# Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference

arXiv: https://arxiv.org/abs/2402.03175 · HTML: https://mlsanity.com/paper/2402.03175/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Can language models learn from explanations in context?](https://mlsanity.com/paper/2204.02329/) (2022)
- [WT5?! Training Text-to-Text Models to Explain their Predictions](https://mlsanity.com/paper/2004.14546/) (2020)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [On the marginal likelihood and cross-validation](https://mlsanity.com/paper/1905.08737/) (2019)
- [On Masked Pre-training and the Marginal Likelihood](https://mlsanity.com/paper/2306.00520/) (2023)

## Built on by (most cited first, 2 of 2)

- [Integrating Local and Global Entropy for Uncertainty Quantification in LLMs](https://mlsanity.com/paper/2606.09875/) (2026)
- [Not All Answers Are Contextually Persuadable: Inference Dynamics in Large Language Models under Contextual Influence](https://mlsanity.com/paper/2610.04791/) (2026)

## Abstract (arXiv)

This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs), focusing on their core optimization metric of next token prediction. We develop a theoretical framework based on an ideal generative text model represented by a multinomial transition probability matrix with a prior, and examine how LLMs approximate this matrix. Key contributions include: (i) a continuity theorem relating embeddings to multinomial distributions, (ii) a demonstration that LLM text generation aligns with Bayesian learning principles, (iii) an explanation for the emergence of in-context learning in larger models, (iv) empirical validation using visualizations of next token probabilities from an instrumented Llama model Our findings provide new insights into LLM functioning, offering a statistical foundation for understanding their capabilities and limitations. This framework has implications for LLM design, training, and application, potentially guiding future developments in the field.