# The Geometry of Creative Variability: How Credal Sets Expose Calibration Gaps in Language Models

arXiv: https://arxiv.org/abs/2509.23088 · HTML: https://mlsanity.com/paper/2509.23088/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Calibrating Large Language Models Using Their Generations Only](https://mlsanity.com/paper/2403.05973/) (2024)
- [What Comes Next? Evaluating Uncertainty in Neural Text Generators Against Human Production Variability](https://mlsanity.com/paper/2305.11707/) (2023)
- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [Adaptive Contrastive Search: Uncertainty-Guided Decoding for Open-Ended Text Generation](https://mlsanity.com/paper/2407.18698/) (2024)
- [GUARD: Glocal Uncertainty-Aware Robust Decoding for Effective and Efficient Open-Ended Text Generation](https://mlsanity.com/paper/2508.20757/) (2025)
- [Towards Better Open-Ended Text Generation: A Multicriteria Evaluation Framework](https://mlsanity.com/paper/2410.18653/) (2024)
- [Statistical Multicriteria Evaluation of LLM-Generated Text](https://mlsanity.com/paper/2506.18082/) (2025)

## Built on by (most cited first, 4 of 4)

- [LLMs Exhibit Significantly Lower Uncertainty in Creative Writing Than Professional Writers](https://mlsanity.com/paper/2602.16162/) (2026)
- [The Truncation Blind Spot: How Decoding Strategies Systematically Exclude Human-Like Token Choices](https://mlsanity.com/paper/2603.18482/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [Reference-Based Analysis of Coherence and Diversity in Open-Ended Text Generation](https://mlsanity.com/paper/2609.28080/) (2026)

## Abstract (arXiv)

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.