从种子 AI 到递归自我改进自指、极限与最新进展|自指与AI读书…

From Seed AI to Recursive Self‑Improvement Self‑Reference, Limits and Latest Advances | Self‑Reference and AI Reading…

Introduction

Starting from Turing’s “child machine” concept and Good’s “intelligence explosion” prophecy, the question of whether AI can learn, rewrite, and surpass itself has always been the ultimate inquiry in artificial intelligence. Today, recursive self‑improvement (RSI) has moved from philosophical speculation to cutting‑edge laboratory validation, continuously reshaping our understanding of artificial general intelligence, superintelligence, and the technological singularity. In this fourth session of the Self‑Reference and AI Book Club, Professor Yuan Bing will focus on RSI, systematically dissecting the complete theoretical framework of AI’s infinite self‑iteration, the theoretical boundaries built from various mathematical theorems and self‑reference paradoxes, and, combined with Gödel machine series proposals and the latest 2025‑2026 agent experiments, detail the current technical progress, closed‑loop bottlenecks, and macro‑intelligence acceleration debates surrounding AI self‑evolution. Attendees will grasp the underlying code and core unsolved challenges of large‑model self‑evolution.

To systematically review the latest advances in self-reference and AI, Professor Zhang Jiang from the School of Systems Science at Beijing Normal University and founder of the Jizhi Club, together with Ph.D. student Li Xiaojian from the Institute of Artificial Intelligence at Tsinghua University, jointly launched the “Self-Reference and AI: From Large Model Self‑Improvement to Consciousness Research” reading group. The group brings together researchers and explorers interested in this topic to study cutting‑edge literature and exchange research ideas. The reading group will run online every Saturday from 14:00 to 16:00 starting September 5, 2026, for about ten weeks, featuring presentations, discussions, and post‑session video recordings. Researchers in related fields and anyone with interdisciplinary interest are warmly invited to join.

Report Overview

From Turing’s 1950 proposal of a “child machine” to Good’s 1966 prediction of an “intelligence explosion,” humanity has continually asked: what would happen if a machine could not only learn but also rewrite itself, and enable its successors to be even better at further improvement? Recursive Self‑Improvement (Recursive Self‑Improvement, RSI) is the most radical expression of this idea. It constitutes the core pathway for a “seed AI” to reach superintelligence and even the technological singularity, and it brings an age‑old philosophical problem into computer science: when a system includes itself as the object of analysis, judgment, and modification, can it truly understand and reliably surpass itself?

This lecture will focus on Roman Yampolskiy’s classic paper “From Seed AI to the Technological Singularity: Software Through Recursive Self‑Improvement,” outlining the differences between self‑modification, self‑improvement, and recursive self‑improvement, and discussing RSI classifications, the convergence hypothesis, and their implications for the future of intelligence. We will then dive into the deep end of self‑referential logic, examining how Rice’s theorem, Löb’s theorem, computational irreducibility, and the “Minsky‑Hawthorne barrier” set theoretical limits on infinite self‑improvement.

The lecture will also start from the Gödel machine, trace empirical schemes such as STOP, Gödel Agent, Darwin Gödel Machine, and expand the view to the civilization‑scale self‑referential system envisioned by Save 2050. Combined with the latest experiments on self‑developing agents in 2025‑2026, we will see that current systems can already modify code, tools, workflows, and memory mechanisms, but the true closed loop is still stuck at goal formation, self‑judgment, and verification. At the same time, a new working paper co‑authored by 22 scholars including Hinton and Bengio is pushing the debate from philosophy to measurement: they rephrase the “intelligence explosion” using a research return parameter r, and the central estimate based on historical data is already greater than 1—if the trend continues, AI progress after full automation will roughly increase tenfold every one and a half years. Microscopic experiments say the loop is not yet closed, macro estimates say acceleration may already have started—RSI has moved from philosophical speculation into the laboratory, and whether it can bridge this gap has become one of the most important and also most dangerous open questions in AI research.

Share Outline

1. A 75-Year Dream
2. Definition, Types, and Convergence Theory of RSI
3. Logical Constraints of Self-Reference
4. From Proof to Evolution, From Machines to Civilization
5. Empirical Inaugural Year of RSI
6. Conclusion and Discussion

Core Concepts

Recursive self-improvement, RSI convergence theorem, multidimensional optimization dilemma, Rice’s theorem, Lebesgue theorem, Minsky–Hawthorne barrier, Gödel machine

Speaker Introduction

Speaker:Yuan Bing, Technical and Product Consultant at the Jizhi Science Research Center. Research interests include causal inference, complex systems, and artificial intelligence. Previously worked in R&D departments of Siemens, Oracle, Vipshop, and other companies.

References

1. Yampolskiy, R. V. (2015). From Seed AI to Technological Singularity via Recursively Self-Improving Software. arXiv:1502.06512.

Good, I. J. (1966). Speculations Concerning the First Ultraintelligent Machine. Advances in Computers, 6, 31–88.

Chalmers, D. (2010). The Singularity: A Philosophical Analysis. Journal of Consciousness Studies, 17, 7–65.

Yudkowsky, E., & Hanson, R. (2008). The Hanson-Yudkowsky AI-Foom Debate. MIRI Technical Report.

Rice, H. G. (1953). Classes of Recursively Enumerable Sets and Their Decision Problems. Transactions of the AMS, 74(2), 358–366.

Löb, M. H. (1955). Solution of a Problem of Leon Henkin. Journal of Symbolic Logic, 20(2), 115–118.

Schmidhuber, J. (2003). Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements. arXiv:cs.LO/0309048.

Zhang, J., Yuan, B., & Zhang, Q. (2026). Save 2050: A Planetary-Scale Collective Prediction System for the Singularity Crisis. arXiv:2608.28703.

Zhang, J., et al. (2025). Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agents. arXiv:2505.22954（ICLR 2026）.

The Path to Recursive Self-Improving Agents: Foundation, Framework, and Future Directions. Preprints 202608.0051 (2026).

Chan, A., Winter, C., Barto, A., Pachocki, J., Hinton, G., Horvitz, E., Bengio, Y., et al. (2026). What If Automating AI R&D Triggers an Intelligence Explosion? Frontier AI Working Paper Series No. 2/2026, CASP / GovAI. arXiv:2609.36054.

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Event Preview

⏰ Time: October 17, 2026 (Saturday) 14:00-16:00 

📍 Online: Tencent Meeting 

📍Live: Simultaneous streaming on Jizhi Club WeChat Video Channel and Bilibili account

If you’re interested, please scan the QR code to sign up for the reading group. After registering, you can join the participants’ group for discussion. Looking forward to exploring the deep connection between self-reference and AI with you.

Sign up for the reading club: “Self-reference and AI”

Professor Zhang Jiang from the School of Systems Science, Beijing Normal University, and founder of the JiZhi Club, together with Ph.D. student Li Xiaojian from the Institute for AI, Tsinghua University, jointly launch“Self‑Reference and AI: From Recursive Self‑Improvement to AI Consciousness Research” reading group, organizing researchers and explorers interested in this topic to jointly study cutting‑edge literature and exchange research ideas.

The reading group will run online every Saturday from 14:00 to 16:00 starting August 29, 2026, for an estimated 8–10 weeks, featuring presentations, discussions, and post‑session video recordings. Researchers in related fields and interdisciplinary enthusiasts are warmly invited to join.

Scan the QR code in the poster to register for the reading group

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PS:

We encourage in‑depth discussions on complex systems, artificial intelligence, and related specific issues. To ensure discussion quality, please avoid posting content that is unrelated to the current book club theme, lacks empirical basis, or is overly abstract philosophical speculation.

If the discussion content clearly deviates from the topic and does not adjust after a reminder from the host, we will have to remove that member from the discussion group to maintain the overall learning environment, and refund the unparticipated portion proportionally based on their actual participation progress.

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   Claim and successfully complete any two subtitle tasks, and you will receive a full refund of the registration fee, plus an exclusive JiZhi merchandise reward.

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After successfully completing a subtitle task, you can apply to become an Operations Assistant. Once the reading club project is successfully concluded, the tuition fee will be refunded. Outstanding performers also have the chance to receive additional scholarships.

Recommended Reading

1. “Self-Reference and AI” reading group recommended reading material

Scan the QR code below to go to the Jizhi BanTu website to read the article: “Self-Reference and AI: From Large Model Self-Improvement to Consciousness Research”, the reading material recommended by the book club.

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