# Do Large Language Models (Really) Need Statistical Foundations?

arXiv: https://arxiv.org/abs/2505.19145 · HTML: https://mlsanity.com/paper/2505.19145/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 96 of its 139 references that are in the map.
- First posted on arXiv 25 May 2025.

## Builds on (most cited first, 30 of 96)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)

## Built on by (most cited first, 5 of 5)

- [Do Repetitions Matter? Strengthening Reliability in LLM Evaluations](https://mlsanity.com/paper/2509.24086/) (2025)
- [Uncertainty Quantification for Large Language Model Reward Learning under Heterogeneous Human Feedback](https://mlsanity.com/paper/2512.03208/) (2025)
- [AI Must Embrace Specialization via Superhuman Adaptable Intelligence](https://mlsanity.com/paper/2602.23643/) (2026)
- [Offline and Online KL-Regularized RLHF under Differential Privacy](https://mlsanity.com/paper/2510.13512/) (2025)
- [Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards](https://mlsanity.com/paper/2604.10727/) (2026)

## Abstract (arXiv)

Large language models (LLMs) represent a new paradigm for processing unstructured data, with applications across an unprecedented range of domains. In this paper, we address, through two arguments, whether the development and application of LLMs would genuinely benefit from foundational contributions from the statistics discipline. First, we argue affirmatively, beginning with the observation that LLMs are inherently statistical models due to their profound data dependency and stochastic generation processes, where statistical insights are naturally essential for handling variability and uncertainty. Second, we argue that the persistent black-box nature of LLMs -- stemming from their immense scale, architectural complexity, and development practices often prioritizing empirical performance over theoretical interpretability -- renders closed-form or purely mechanistic analyses generally intractable, thereby necessitating statistical approaches due to their flexibility and often demonstrated effectiveness. To substantiate these arguments, the paper outlines several research areas -- including alignment, watermarking, uncertainty quantification, evaluation, and data mixture optimization -- where statistical methodologies are critically needed and are already beginning to make valuable contributions. We conclude with a discussion suggesting that statistical research concerning LLMs will likely form a diverse ``mosaic'' of specialized topics rather than deriving from a single unifying theory, and highlighting the importance of timely engagement by our statistics community in LLM research.