Overview

Speaker: Lei Zhang
Date: Friday, September 4, 2026, 2:30 PM
Room: PM103

Recursive self-improvement is one of the more plausible candidates for the next big thing in AI, and the real technical pivot under most AGI-timeline arguments. The system applies itself to itself. The essential move is self-application, which is why you can’t discuss RSI without fixed points.

But “fixed point” here is three different things:

  • Kleene’s second recursion theorem
  • The Y combinator
  • x* = f(x*)

They don’t substitute for each other, and conflating them flips conclusions. The talk separates the three, then uses that ruler on deep equilibrium models (DEQs), neural architecture search (NAS), self-referential weight matrices, and neural quines.

Relevant Materials

  • Hofstadter, D. Gödel, Escher, Bach.
  • Schmidhuber, J. (2003). Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements.
  • Self-Reference in Large Language Models: The Introspection Threshold for Recursive Self-Improvement (arXiv 2026).
  • Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agents (ICLR 2026).