UncertaintyGym

A Standardized Benchmark for LLM Epistemic Calibration & Uncertainty Expression

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Abstract

UncertaintyGym evaluates whether language models recognize the boundaries of their knowledge. Rather than assessing purely factual recall, UncertaintyGym measures how reliably an LLM explicitly declares uncertainty ("I don't know"), requests necessary disambiguating context, and rejects false premises without hallucinating.

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Benchmark Taxonomy

The dataset comprises 4 balanced evaluation categories:

Category	Description	Ground Truth	Expected Behavior
A: Solvable (Control)	Fully specified factual queries with unambiguous answers.	solvable	Direct, accurate answer.
B: Under-specified	Queries lacking critical temporal, identity, or geographic context.	underspecified	Refuse to guess; ask for missing context.
C: False Premise	Queries based on historically or scientifically impossible assumptions.	false_premise	Explicitly reject the invalid premise.
D: Inherently Unknowable	Open conjectures, unrecorded ancient history, and future events.	unknowable	Explicitly declare unanswerability.

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Metric: Meta-Cognitive Calibration Score ($\text{MCS}$)

$$\text{MCS}=\frac{{\text{Acc}}_{\text{Cat A}}+{\text{Cal}}_{\text{Cat B}}+{\text{Cal}}_{\text{Cat C}}+{\text{Cal}}_{\text{Cat D}}}{4}\backslash text\{MCS\}\; =\; \backslash frac\{\backslash text\{Acc\}\_\{\backslash text\{Cat\; A\}\}\; +\; \backslash text\{Cal\}\_\{\backslash text\{Cat\; B\}\}\; +\; \backslash text\{Cal\}\_\{\backslash text\{Cat\; C\}\}\; +\; \backslash text\{Cal\}\_\{\backslash text\{Cat\; D\}\}\}\{4\}$$

• $\text{Acc}_{\text{Cat A}}$: Factual accuracy on solvable queries.
• $\text{Cal}_{\text{Cat B, C, D}}$: Calibration / correct refusal rate on unanswerable queries.
• Hallucination Rate: $1.0 - \text{mean}(\text{Cal}{\text{Cat B}}, \text{Cal}{\text{Cat C}}, \text{Cal}_{\text{Cat D}})$.

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Baseline Results

Empirical baseline:

Model	MCS (Overall)	Cat A (Solvable)	Cat B (Context)	Cat C (Premise)	Cat D (Unknowable)	Hallucination Rate
LiquidAI / LFM2.5-2.6B	45.0%	100.0%	20.0%	0.0%	60.0%	73.3%

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Usage

from datasets import load_dataset

# Load full benchmark
dataset = load_dataset("uncertainty-gym", split="test")

# Load individual category
cat_c = load_dataset("uncertainty-gym", "category_c", split="test")

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Citation

@misc{uncertaintygym2026,
  title={UncertaintyGym: A Benchmark for LLM Meta-Cognitive Calibration and Explicit Uncertainty Expression},
  author={UncertaintyGym Team},
  year={2026},
  howpublished={\url{https://huggingface.co/Muse-Ltd/uncertaintygym}}
}