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

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 G\"odel Machine would behave under certain assumptions. We introduce the Huxley-G\"odel 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 less wall-clock time. 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 available at https://github.com/metauto-ai/HGM.