Huxley-G\"odel 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, grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, considering 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 \emph{Metaproductivity-Performance~Mismatch}. Inspired by Huxley’s concept of clade, we propose a metric ($\mathrm{CMP}$) that aggregates the benchmark performances of the \emph{descendants} of an agent as an indicator of its potential for self-improvement. We show that the G\"odel Machine, the optimal self-improving machine, is achieved with access to true $\mathrm{CMP}$. 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 search methods while using less wall-clock time. Moreover, the agent optimized by HGM on SWE-bench Verified outperforms SWE-agent, a leading human-engineered open source coding agent on SWE-bench Lite, where SWE-agent ranks the best on the official leaderboard, when both use the GPT-5-mini backbone, demonstrating that HGM self-improvement indeed enhances genuine coding capability.