Ashish Kumar

A three-part series · 71 min of reading

Recursive self-improvement

A three-part series on machines that improve the process that improves them: the theory from Good’s intelligence explosion to the Gödel machine, the self-play and self-training loops that work and the verifier that bounds them, and code that rewrites its own coder, with the evidence on what goes wrong and what to build.

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Part 1 of 3
Infographic: a six-rung ladder of self-improvement, from answers revised at inference time to a Gödel machine that rewrites itself only with a proof, with the top two rungs marked recursive and annotated with their numbers (80 iterations in about two weeks, 7 rewrites in 8 days, 4,000 TPU-months for VeLO); beside it Bostrom's dI/dt = O/R with three illustrative takeoff curves and Anthropic's 26 percent of model R&D led by Claude, and a timeline from Good in 1965 to the Löbian wall of 2013, after which every system from STOP to AIDE² accepts changes by measurement instead of proof.
Part 1 of 3 · 11 October 2026

Recursive self-improvement, part 1: the idea, the Gödel machine, and the wall it hit

In September 2026 Anthropic said Claude leads a quarter of its model research and Sakana opened a lab for recursive self-improvement. Part 1 of three makes the term precise: Good’s 1965 argument, Bostrom’s takeoff equation, Schmidhuber’s Gödel machine line by line, AIXI as the ceiling, and the Löbian wall that pushed the field from proof to measurement.

23 min readStart reading Part 1 →

Then read on

Parts 2 to 3, in order
  1. Part 2Data infographic: six columns show how far each self-improvement loop climbed and where it stopped, from AlphaGo Zero (100–0 over AlphaGo Lee after three days, past AlphaGo Master by day 40, no ceiling) through Reflexion (HumanEval 80.1 to 91.0), STaR (CommonsenseQA 60.0 to 72.5), ReST-EM (MATH +6.34, worse in round two) and Self-Rewarding (9.94, 15.38, 20.44) to model collapse with no anchor, beside panels on less human input, learned improvers and DSPy.

    Recursive self-improvement, part 2: self-play, self-training, and the verifier ceiling

    Self-play, learning to learn, and language models that train on their own output: the algorithms, the measured gains, why they stall when the model judges itself, and a worked self-training loop for text-to-SQL.

    11 October 2026 · 23 min read
  2. Part 3Data infographic: a timeline of six code-evolving systems from STOP (October 2023) to AIDE² (September 2026), with what each gained above the line, such as SWE-bench 20.0 to 50.0 percent for the Darwin Gödel Machine and 0.7 percent of Google’s compute for AlphaEvolve, and below it what each reported going wrong, from STOP switching its sandbox off in 0.42 percent of rewrites to AIDE² reward hacking falling from 55 to 32 percent, above a strip of 2026 figures from Anthropic and METR RE-Bench.

    Recursive self-improvement, part 3: code that rewrites its coder, from FunSearch to AIDE²

    From FunSearch to AIDE²: how code-evolving agents improve their own improvers, what they measured, how each gamed its evaluator, and the harness to build before running one.

    11 October 2026 · 25 min read