# Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs

arXiv: https://arxiv.org/abs/2509.10739 · HTML: https://mlsanity.com/paper/2509.10739/

## Key facts

- Cited by 8 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 36 of its 41 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## 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, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Injecting Numerical Reasoning Skills into Language Models](https://mlsanity.com/paper/2004.04487/) (2020)
- [Are LLMs Capable of Data-based Statistical and Causal Reasoning? Benchmarking Advanced Quantitative Reasoning with Data](https://mlsanity.com/paper/2402.17644/) (2024)
- [Decision-Making Behavior Evaluation Framework for LLMs under Uncertain Context](https://mlsanity.com/paper/2406.05972/) (2024)
- [Why Do Large Language Models (LLMs) Struggle to Count Letters?](https://mlsanity.com/paper/2412.18626/) (2024)
- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [Counting Ability of Large Language Models and Impact of Tokenization](https://mlsanity.com/paper/2410.19730/) (2024)
- [What Are the Odds? Language Models Are Capable of Probabilistic Reasoning](https://mlsanity.com/paper/2406.12830/) (2024)
- [ThinkSum: Probabilistic reasoning over sets using large language models](https://mlsanity.com/paper/2210.01293/) (2022)
- [DeLLMa: Decision Making Under Uncertainty with Large Language Models](https://mlsanity.com/paper/2402.02392/) (2024)

## Built on by (most cited first, 8 of 8)

- [Cosmos 3: Omnimodal World Models for Physical AI](https://mlsanity.com/paper/2606.02800/) (2026)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)
- [Mini Amusement Parks (MAPs): A Testbed for Modelling Business Decisions](https://mlsanity.com/paper/2511.15830/) (2025)
- [Humans and LLMs Diverge on Probabilistic Inferences](https://mlsanity.com/paper/2602.23546/) (2026)
- [When Does In-Context Search Help? A Sampling-Complexity Theory of Reflection-Driven Reasoning](https://mlsanity.com/paper/2607.06720/) (2026)
- [Explicit Logic Channel for Validation and Enhancement of MLLMs on Zero-Shot Tasks](https://mlsanity.com/paper/2603.11689/) (2026)
- [Can LLMs Take Retrieved Information with a Grain of Salt?](https://mlsanity.com/paper/2605.06919/) (2026)
- [Bayesian Fine-tuning Yields Language Models that are as Bayesian as their Beliefs Allow](https://mlsanity.com/paper/2610.00679/) (2026)

## Abstract (arXiv)

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.