# Boundless Socratic Learning with Language Games

arXiv: https://arxiv.org/abs/2411.16905 · HTML: https://mlsanity.com/paper/2411.16905/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 26 of 26)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [Deal or No Deal? End-to-End Learning for Negotiation Dialogues](https://mlsanity.com/paper/1706.05125/) (2017)
- [FANToM: A Benchmark for Stress-testing Machine Theory of Mind in Interactions](https://mlsanity.com/paper/2310.15421/) (2023)
- [Supervising strong learners by amplifying weak experts](https://mlsanity.com/paper/1810.08575/) (2018)
- [AutoDefense: Multi-Agent LLM Defense against Jailbreak Attacks](https://mlsanity.com/paper/2403.04783/) (2024)
- [Generative agent-based modeling with actions grounded in physical, social, or digital space using Concordia](https://mlsanity.com/paper/2312.03664/) (2023)
- [Levels of AGI for Operationalizing Progress on the Path to AGI](https://mlsanity.com/paper/2311.02462/) (2023)
- [Open-Endedness is Essential for Artificial Superhuman Intelligence](https://mlsanity.com/paper/2406.04268/) (2024)
- [Autocurricula and the Emergence of Innovation from Social Interaction: A Manifesto for Multi-Agent Intelligence Research](https://mlsanity.com/paper/1903.00742/) (2019)
- [Empirical Design in Reinforcement Learning](https://mlsanity.com/paper/2304.01315/) (2023)
- [Thousands of AI Authors on the Future of AI](https://mlsanity.com/paper/2401.02843/) (2024)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [GAVEL: Generating Games Via Evolution and Language Models](https://mlsanity.com/paper/2407.09388/) (2024)
- [When should agents explore?](https://mlsanity.com/paper/2108.11811/) (2021)
- [Eliminating Meta Optimization Through Self-Referential Meta Learning](https://mlsanity.com/paper/2212.14392/) (2022)
- [Three Dogmas of Reinforcement Learning](https://mlsanity.com/paper/2407.10583/) (2024)
- [Does Thought Require Sensory Grounding? From Pure Thinkers to Large Language Models](https://mlsanity.com/paper/2408.09605/) (2024)

## Built on by (most cited first, 12 of 12)

- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Multi-agent KTO: Reinforcing Strategic Interactions of Large Language Model in Language Game](https://mlsanity.com/paper/2501.14225/) (2025)
- [Automated Capability Discovery via Foundation Model Self-Exploration](https://mlsanity.com/paper/2502.07577/) (2025)
- [Improving Interactive In-Context Learning from Natural Language Feedback](https://mlsanity.com/paper/2602.16066/) (2026)
- [Position: Introspective Experience from Conversational Environments as a Path to Better Learning](https://mlsanity.com/paper/2602.14910/) (2026)
- [Playing with Words, Improving with Rewards: Training Language Models for Creative Association](https://mlsanity.com/paper/2605.27832/) (2026)
- [An Information-Theoretic Definition for Open-Ended Learning](https://mlsanity.com/paper/2606.08369/) (2026)
- [Hallucination Self-Play: Bootstrapping Reinforced Detector via Evolved Generator](https://mlsanity.com/paper/2607.07993/) (2026)
- [Structured Synthetic Reasoning Data for Arithmetic Fine-Tuning of Small Language Models](https://mlsanity.com/paper/2607.18266/) (2026)

## Abstract (arXiv)

An agent trained within a closed system can master any desired capability, as long as the following three conditions hold: (a) it receives sufficiently informative and aligned feedback, (b) its coverage of experience/data is broad enough, and (c) it has sufficient capacity and resource. In this position paper, we justify these conditions, and consider what limitations arise from (a) and (b) in closed systems, when assuming that (c) is not a bottleneck. Considering the special case of agents with matching input and output spaces (namely, language), we argue that such pure recursive self-improvement, dubbed "Socratic learning", can boost performance vastly beyond what is present in its initial data or knowledge, and is only limited by time, as well as gradual misalignment concerns. Furthermore, we propose a constructive framework to implement it, based on the notion of language games.