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Doing Experiments and Revising Rules with Natural Language and Probabilistic Reasoning
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Proposes LLM-SMC-S, an online sequential Monte Carlo method where an LLM revises natural-language rule hypotheses and proposes experiments ranked by information gain, evaluated on Zendo and ActiveACRE and compared against humans and batch LLM inference.
Problem
Modeling how humans infer natural-language rules through active experimentation, requiring online belief updates over hypotheses and experiment selection under uncertainty.
Approach
Combines an LLM as a proposal distribution with Sequential Monte Carlo Samplers so that only the worst particles are revised by the LLM each step, enabling online natural-language hypothesis revision; experiments proposed by an LLM are reranked by expected information gain, and fuzzy (probabilistic) rules are added to better match humans.
Key results
- Online, Hard reaches 6.55/8 average predictive posterior on Zendo versus 5.26/8 for humans and 4.60/8 for Direct LLM.
- Online, Fuzzy achieves the best human log likelihood (-1478.82) and R^2=.35 on per-judgment prediction, while Online, Hard has R^2=.10 on fine-grained accuracy.
- On ActiveACRE, Online, Hard achieves 0.35 task solving versus 0.10 for batch hard inference.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use online inference instead of batch inference with hard rules | Rule induction model · Zendo | Avg Pred Posterior: 6.18 ± 0.14 -> 6.55 ± 0.13 | Helped |
| Use online inference instead of batch inference with hard rules | Rule induction model · ActiveACRE | Task Solving: 0.15 ± 0.08 -> 0.35 ± 0.11 | Helped |
| Use fuzzy probabilistic rules rather than hard deterministic rules (ablation) | Online inference model · Zendo | Avg Pred Posterior: 6.55 ± 0.13 -> 5.35 ± 0.09 | Hurt |
| Use fuzzy probabilistic rules rather than hard deterministic rules (ablation) | Online inference model · ActiveACRE | ROC AUC: 0.87 ± 0.04 -> 0.90 ± 0.03 | Helped |
| Use fuzzy probabilistic rules rather than hard deterministic rules (ablation) | Online inference model · Zendo human data | LogL: -5209.93 -> -1478.82 | Helped |
| Use online inference with fuzzy rules instead of batch fuzzy inference | Rule induction model · Zendo human accuracy patterns | R²: 0.05 -> .57 | Helped |
| Select experiments by information gain instead of random selection (ablation) | Online hard-rule model · Zendo | Avg Pred Posterior: 5.84 ± 0.19 -> 6.55 ± 0.13 | Helped |
| Select experiments by information gain instead of direct LLM proposals (ablation) | Online hard-rule model · Zendo | Avg Pred Posterior: 4.72 ± 0.08 -> 6.55 ± 0.13 | Helped |
| Select experiments by information gain instead of random selection (ablation) | Online fuzzy-rule model · Zendo | Avg Pred Posterior: 5.03 ± 0.11 -> 5.35 ± 0.09 | Helped |
| Select experiments by information gain instead of direct LLM proposals (ablation) | Online fuzzy-rule model · Zendo | Avg Pred Posterior: 4.52 ± 0.08 -> 5.35 ± 0.09 | Helped |
| Use a random rather than an LLM experiment proposer for information-gain selection (ablation) | Online hard-rule model · Zendo | Avg Pred Posterior: 5.84 ± 0.19 -> 5.84 ± 0.19 | No clear effect |
| Increase online hard-rule inference LLM calls per iteration from 1 to 5 (ablation) | Online hard-rule model · Zendo | Avg Pred Posterior: 6.15 ± 0.26 -> 6.55 ± 0.13 | Helped |
Surprising findings
- A random experiment proposer performs about as well as the LLM experiment proposer when reranked by information gain.
- Vanilla LLM experiment proposals (without information-gain reranking) underperform random experiments.
Limitations
- Hypotheses considered are simple and stereotyped in form
- Does not model abductive reasoning about unseen objects or paradigm shifts
- Hard-rule online model fits human fine-grained judgments poorly (R^2=.10) despite high accuracy
Experimental setup
Datasets: Zendo human data (Bramley et al. 2018) ACRE dataset
Benchmarks: Zendo ActiveACRE
Metrics: average predictive posterior ROC AUC F1 task solving R^2 vs human accuracy log likelihood of human data BIC
Baselines: Direct LLM (ReAct-style) Batch inference (fuzzy) Batch inference (hard) Batch with refinement (hard) Bramley et al. 2018 Bayesian model Random experiment proposer
Builds on: Sequential Monte Carlo Samplers Bayesian optimal experiment design hypothesis refinement
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