# When Is Next-Token Prediction Useful? Marginalization, Ergodicity, Mixture Identifiability, Local Sufficiency, RAG, Tools, and Programming

arXiv: https://arxiv.org/abs/2605.23278 · HTML: https://mlsanity.com/paper/2605.23278/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 20 of 20)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [MRKL Systems: A modular, neuro-symbolic architecture that combines large language models, external knowledge sources and discrete reasoning](https://mlsanity.com/paper/2205.00445/) (2022)
- [How to Build an Adaptive AI Tutor for Any Course Using Knowledge Graph-Enhanced Retrieval-Augmented Generation (KG-RAG)](https://mlsanity.com/paper/2311.17696/) (2023)

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

- [The Need for an External Observer Formalizing the Sufficiency Gap: A Mathematical Extension of Mixture Identifiability and Contextual Grounding in Sequence Models](https://mlsanity.com/paper/2605.26711/) (2026)
- [Language Has Two Parameters: Narrative-Induced Semantic Plasticity and Phase-Sensitive Interpretation](https://mlsanity.com/paper/2608.18041/) (2026)

## Abstract (arXiv)

Language models trained on observed sequences are often described as learning the conditional distribution of the next token given previous tokens. This description is only conditionally correct. A model trained on realized token trajectories does not observe full conditional laws; it receives sampled continuations. Moreover, real language generation is conditioned not only on previous words but also on non-textual circumstances: facts, events, intentions, goals, beliefs, social context, and task-specific constraints. This paper distinguishes three objects that are often conflated: the full conditional language process conditioned on latent circumstances, the marginal text-only process obtained by integrating those circumstances out, and the model-induced distribution learned from finite observed corpora. The paper argues that interpreting model training as estimating the marginal text-only law requires strong assumptions of stationarity, representativeness, and ergodicity, assumptions that are standard in statistical estimation but problematic when applied to heterogeneous language corpora. Even if these assumptions hold, the marginal text-only law is useful only when the observed prefix is an approximately sufficient statistic for the latent circumstances relevant to continuation. In information-theoretic terms, usefulness requires that the residual conditional mutual information between the next token and the omitted circumstances, given the observed text, be small. The paper then extends this argument to heterogeneous training corpora. Finally, the paper interprets Retrieval Augmented Generation (RAG) and tool use as conditional sufficiency devices.