# HypoSpace: A Diagnostic Benchmark for Set-Valued Hypothesis Generation under Underdetermination and Sublinear Coverage Bounds

arXiv: https://arxiv.org/abs/2510.15614 · HTML: https://mlsanity.com/paper/2510.15614/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [A Performance Study of LLM-Generated Code on Leetcode](https://mlsanity.com/paper/2407.21579/) (2024)
- [HypoBench: Towards Systematic and Principled Benchmarking for Hypothesis Generation](https://mlsanity.com/paper/2504.11524/) (2025)
- [Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction](https://mlsanity.com/paper/2504.15266/) (2025)
- [IdeaBench: Benchmarking Large Language Models for Research Idea Generation](https://mlsanity.com/paper/2411.02429/) (2024)
- [CreativEval: Evaluating Creativity of LLM-Based Hardware Code Generation](https://mlsanity.com/paper/2404.08806/) (2024)
- [Can AI Be as Creative as Humans?](https://mlsanity.com/paper/2401.01623/) (2024)
- [Gravity-Bench-v1: A Benchmark on Gravitational Physics Discovery for Agents](https://mlsanity.com/paper/2501.18411/) (2025)

## Built on by (most cited first, 6 of 6)

- [Unlocking LLM Creativity in Science through Analogical Reasoning](https://mlsanity.com/paper/2605.11258/) (2026)
- [WeatherReasonSeg: A Benchmark for Weather-Aware Reasoning Segmentation in Visual Language Models](https://mlsanity.com/paper/2603.17680/) (2026)
- [Universe of Thoughts: Enabling Creative Reasoning with Large Language Models](https://mlsanity.com/paper/2511.20471/) (2025)
- [Evaluating Multiple LLM Generations with Validated Task Coverage](https://mlsanity.com/paper/2608.24228/) (2026)
- [From Scientific Observations to Mechanisms: Benchmarking Hypothesis Generation by AI Scientists](https://mlsanity.com/paper/2610.05197/) (2026)
- [Searching for What Matters: Open-Ended Discovery of Multiple Hypotheses with Agentic Data Exploration](https://mlsanity.com/paper/2610.17874/) (2026)

## Abstract (arXiv)

Many scientific problems are underdetermined: multiple distinct hypotheses are equally consistent with the same observations. In such settings, effective inference requires not only producing valid explanations, but also systematically exploring and covering the admissible hypothesis set. We introduce HypoSpace, a benchmark that treats large language models (LLMs) as samplers over finite hypothesis spaces and evaluates them on three metrics: Validity, Uniqueness, and Recovery. HypoSpace spans three structured domains (causal graph inference, gravity-constrained 3D voxel reconstruction, and Boolean genetic interaction modeling) with deterministic validators and exactly enumerable solution spaces, plus real-world anchored case studies. Empirically, HypoSpace reveals a capability- and scale-dependent coverage failure: models can maintain high Validity while exhibiting reduced Uniqueness and Recovery as admissible hypothesis spaces become larger or more combinatorial. We further show that the analysis on stratified decoding partially mitigates this collapse, demonstrating HypoSpace's utility as a diagnostic benchmark for set-valued inference. Code is available at: https://github.com/CTT-Pavilion/_HypoSpace.