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Exploiting LLMs for Automatic Hypothesis Assessment via a Logit-Based Calibrated Prior
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Proposes Logit-based Calibrated Prior (LCP), which turns an LLM's top-k token logits over a numeric correlation answer into a smoothed, truncated density used to score how surprising observed correlations are for automatic hypothesis assessment.
Problem
Hypothesis generation systems surface thousands of correlations, but there is no automatic way to judge which are novel or surprising; the paper asks whether an LLM's prior over correlation values can serve as an assessment signal.
Approach
Construct a continuous predictive distribution over Pearson correlation directly from the LLM's raw token logits (enumerating top-k numeric token sequences, aggregating joint log-probs, softmax-normalizing, then Gaussian kernel smoothing with a bandwidth tuned by validation NLL), avoiding parametric Gaussian elicitation and sampling.
Key results
- LCP achieves 78.8% sign accuracy, 0.26 MAE, and 89.2% 95% interval coverage on predicting Pearson correlation, versus 59.9% coverage for uncalibrated KDE and 49.1% for Gaussian.
- LCP reduces average information content from 0.69 (uniform) to 0.27, while Gaussian and KDE priors raise it to 4.10 and 1.73.
- On Nexus, LCP ranking reaches Precision@10 of 0.80 and average expert-label rank 21.5, vs 30.9 for fine-tuned RoBERTa and 58.0 for random.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LCP instead of a uniform prior | Correlation prediction · Correlation benchmark (2,096 pairs) | average information content: 0.69 -> 0.27 | Helped |
| Use LCP instead of the Gaussian prior | Correlation prediction · Correlation benchmark (2,096 pairs) | 95% credible interval coverage: 49.1% -> 89.2% | Helped |
| Use LCP instead of KDE | Correlation prediction · Correlation benchmark (2,096 pairs) | 95% credible interval coverage: 59.9% -> 89.2% | Helped |
| Use LCP instead of a uniform prior | Correlation prediction · Correlation benchmark (2,096 pairs) | absolute error: 0.51 -> 0.26 | Helped |
| Use LCP instead of the Gaussian prior | Correlation prediction · Correlation benchmark (2,096 pairs) | average information content: 4.10 -> 0.27 | Helped |
| Use LCP instead of KDE | Correlation prediction · Correlation benchmark (2,096 pairs) | average information content: 1.73 -> 0.27 | Helped |
| Rank by LCP prior likelihood instead of fine-tuned RoBERTa probability | Hypothesis-worthy correlation retrieval · Nexus Chicago Open Data (115-pair pool) | Precision@10: 0.60 -> 0.80 | Helped |
| Rank by LCP prior likelihood instead of absolute correlation magnitude | Hypothesis-worthy correlation retrieval · Nexus Chicago Open Data (115-pair pool) | Precision@5: 0 -> 0.60 | Helped |
| Supply contradictory context rather than the original context | LCP · Contradictory contexts (84 pairs) | sign accuracy: 100% -> 95.2% | Hurt |
| Use LCP instead of a uniform prior | Correlation prediction with contradictory contexts · Contradictory contexts (84 pairs) | sign accuracy: 0.464 -> 0.952 | Helped |
| Use LCP instead of a uniform prior | Correlation prediction with contradictory contexts · Contradictory contexts (84 pairs) | average information content: 0.69 -> 0.25 | Helped |
Surprising findings
- Gaussian priors from GPT-4o default to sigma=0.1 in 74% of cases, implicitly assuming sample size n=100 rather than reflecting epistemic uncertainty.
- Ranking by absolute correlation |r| performs worst on the Nexus task (zero precision), since extreme correlations are often trivial or redundant.
Limitations
- One LLM call per variable pair is costly at scale.
- LLMs can produce false positives and false negatives relative to expert knowledge.
- Sigma must be re-tuned if the model, prompt, or target metric changes.
Experimental setup
Datasets: Cause-Effect Pairs Kaggle tables Nexus Chicago Open Data correlations
Benchmarks: 2,096-pair correlation benchmark Nexus expert-flagged correlations (15 of 115) Cause-Effect counterfactual contexts (84 pairs)
Metrics: sign accuracy mean absolute error 95% credible interval coverage information content accuracy F1 MCC Precision@K average rank
Baselines: Uniform prior Gaussian prior (LLM-verbalized mean and std) KDE prior (Scott's rule) RoBERTa classifier Random ranking |r| ranking
Builds on: SHELF expert elicitation Scott's rule Nexus
Closest papers by meaning
- Can Large Language Models Infer Causation from Correlation? (ICLR 2024 · similarity 0.87)
- MOOSE-Chem2: Exploring LLM Limits in Fine-Grained Scientific Hypothesis Discovery via Hierarchical Search (NeurIPS 2025 · similarity 0.86)
- The Silent Hyperparameter: Quantifying the Impact of Inference Backends on LLM Reproducibility (NeurIPS 2026 · similarity 0.86)
- Fisher-R1: Training LLM Agents for Reliable Hypothesis Testing (NeurIPS 2026 · similarity 0.86)
- Calibration without labels in multiple testing (NeurIPS 2026 · similarity 0.86)
- LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language (NeurIPS 2024 · similarity 0.85)
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