# ThinkSum: Probabilistic reasoning over sets using large language models

arXiv: https://arxiv.org/abs/2210.01293 · HTML: https://mlsanity.com/paper/2210.01293/

## Key facts

- Cited by 23 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 19 of its 43 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## 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, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [The Unreliability of Explanations in Few-shot Prompting for Textual Reasoning](https://mlsanity.com/paper/2205.03401/) (2022)
- [Maieutic Prompting: Logically Consistent Reasoning with Recursive Explanations](https://mlsanity.com/paper/2205.11822/) (2022)
- [A Token-level Reference-free Hallucination Detection Benchmark for Free-form Text Generation](https://mlsanity.com/paper/2104.08704/) (2021)
- [Rationale-Augmented Ensembles in Language Models](https://mlsanity.com/paper/2207.00747/) (2022)
- [The Consciousness Prior](https://mlsanity.com/paper/1709.08568/) (2017)
- [Language Model Cascades](https://mlsanity.com/paper/2207.10342/) (2022)

## Built on by (most cited first, 23 of 23)

- [ToolkenGPT: Augmenting Frozen Language Models with Massive Tools via Tool Embeddings](https://mlsanity.com/paper/2305.11554/) (2023)
- [PromptAgent: Strategic Planning with Language Models Enables Expert-level Prompt Optimization](https://mlsanity.com/paper/2310.16427/) (2023)
- [Prompting Is Programming: A Query Language for Large Language Models](https://mlsanity.com/paper/2212.06094/) (2022)
- [The Life Cycle of Knowledge in Big Language Models: A Survey](https://mlsanity.com/paper/2303.07616/) (2023)
- [Holistic Evaluation of GPT-4V for Biomedical Imaging](https://mlsanity.com/paper/2312.05256/) (2023)
- [BIRD: A Trustworthy Bayesian Inference Framework for Large Language Models](https://mlsanity.com/paper/2404.12494/) (2024)
- [Benchmarking Reward Hack Detection in Code Environments via Contrastive Analysis](https://mlsanity.com/paper/2601.20103/) (2026)
- [GPT is becoming a Turing machine: Here are some ways to program it](https://mlsanity.com/paper/2303.14310/) (2023)
- [Iterated Decomposition: Improving Science Q&A by Supervising Reasoning Processes](https://mlsanity.com/paper/2301.01751/) (2023)
- [A Survey on Parallel Reasoning](https://mlsanity.com/paper/2510.12164/) (2025)
- [Always Tell Me The Odds: Fine-grained Conditional Probability Estimation](https://mlsanity.com/paper/2505.01595/) (2025)
- [Towards Building Specialized Generalist AI with System 1 and System 2 Fusion](https://mlsanity.com/paper/2407.08642/) (2024)
- [Codenames as a Benchmark for Large Language Models](https://mlsanity.com/paper/2412.11373/) (2024)
- [Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2509.10739/) (2025)
- [Disentangling Extraction and Reasoning in Multi-hop Spatial Reasoning](https://mlsanity.com/paper/2310.16731/) (2023)
- [Exploring the Reversal Curse and Other Deductive Logical Reasoning in BERT and GPT-Based Large Language Models](https://mlsanity.com/paper/2312.03633/) (2023)
- [DeFine: Decision-Making with Analogical Reasoning over Factor Profiles](https://mlsanity.com/paper/2410.01772/) (2024)
- [Prompt Sketching for Large Language Models](https://mlsanity.com/paper/2311.04954/) (2023)
- [Ad-hoc Concept Forming in the Game Codenames as a Means for Evaluating Large Language Models](https://mlsanity.com/paper/2502.11707/) (2025)
- [Bonsai: Interpretable Tree-Adaptive Grounded Reasoning](https://mlsanity.com/paper/2504.03640/) (2025)
- [D-Models and E-Models: Diversity-Stability Trade-offs in the Sampling Behavior of Large Language Models](https://mlsanity.com/paper/2601.17865/) (2026)
- [A Multi-Agent LLM Framework for Rating the Quality of Surgical Feedback](https://mlsanity.com/paper/2605.25440/) (2026)
- [PrimeScientist: Strategic Allocation of Research Effort in Autonomous Research](https://mlsanity.com/paper/2609.17846/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context learning). However, recent studies show that even the more advanced LLMs fail in scenarios that require reasoning over multiple objects or facts and making sequences of logical deductions. We propose a two-stage probabilistic inference paradigm, ThinkSum, which reasons over sets of objects or facts in a structured manner. In the first stage (Think - retrieval of associations), a LLM is queried in parallel over a set of phrases extracted from the prompt or an auxiliary model call. In the second stage (Sum - probabilistic inference or reasoning), the results of these queries are aggregated to make the final prediction. We demonstrate the possibilities and advantages of ThinkSum on the BIG-bench suite of LLM evaluation tasks, achieving improvements over the state of the art using GPT-family models on thirteen difficult tasks, often with far smaller model variants. We also compare and contrast ThinkSum with other proposed modifications to direct prompting of LLMs, such as variants of chain-of-thought prompting. Our results suggest that because the probabilistic inference in ThinkSum is performed outside of calls to the LLM, ThinkSum is less sensitive to prompt design, yields more interpretable predictions, and can be flexibly combined with latent variable models to extract structured knowledge from LLMs. Overall, our proposed paradigm represents a promising approach for enhancing the reasoning capabilities of LLMs.