Huxley-Gödel Machine: Human-Level Coding Agent Development by an Approximation of the Optimal Self-Improving Machine

TL;DR

This work identifies a fundamental gap between short-term benchmark performance and long-term self-improvement potential in coding agents. It introduces Clade-Metaproductivity (CMP) as a lineage-based metric and proves that CMP suffices to emulate Gödel Machine behavior under a fixed-budget, repeatable-evaluation setting. Building on CMP, the Huxley–Gödel Machine (HGM) guides a tree-search over self-modifications via Thompson sampling and asynchronous execution, achieving higher-quality agents with fewer CPU-hours than prior methods. Empirical results on SWE-bench Verified, Polyglot, and transfer to SWE-bench Lite show state-of-the-art performance, including human-level capabilities, and demonstrate robust generalization across datasets and backbones. The work proposes a paradigm shift from short-term benchmarks toward long-horizon, lineage-aware self-improvement, with public code to facilitate further research.

Abstract

Recent studies operationalize self-improvement through coding agents that edit their own codebases. They grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, assuming that this implies more promising subsequent self-modifications. However, we identify a mismatch between the agent's self-improvement potential (metaproductivity) and its coding benchmark performance, namely the Metaproductivity-Performance Mismatch. Inspired by Huxley's concept of clade, we propose a metric ($\mathrm{CMP}$) that aggregates the benchmark performances of the descendants of an agent as an indicator of its potential for self-improvement. We show that, in our self-improving coding agent development setting, access to the true $\mathrm{CMP}$ is sufficient to simulate how the Gödel Machine would behave under certain assumptions. We introduce the Huxley-Gödel Machine (HGM), which, by estimating $\mathrm{CMP}$ and using it as guidance, searches the tree of self-modifications. On SWE-bench Verified and Polyglot, HGM outperforms prior self-improving coding agent development methods while using fewer allocated CPU hours. Last but not least, HGM demonstrates strong transfer to other coding datasets and large language models. The agent optimized by HGM on SWE-bench Verified with GPT-5-mini and evaluated on SWE-bench Lite with GPT-5 achieves human-level performance, matching the best officially checked results of human-engineered coding agents. Our code is publicly available at https://github.com/metauto-ai/HGM.

Figures (2)

• Figure 1: (Left) Weak correlation between the guidance metrics of other methods (based on benchmark performance) and long-term self improvement; HGM mitigates this mismatch by leveraging clade-level metaproductivity. (Right) On SWE-bench Verified, HGM achieves higher accuracy with $2.38$ time less allocated CPU-hours. Together, the results indicate the practical advantage of approximating Gödel Machines with long-term self-improvement estimates. Note that SICA encountered repeated errors after consuming 45% of its budget, preventing any further self-modifications.
• Figure :

Theorems & Definitions (2)

• Theorem 1
• proof