# Doing Experiments and Revising Rules with Natural Language and Probabilistic Reasoning

arXiv: https://arxiv.org/abs/2402.06025 · HTML: https://mlsanity.com/paper/2402.06025/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 85 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [Large Language Models as Commonsense Knowledge for Large-Scale Task Planning](https://mlsanity.com/paper/2305.14078/) (2023)
- [Language models show human-like content effects on reasoning tasks](https://mlsanity.com/paper/2207.07051/) (2022)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [Language Model Cascades](https://mlsanity.com/paper/2207.10342/) (2022)
- [Eliciting Human Preferences with Language Models](https://mlsanity.com/paper/2310.11589/) (2023)
- [Phenomenal Yet Puzzling: Testing Inductive Reasoning Capabilities of Language Models with Hypothesis Refinement](https://mlsanity.com/paper/2310.08559/) (2023)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Training Chain-of-Thought via Latent-Variable Inference](https://mlsanity.com/paper/2312.02179/) (2023)
- [Human-Level Reinforcement Learning through Theory-Based Modeling, Exploration, and Planning](https://mlsanity.com/paper/2107.12544/) (2021)
- [FIND: A Function Description Benchmark for Evaluating Interpretability Methods](https://mlsanity.com/paper/2309.03886/) (2023)
- [ACRE: Abstract Causal REasoning Beyond Covariation](https://mlsanity.com/paper/2103.14232/) (2021)
- [Active Preference Inference using Language Models and Probabilistic Reasoning](https://mlsanity.com/paper/2312.12009/) (2023)
- [Learning abstract structure for drawing by efficient motor program induction](https://mlsanity.com/paper/2008.03519/) (2020)
- [Human-like Few-Shot Learning via Bayesian Reasoning over Natural Language](https://mlsanity.com/paper/2306.02797/) (2023)
- [Using Natural Language and Program Abstractions to Instill Human Inductive Biases in Machines](https://mlsanity.com/paper/2205.11558/) (2022)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [Bayesian Synthesis of Probabilistic Programs for Automatic Data Modeling](https://mlsanity.com/paper/1907.06249/) (2019)
- [Modeling infant object perception as program induction](https://mlsanity.com/paper/2309.07099/) (2023)

## Built on by (most cited first, 24 of 24)

- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [Is Programming by Example solved by LLMs?](https://mlsanity.com/paper/2406.08316/) (2024)
- [PoE-World: Compositional World Modeling with Products of Programmatic Experts](https://mlsanity.com/paper/2505.10819/) (2025)
- [AutoToM: Scaling Model-based Mental Inference via Automated Agent Modeling](https://mlsanity.com/paper/2502.15676/) (2025)
- [WorldLLM: Improving LLMs' world modeling using curiosity-driven theory-making](https://mlsanity.com/paper/2506.06725/) (2025)
- [Shoot First, Ask Questions Later? Building Rational Agents that Explore and Act Like People](https://mlsanity.com/paper/2510.20886/) (2025)
- [Failing to Falsify: Evaluating and Mitigating Confirmation Bias in Language Models](https://mlsanity.com/paper/2604.02485/) (2026)
- [OPINE-World: Programmatic World Modeling with Ontology-error-Prioritized Interactive Exploration for ARC-AGI-3](https://mlsanity.com/paper/2607.01531/) (2026)
- [The Curious Language Model: Strategic Test-Time Information Acquisition](https://mlsanity.com/paper/2506.09173/) (2025)
- [Wiring the 'Why': A Unified Taxonomy and Survey of Abductive Reasoning in LLMs](https://mlsanity.com/paper/2604.08016/) (2026)
- [Program Synthesis via Test-Time Transduction](https://mlsanity.com/paper/2509.17393/) (2025)
- [Disentangling Exploration of Large Language Models by Optimal Exploitation](https://mlsanity.com/paper/2501.08925/) (2025)
- [Bonsai: Interpretable Tree-Adaptive Grounded Reasoning](https://mlsanity.com/paper/2504.03640/) (2025)
- [Beyond Either-Or Reasoning: Transduction and Induction as Cooperative Problem-Solving Paradigms](https://mlsanity.com/paper/2505.14744/) (2025)
- [Information Seeking for Robust Decision Making under Partial Observability](https://mlsanity.com/paper/2510.01531/) (2025)
- [Playing ZendoWorld: Challenging AI Agents on Active Visual Concept Induction](https://mlsanity.com/paper/2607.08233/) (2026)
- [Analysis of Error Sources in LLM-based Hypothesis Search for Few-Shot Rule Induction](https://mlsanity.com/paper/2509.01016/) (2025)
- [Uncertainty as a Planning Signal: Multi-Turn Decision Making for Goal-Oriented Conversation](https://mlsanity.com/paper/2604.03924/) (2026)
- [Hypothesis Generation and Inductive Inference in Children and Language Models](https://mlsanity.com/paper/2605.24528/) (2026)
- [Human Adults and LLMs as Scientists: Who Benefits from Active Exploration?](https://mlsanity.com/paper/2606.06464/) (2026)
- [Solver-Aware Decompositions for Programming-by-Example: When Dividing Requires Knowing how to Conquer](https://mlsanity.com/paper/2608.03461/) (2026)
- [Schema: Discovering Unknown Environments via Agentic Program Induction](https://mlsanity.com/paper/2609.39140/) (2026)
- [Bayesian Fine-tuning Yields Language Models that are as Bayesian as their Beliefs Allow](https://mlsanity.com/paper/2610.00679/) (2026)
- [Hypothesis-guided discovery of cognitive algorithms via program refinement](https://mlsanity.com/paper/2610.02523/) (2026)

## Abstract (arXiv)

We give a model of how to infer natural language rules by doing experiments. The model integrates Large Language Models (LLMs) with Monte Carlo algorithms for probabilistic inference, interleaving online belief updates with experiment design under information-theoretic criteria. We conduct a human-model comparison on a Zendo-style task, finding that a critical ingredient for modeling the human data is to assume that humans also consider fuzzy, probabilistic rules, in addition to assuming that humans perform approximately-Bayesian belief updates. We also compare with recent algorithms for using LLMs to generate and revise hypotheses, finding that our online inference method yields higher accuracy at recovering the true underlying rule, and provides better support for designing optimal experiments.