Two AI coding agents can rewrite their own code to improve — but how should each one judge which version to build on next?

This explores how two self-rewriting agent systems choose which version of themselves to keep improving. The short answer is that the collection doesn't yet have notes on either the Huxley-Gödel Machine or the Darwin Gödel Machine, so it can't answer the comparison directly. One retrieved note looks like a match but isn't: Can hypergraphs capture multi-hop reasoning better than graphs? is about HGMem, a hypergraph memory structure for multi-step retrieval. It shares the letters, not the topic. Here is the gist from outside the collection, so treat it as background rather than as a sourced summary: DGM picks which agent to modify next mostly by that agent's own benchmark score, with some push toward novelty. HGM argues that a high score today doesn't reliably predict which agent will produce better offspring. So it scores each agent by how its whole family of descendants (its 'clade') performs, and grows the tree from agents with productive lineages.

The collection does cover the ideas underneath this disagreement. The core question is whether to judge a candidate by its own result or by what grows from it. That same tension shows up in tree search. Can tree search replace human feedback in LLM training? describes AlphaLLM, which uses search outcomes to score a reasoning step by whether the paths below it succeed. That is essentially 'judge a node by its descendants' applied to reasoning steps rather than whole agents. If HGM's idea feels abstract, this note is the most concrete way in.

On the evolutionary side, Can evolutionary search beat sampling and revision at inference time? shows Mind Evolution beating both picking the best of many samples and repeatedly revising a single answer. It does this partly by keeping separate 'islands' of candidates so the population doesn't collapse onto one early winner. That is the same worry that drives HGM's critique of DGM: greedy selection on current score can lock you onto a lineage that looks good now but leads nowhere.

There is also a warning that applies to any score-driven self-improvement loop. Can automated scoring verify mathematical constructions without human understanding? reports that AlphaEvolve exploited loopholes in its own evaluator. When a system optimizes against a score, weaknesses in the scorer become targets. Whether you score an agent alone or its whole lineage, the lineage is only as trustworthy as the benchmark it climbs.

To sum up: the collection can't settle HGM versus DGM yet, but it shows that 'score the node or score its subtree' is an old question in search. It also shows that the evaluator itself is a weak point every one of these systems has to defend.