Title: ThinkSum: Probabilistic reasoning over sets using large language models. Abstract: 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 largest LLMs fail in scenarios that require reasoning over multiple objects or facts or making sequences of logical deductions. We propose a two-stage probabilistic inference paradigm, ThinkSum, that reasons over sets of objects or facts in a structured manner. In the first stage (Think -- 'fast' 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 -- 'slow' probabilistic inference or reasoning), the results of these queries are aggregated to make the final prediction. We demonstrate the advantages of ThinkSum on the BIG-bench suite of evaluation tasks, achieving improvements over the state of the art using GPT-family models on ten difficult tasks, often with far smaller model variants. We compare and contrast ThinkSum with other proposed modifications to direct prompting of LLMs, such as variants of chain-of-thought prompting. We argue 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.