# Epidemiology of Large Language Models: A Benchmark for Observational Distribution Knowledge

arXiv: https://arxiv.org/abs/2511.03070 · HTML: https://mlsanity.com/paper/2511.03070/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 67 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Improving alignment of dialogue agents via targeted human judgements](https://mlsanity.com/paper/2209.14375/) (2022)
- [Learning Gender-Neutral Word Embeddings](https://mlsanity.com/paper/1809.01496/) (2018)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [CLadder: Assessing Causal Reasoning in Language Models](https://mlsanity.com/paper/2312.04350/) (2023)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [Context-faithful Prompting for Large Language Models](https://mlsanity.com/paper/2303.11315/) (2023)
- [Questioning the Survey Responses of Large Language Models](https://mlsanity.com/paper/2306.07951/) (2023)
- [FELM: Benchmarking Factuality Evaluation of Large Language Models](https://mlsanity.com/paper/2310.00741/) (2023)
- [Walk the Talk? Measuring the Faithfulness of Large Language Model Explanations](https://mlsanity.com/paper/2504.14150/) (2025)

## Built on by (most cited first, 3 of 3)

- [Diagnosing and Mitigating Sycophancy and Skepticism in LLM Causal Judgment](https://mlsanity.com/paper/2601.08258/) (2026)
- [Causal Bias Detection in Generative Artificial Intelligence](https://mlsanity.com/paper/2605.11365/) (2026)
- [UnpredictaBench: A Benchmark for Evaluating Distributional Randomness in LLMs](https://mlsanity.com/paper/2606.06622/) (2026)

## Abstract (arXiv)

Artificial intelligence (AI) systems hold great promise for advancing various scientific disciplines, and are increasingly used in real-world applications. Despite their remarkable progress, further capabilities are expected in order to achieve more general types of intelligence. A critical distinction in this context is between factual knowledge, which can be evaluated against true or false answers (e.g., "what is the capital of England?"), and probabilistic knowledge, reflecting probabilistic properties of the real world (e.g., "what is the sex of a computer science graduate in the US?"). In this paper, our goal is to build a benchmark for understanding the capabilities of LLMs in terms of knowledge of probability distributions describing the real world. Given that LLMs are trained on vast amounts of text, it may be plausible that they internalize aspects of these distributions. Indeed, LLMs are touted as powerful universal approximators of real-world distributions. At the same time, classical results in statistics, known as curse of dimensionality, highlight fundamental challenges in learning distributions in high dimensions, challenging the notion of universal distributional learning. In this work, we develop the first benchmark to directly test this hypothesis, evaluating whether LLMs have access to empirical distributions describing real-world populations across domains such as economics, health, education, and social behavior. Our results demonstrate that LLMs perform poorly overall, and do not seem to internalize real-world statistics naturally. When interpreted in the context of Pearl's Causal Hierarchy (PCH), our benchmark demonstrates that language models do not contain knowledge on observational distributions (Layer 1 of PCH), and thus the Causal Hierarchy Theorem implies that interventional (Layer 2) and counterfactual (Layer 3) knowledge of these models is also limited.