduces a novel geometric framework based on credal sets—convex hulls of probability distributions—to address this gap. By representing the diversity of human and model-generated continuations as geometric objects, the authors provide a visual and quantitative measure of how well models emulate human creative variation. Analyzing 500 prompts with 10 human responses each, the study evaluates four models across five decoding strategies, generating a total of 100,000 stories. The results reveal that the best calibration score achieved is only 0.434, indicating substantial misalignment with human diversity.
A key insight from the analysis is that decoding strategy choice significantly influences epistemic uncertainty, contributing up to 72%. Interestingly, model size shows only a weak correlation with calibration, and instruction tuning does not markedly improve diversity capture. The credal set approach enables a detailed decomposition of uncertainty, distinguishing between inherent variability (aleatoric) and model-related uncertainty (epistemic). This distinction is crucial for guiding model improvements and deployment strategies.
Overall, this work offers a rigorous, interpretable, and practical framework for uncertainty analysis in creative language generation. It highlights the importance of decoding strategies and geometric measures in achieving human-aligned AI systems. Future directions include extending the framework to multi-modal tasks, refining credal set construction with semantic features, and developing adaptive calibration methods to enhance the reliability and diversity of AI-generated content.
Deep Dive
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 WritingPrompts 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.