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

TL;DR

This work reframes open-ended generation challenges around Generation Space Size (GSS), the scope of outputs a model considers for a given prompt. It introduces GSSBench as a suite of prompt-pair tasks with known GSS relations and identifies EigenScore variants as the strongest proxies for a model’s GSS, enabling analysis of grounding, reasoning, and diversity calibration. Key findings show EigenScore variants reliably predict prompt ambiguity, model clarification behavior, and reasoning token-length correlations, while larger instruction-tuned models do not universally improve calibration. A Leave-One-Out EigenScore (LOOE) extension demonstrates a semantically aware, internal-representation–based approach to promoting diverse, high-quality outputs. Overall, the framework provides a structured path to calibrate generation space size across tasks and models, with potential for GSS-aware alignment and grounding improvements.

Abstract

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.

Figures (11)

• Figure 1: Overview of two failure modes of LLMs under the lens of generation space size. An LLM may generate overly homogenous responses when the true GSS ought to be larger (left) or generate incorrect hallucinations when the true GSS ought to be small (right).
• Figure 2: The distribution of metric scores for prompts with smaller GSS (original) versus larger (complement). Here we show the distributions for Llama-8B-Instruct on the Complement Dataset as an example; see Appendix \ref{['appendix:distribution']} for all models and datasets.
• Figure 3: Pearson's $r$ correlation between reasoning token length and various metrics across three datasets (BRT is short for Big Reasoning Traces; Modal is short for Modal Logic; Epistemic is short for Epistemic Logic), and three Qwen3 model sizes.
• Figure A1: The distribution of metric scores for the two types of prompts for Llama-8B-Instruct on the FactualQA Dataset.
• Figure A2: The distribution of metric scores for the two types of prompts for Llama-8B-Instruct on the Random Choice Dataset.