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Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements

10 Pith papers cite this work. Polarity classification is still indexing.

10 Pith papers citing it
abstract

We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problem-dependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof searcher which is also part of the initial code. The searcher systematically and efficiently tests computable proof techniques (programs whose outputs are proofs) until it finds a provably useful, computable self-rewrite. We show that such a self-rewrite is globally optimal - no local maxima! - since the code first had to prove that it is not useful to continue the proof search for alternative self-rewrites. Unlike previous non-self-referential methods based on hardwired proof searchers, ours not only boasts an optimal order of complexity but can optimally reduce any slowdowns hidden by the O()-notation, provided the utility of such speed-ups is provable at all.

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representative citing papers

Automated Design of Agentic Systems

cs.AI · 2024-08-15 · conditional · novelty 7.0

Meta Agent Search uses a meta-agent to iteratively program novel agentic systems in code, producing agents that outperform state-of-the-art hand-designed ones across coding, science, and math while transferring across domains and models.

Self-Evolving Agents with Anytime-Valid Certificates

cs.AI · 2026-07-01 · unverdicted · novelty 5.0

SEA architecture gates self-modifications via anytime-valid certificates on a frozen base model plus five verifier mechanisms, yielding +4 to +5 gains on a SWE-bench subset for two strong bases.

Agentic Safety is an Epistemic Property, Not a Behavioral One

cs.CY · 2026-06-02 · unverdicted · novelty 4.0

The paper reframes agentic safety as an epistemic property defined by teachability—the capacity to preserve future corrective leverage—rather than a behavioral property of the current policy.

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