# A Mathematical Theory of Discursive Networks

arXiv: https://arxiv.org/abs/2507.06565 · HTML: https://mlsanity.com/paper/2507.06565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 30 of 35)

- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Jailbreaking Black Box Large Language Models in Twenty Queries](https://mlsanity.com/paper/2310.08419/) (2023)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Ethical and social risks of harm from Language Models](https://mlsanity.com/paper/2112.04359/) (2021)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [GLTR: Statistical Detection and Visualization of Generated Text](https://mlsanity.com/paper/1906.04043/) (2019)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [Can AI-Generated Text be Reliably Detected?](https://mlsanity.com/paper/2303.11156/) (2023)
- [Automatic Detection of Generated Text is Easiest when Humans are Fooled](https://mlsanity.com/paper/1911.00650/) (2019)
- [Self-contradictory Hallucinations of Large Language Models: Evaluation, Detection and Mitigation](https://mlsanity.com/paper/2305.15852/) (2023)
- [Truthful AI: Developing and governing AI that does not lie](https://mlsanity.com/paper/2110.06674/) (2021)
- [Towards Mitigating Hallucination in Large Language Models via Self-Reflection](https://mlsanity.com/paper/2310.06271/) (2023)
- [Self-Alignment for Factuality: Mitigating Hallucinations in LLMs via Self-Evaluation](https://mlsanity.com/paper/2402.09267/) (2024)
- [JSONSchemaBench: A Rigorous Benchmark of Structured Outputs for Language Models](https://mlsanity.com/paper/2501.10868/) (2025)
- [Political Discourse on Social Media: Echo Chambers, Gatekeepers, and the Price of Bipartisanship](https://mlsanity.com/paper/1801.01665/) (2018)

## Abstract (arXiv)

Large language models (LLMs) turn writing into a live exchange between humans and software. We characterize this new medium as a discursive network that treats people and LLMs as equal nodes and tracks how their statements circulate. We define the generation of erroneous information as invalidation (any factual, logical, or structural breach) and show it follows four hazards: drift from truth, self-repair, fresh fabrication, and external detection. We develop a general mathematical model of discursive networks that shows that a network governed only by drift and self-repair stabilizes at a modest error rate. Giving each false claim even a small chance of peer review shifts the system to a truth-dominant state. We operationalize peer review with the open-source Flaws-of-Others (FOO) algorithm: a configurable loop in which any set of agents critique one another while a harmonizer merges their verdicts. We identify an ethical transgression, epithesis, that occurs when humans fail to engage in the discursive network. The takeaway is practical and cultural: reliability in this new medium comes not from perfecting single models but from connecting imperfect ones into networks that enforce mutual accountability.