Gödel machine
In plain wordsA purely theoretical design, proposed by Jürgen Schmidhuber, for a program allowed to change anything about itself, including how it learns, but only once it has proved that the change is an improvement.
A formal blueprint for a fully self-referential problem solver: nothing in its own program is off-limits to modification, not even its learning method or the machinery that makes the modifications, but a change is carried out only when a built-in theorem prover has derived a proof that it raises the system's expected utilityutility function, n.: A way of scoring every possible outcome by how much someone, or some AI, wants it. A rational agent is often modeled as choosing whatever maximizes its expected score., measured against a fixed goal and axioms describing the system's own hardware, initial software and environment. Because the proof must also account for the time spent searching, Jürgen Schmidhuber argued that each accepted self-rewrite is globally optimal relative to those axioms rather than a local improvement. The design is not practical: useful changes can rarely be proved beneficial in advance, and its self-reference inherits the limits of Gödel's incompleteness theorems. It remains a reference point in discussions of recursive self-improvementrecursive self-improvement, n.: An AI improving its own design or training, so that each improved version is better at making the next improvement. It is the engine usually imagined behind an intelligence explosion..
Unlike a Gödel machine, the agent accepts a self-edit after a benchmark run, not a proof.
Origin
Proposed by Jürgen Schmidhuber in a technical report posted to arXiv on 25 September 2003, 'Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements', and developed in later papers. Named after the logician Kurt Gödel, whose 1931 self-referential formulas inspired the construction.
Usage note
Revived in 2025 by the Darwin Gödel MachineDarwin Gödel Machine, prop. n.: An experimental AI coding assistant that improves itself by rewriting its own code, testing each new version and keeping a family tree of variants to build on., which replaces proofs with empirical testing.
Related
- recursive self-improvementrecursive self-improvement, n.: An AI improving its own design or training, so that each improved version is better at making the next improvement. It is the engine usually imagined behind an intelligence explosion.
- Darwin Gödel MachineDarwin Gödel Machine, prop. n.: An experimental AI coding assistant that improves itself by rewriting its own code, testing each new version and keeping a family tree of variants to build on.
- seed AIseed AI, n.: An early AI built mainly to understand and upgrade itself, so that it could grow, like a seed, into a far more capable mind.
- AIXIAIXI, prop. n.: A mathematical description of a perfect learning agent that weighs every possible explanation of its experience and acts to get the most future reward. It cannot actually be built, but it defines an ideal.
- Jürgen SchmidhuberJürgen Schmidhuber, prop. n.: A German computer scientist who co-invented the LSTM, a neural network with memory that powered much of speech recognition and translation in the 2010s, and who argues that early pioneers go under-credited.
- intelligence explosionintelligence explosion, n.: The idea that once AI gets good enough at improving AI, each smarter version could build a smarter one faster still, so abilities would snowball far beyond human level in a short time.
- automated theorem provingautomated theorem proving, n.: Getting computers to prove mathematical or logical statements by themselves, by searching for a chain of valid steps that leads from basic assumptions to the statement.
Sources
- Schmidhuber, J. (2003). Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements. arXiv:cs/0309048. arxiv.org/abs/cs/0309048
Mentioned in
Gödel's incompleteness theoremsGödel's incompleteness theorems, n.: Two famous results from 1931 showing that any consistent set of rules for doing arithmetic leaves some true statements unprovable, and cannot prove that it is itself free of contradictions., Jürgen SchmidhuberJürgen Schmidhuber, prop. n.: A German computer scientist who co-invented the LSTM, a neural network with memory that powered much of speech recognition and translation in the 2010s, and who argues that early pioneers go under-credited., recursive self-improvementrecursive self-improvement, n.: An AI improving its own design or training, so that each improved version is better at making the next improvement. It is the engine usually imagined behind an intelligence explosion., Darwin Gödel MachineDarwin Gödel Machine, prop. n.: An experimental AI coding assistant that improves itself by rewriting its own code, testing each new version and keeping a family tree of variants to build on., seed AIseed AI, n.: An early AI built mainly to understand and upgrade itself, so that it could grow, like a seed, into a far more capable mind.