Wright–G\"odel Machine: Mitigating Homogenization in Self-Improving Agents

Recent self-improving agents retain previously discovered implementations in an archive so that improvement can proceed from multiple starting points. However, we find that parent selection can repeatedly favor closely related agents, leaving alternative designs with few opportunities to produce descendants. We refer to this phenomenon as genetic homogenization, which can cause the search to miss useful directions for improvement. We characterize it through the effective number of reproductive lineages and parent diversity, and prove that Thompson-sampling parent selection concentrates reproduction on a single lineage in the standard stochastic bandit model, even when every lineage remains in the archive. Inspired by Wright's shifting-balance theory, we propose the Wright–G\"odel Machine (WGM). WGM selects parents with a rule based on the Exponential-weight algorithm for Exploration and Exploitation (EXP3), which combines clade statistics with a uniform exploration floor, and uses best arm identification (BAI) to allocate additional evaluations and select the final agent. We prove that WGM gives every lineage a polynomially growing expected number of expansions under any reward sequence. On SWE-bench Verified and Polyglot, WGM discovers agents that outperform state-of-the-art methods under matched evaluation budgets, and these agents transfer to held-out coding tasks and other backbone models.