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Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models
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Proposes Inv-Entropy, a fully probabilistic dual-random-walk UQ framework for LLMs that measures input diversity conditioned on outputs, plus the GAAP genetic perturbation algorithm and the TSU temperature-sensitivity metric.
Problem
Uncertainty quantification for LLMs relies on heuristic consistency checks lacking a probabilistic foundation, and correctness-based evaluation of UQ needs labels and can fail in open-ended settings.
Approach
Model input-output pairs as two Markov chains whose transitions follow semantic similarity, derive P(X|Y) from their composition, and define Inv-Entropy as conditional entropy of inputs given outputs over perturbed inputs with bootstrapped replications; GAAP generates diverse perturbations via genetic operators.
Key results
- Inv-Entropy achieves AUROC 0.788 on TriviaQA and 0.780 on MMLU, best among compared methods in all five datasets for AUROC.
- On MMLU, Inv-Entropy reaches PRR 0.898, versus 0.798 for the best baseline (P(True)... LUQ 0.787 and DegMat 0.771).
- Inv-Entropy TSU(0.7-1.4) on TriviaQA is 47.21 versus 27.63 for the best baseline LUQ.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · MMLU | AUROC: 0.648 -> 0.780 | Helped |
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · MMLU | PRR: 0.787 -> 0.898 | Helped |
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · TriviaQA | AUROC: 0.734 -> 0.788 | Helped |
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · SciQ | AUROC: 0.726 -> 0.740 | Helped |
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · NQ | AUROC: 0.627 -> 0.661 | Helped |
| Use Inv-Entropy rather than the strongest baseline | GPT-3.5-Turbo uncertainty estimation · GSM8K | AUROC: 0.678 -> 0.695 | Helped |
| Use inverse conditional entropy P(X|Y) instead of non-inverse P(Y|X) (ablation) | Inv-Entropy · TriviaQA | AUROC: 0.786 -> 0.788 | Helped |
| Use inverse conditional entropy P(X|Y) instead of non-inverse P(Y|X) (ablation) | Inv-Entropy · MMLU | AUROC: 0.710 -> 0.780 | Helped |
| Add replications and bootstrapping (ablation) | NR-Inv-Entropy · MMLU | AUROC: 0.604 -> 0.780 | Helped |
| Add replications and bootstrapping (ablation) | NR-Inv-Entropy · TriviaQA | AUROC: 0.743 -> 0.788 | Helped |
| Replace ChatGPT-based paraphrasing with GAAP perturbations | Inv-Entropy · Three datasets across both LLMs | AUROC | Helped |
| Use a larger embedding encoder rather than a lightweight encoder (ablation) | Inv-Entropy · Several tasks | uncertainty score | Helped |
Surprising findings
- Replication alone can yield identical responses and falsely low uncertainty even when all answers are wrong, motivating input perturbations.
- Even without replications (NR-Inv-Entropy), the method remains competitive with many baselines.
Limitations
- Computational cost grows with number of perturbations and replications.
- Evaluation relies on GPT-3.5-Turbo as correctness judge for most datasets.
- Perturbation count fixed at nine per question for comparability.
Experimental setup
Datasets: TriviaQA SciQ Natural Questions MMLU GSM8K
Benchmarks: TriviaQA SciQ Natural Questions MMLU GSM8K
Metrics: AUROC PRR Brier score TSU
Baselines: Semantic Entropy Kernel Entropy Verbalized Uncertainty P(True) LexSim DegMat LUQ KLE
Builds on: Semantic Entropy SPUQ KeyBERT Sentence-BERT
Closest papers by meaning
- Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities (NeurIPS 2024 · similarity 0.92)
- Efficient semantic uncertainty quantification in language models via diversity-steered sampling (NeurIPS 2025 · similarity 0.90)
- Conformal Prediction with Paraphrase-Aware Scoring for LLM Uncertainty Quantification (NeurIPS 2026 · similarity 0.90)
- Integrating Local and Global Entropy for Uncertainty Quantification in LLMs (NeurIPS 2026 · similarity 0.90)
- SPANUQ: Span-Level Uncertainty Quantification for Large Language Model Generation (NeurIPS 2026 · similarity 0.89)
- FLUE: Streamlined Uncertainty Estimation for Large Language Models (AAAI 2025 · similarity 0.89)
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