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Huxley-G\"odel Machine: Human-Level Coding Agent Development by an Approximation of the Optimal Self-Improving Machine

ICLR 2026 · Multi-agent systems and games › LLM agents · approach: Robust and efficient agent execution

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Proposes the Huxley-Gödel Machine, which estimates clade-level metaproductivity (CMP) and uses Thompson sampling with decoupled, asynchronous expansion/evaluation to guide self-modifying coding agent search, outperforming DGM and SICA on SWE-bench and Polyglot.

Problem

Self-improving coding agents select self-modifications by benchmark score, which is a poor proxy for an agent's long-term ability to produce further improvements (the Metaproductivity-Performance Mismatch), and existing methods are costly in compute.

Approach

Defines clade-level metaproductivity (CMP), aggregating success counts over an agent's descendants, shows a CMP oracle suffices to imitate the Gödel Machine's acceptance mechanism in this setting, and approximates CMP with a Beta-posterior clade estimator guiding Thompson-sampling expansion, with evaluation decoupled from expansion and run asynchronously.

Key results

• On SWE-Verified-60, HGM's best-belief agent reaches 56.7% vs 53.3% for DGM and 50.0% for SICA, using 517 CPU-hours vs 1231 for DGM.
• Optimized on full SWE-Verified with GPT-5-mini, HGM's agent reaches 61.4%, and on SWE-Lite with GPT-5 it scores 57% standard, matching the top checked leaderboard entry (SWE-agent 56.7%).
• The weighted Pearson correlation between the CMP estimator and empirical CMP is 0.778 on SWE-Verified-60 versus 0.444 for SICA and 0.285 for DGM.

Surprising findings

• Benchmark score is an unreliable predictor of an agent's descendants' productivity, so high-scoring agents can seed stagnant lineages.
• SICA encountered repeated context-window errors after consuming part of its budget, halting further self-modification.

Limitations

• Theoretical equivalence to the Gödel Machine holds only under strong assumptions (repeatable trials, zero proof cost, known budget, only final agent utility).
• Leaderboard performance may reflect overfitting to benchmarks, as acknowledged by the authors.

Experimental setup

Datasets: SWE-bench Verified SWE-bench Lite Polyglot

Benchmarks: SWE-bench Verified SWE-bench Lite Polyglot

Metrics: accuracy Pearson correlation allocated CPU-hours

Baselines: DGM SICA SWE-agent SWE-agent + GPT-5-mini

Builds on: Gödel Machine Darwin Gödel Machine Self-Improving Coding Agent UCB-Air

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