# Generation Space Size: Understanding and Calibrating Open-Endedness of LLM Generations

arXiv: https://arxiv.org/abs/2510.12699 · HTML: https://mlsanity.com/paper/2510.12699/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 58 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 30 of 45)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [AmbigQA: Answering Ambiguous Open-domain Questions](https://mlsanity.com/paper/2004.10645/) (2020)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Same Task, More Tokens: the Impact of Input Length on the Reasoning Performance of Large Language Models](https://mlsanity.com/paper/2402.14848/) (2024)
- [SituatedQA: Incorporating Extra-Linguistic Contexts into QA](https://mlsanity.com/paper/2109.06157/) (2021)
- [The PRISM Alignment Dataset: What Participatory, Representative and Individualised Human Feedback Reveals About the Subjective and Multicultural Alignment of Large Language Models](https://mlsanity.com/paper/2404.16019/) (2024)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse](https://mlsanity.com/paper/2410.21333/) (2024)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [Selectively Answering Ambiguous Questions](https://mlsanity.com/paper/2305.14613/) (2023)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Evaluating the Diversity and Quality of LLM Generated Content](https://mlsanity.com/paper/2504.12522/) (2025)
- [Base Models Beat Aligned Models at Randomness and Creativity](https://mlsanity.com/paper/2505.00047/) (2025)
- [Grounding Gaps in Language Model Generations](https://mlsanity.com/paper/2311.09144/) (2023)

## Built on by (most cited first, 2 of 2)

- [Sampling More, Getting Less: Calibration is the Diversity Bottleneck in LLMs](https://mlsanity.com/paper/2605.11128/) (2026)
- [Knowing Your Uncertainty -- On the application of LLM in social sciences](https://mlsanity.com/paper/2512.05461/) (2025)

## Abstract (arXiv)

Different open-ended generation tasks require different degrees of output diversity. However, current LLMs are often miscalibrated. They collapse to overly homogeneous outputs for creative tasks and hallucinate diverse but incorrect responses for factual tasks. We argue that these two failure modes are unified by, and can both be addressed by, the notion of effective generation space size (GSS) -- the set of semantically distinct outputs a model considers for a prompt. We present GSSBench, a task suite of prompt pairs with ground-truth GSS relationships to assess different metrics and understand where models diverge from desired behavior. We find that hallucination detection metrics, particularly EigenScore, consistently outperform standard diversity and uncertainty quantification metrics, while using only model internals, providing interpretable insights into a model's internal task representations. We demonstrate three applications of GSS: (1) detecting prompt ambiguity and predicting clarification questions for better grounding, (2) interpreting overthinking and underthinking in reasoning models, and (3) steering models to expand their generation space to yield high-quality and diverse outputs.