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Huxley-G\"odel Machine: Human-Level Coding Agent Development by an Approximation of the Optimal Self-Improving Machine

Wenyi Wang, Piotr Piękos, Li Nanbo, Firas Laakom, Yimeng Chen, Mateusz Ostaszewski, Mingchen Zhuge, Jürgen Schmidhuber

arXiv:2510.21614v3cs.AI

TL;DR

Benchmark performance does not reliably indicate how much an agent can improve through its descendants. HGM estimates clade-level metaproductivity to guide self-modification search; it outperforms prior methods on SWE-bench Verified and Polyglot and transfers to a dataset and model shift.

  • Problem

    Benchmark scores are an unreliable indicator of an agent’s long-term self-improvement potential because high-scoring agents can lead to stagnant lineages while weaker ones may seed productive ones.

    Source: §1 · p. 2, §3.3 · p. 6

  • Method

    HGM estimates clade-level metaproductivity from descendant outcomes and uses it to guide tree expansion through Thompson sampling with adaptive scheduling.

    Source: §6 · p. 12

  • Results

    HGM consistently outperforms prior self-improving frameworks on SWE-bench Verified and Polyglot and achieves human-level performance on SWE-bench Lite with GPT-5 after optimization on SWE-bench Verified with GPT-5-mini.

    Source: §1 · p. 3, §6 · p. 12

  • Takeaways & Limitations

    Under the stated assumptions, access to a true CMP oracle suffices to implement the Gödel Machine’s acceptance mechanism in this coding-agent development setting.

    Source: §1 · p. 2, §6 · p. 12

    The theoretical setting assumes final-agent utility is the only objective, evaluations are repeatable, each self-modification costs one budget unit, and only self-modification incurs time cost.

    Source: §3.1 · pp. 4–5

Abstract

from arXiv · show

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 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.

1 INTRODUCTION

Benchmark scores can mislead self-modification search because they do not reliably predict an agent’s long-term self-improvement potential. HGM estimates clade-level metaproductivity to guide search, outperforming prior methods and transferring to a dataset and model shift.

1 INTRODUCTION

  • Self-modifying agents can revise their own modification mechanisms and learning strategies, reusing new abilities for subsequent improvements.The paper situates this process in biological evolution and cultural and scientific innovation.Source: §1 · p. 2
  • Benchmark performance can mislead self-modification search: high-scoring agents may produce unproductive descendants, while lower-scoring agents may seed more productive lineages.The paper names this divergence the Metaproductivity–Performance Mismatch.Source: §1 · p. 2
  • CMP measures an agent’s clade productivity by aggregating descendant success, and under Assumption 1 a true CMP oracle suffices to imitate the Gödel Machine.Assumption 1 includes final-agent evaluation as the only quality criterion and repeatable evaluation trials.Source: §1 · p. 2
  • HGM estimates CMP from clade-aggregated descendant outcomes and uses Thompson sampling to select nodes for expansion.It adaptively decouples expansion from evaluation for asynchronous parallel execution.Source: §1 · p. 2
  • HGM consistently outperforms DGM and SICA on SWE-bench Verified and Polyglot, and its discovered agent matches the best officially verified human-engineered agents on SWE-bench Lite with GPT-5.The agent was optimized on SWE-bench Verified with GPT-5-mini; Figure 1 also reports higher SWE-bench Verified accuracy with 2.38 times fewer allocated CPU-hours.Source: Figure 1 · p. 2, §1 · p. 3

2 SELF-IMPROVEMENT AS TREE-SEARCH

The paper models self-improving agent development as a tree search over agent modifications and downstream-task evaluations. Its policy must decide what to expand and evaluate, while HGM allows these actions to be chosen separately.

2 SELF-IMPROVEMENT AS TREE-SEARCH

  • DGM and SICA are self-referential AI methods in which agents modify themselves to generate new agents that are empirically validated on downstream tasks.Source: §2 · p. 3
  • The search policy alternates between modifying an agent to add a child and selecting an agent for additional downstream-task evaluation, then returns a final agent from the completed tree.The objective is expected final-agent utility, defined here as the average of binary success indicators across downstream tasks.Source: §2 · p. 3
  • Prior methods such as SICA and DGM immediately evaluate each newly generated child, so that child can monopolize evaluations despite repeated failures while older agents are ignored.The paper describes the policy choice as a compound decision involving selection, expansion, and evaluation sub-policies.Source: §2 · pp. 3–4
  • HGM decouples expansion from evaluation, adaptively choosing whether to generate an agent or probe an existing one at single agent–task-pair granularity.This finer control enables early stopping on unpromising agents.Source: §2 · p. 4

3 HUXLEY-GÖDEL MACHINE

HGM guides self-improvement using clade-level statistics, estimating the future productivity of an agent’s descendants rather than relying only on immediate performance. Its theoretical basis and algorithm are specialized to a coding-agent development setting with repeatable evaluations and a fixed cost per self-modification.

3 HUXLEY-GÖDEL MACHINE

  • HGM estimates clade-metaproductivity and uses Thompson sampling to guide self-modification search, approximating Gödel Machine behavior in the stated setting.Its evaluation policy favors higher-scoring agents, while its selection policy separates expansion from evaluation.Source: §3 · p. 4, §3.3 · p. 6

3.1 GÖDEL MACHINE IN THE SELF-IMPROVING CODING AGENT DEVELOPMENT SETTING

  • The analysis assumes only the final agent’s utility matters, evaluations are repeatable, proofs consume no budget, and each self-modification costs one budget unit.The coding-agent problem is modeled as a POMDP in which the policy accepts or rejects a child agent.Source: §3.1 · pp. 4–5

3.2 METAPRODUCTIVITY AND CLADE-METAPRODUCTIVITY

  • GMP evaluates self-improvement across the whole agent archive, while CMP localizes that potential to an agent’s descendant clade and captures future evolution.Under Assumption 1, access to a true CMP oracle is sufficient to implement the Gödel Machine.Source: §3.2 · p. 5

3.3 ALGORITHM

  • The CMP estimator aggregates empirical performance across an agent’s clade, using evaluation counts as weights to improve estimates when benchmarks are costly or partly observed.Evaluation prioritizes higher-scoring agents, inducing a soft maximum over the clade.Source: §3.3 · p. 6
  • HGM schedules expansion versus evaluation, selects the final best-belief agent, and supports asynchronous CPU execution through decoupled expansion and evaluation.The scheduler draws on UCB-Air’s evaluation-based rule for adding arms; asynchronous iterations use available CPUs until the budget is exceeded.Source: §3.3 · p. 7

4 EXPERIMENTAL RESULTS

The experiments assess CMP estimation, self-improvement against DGM and SICA, and automatic agent design against human-engineered systems. Across the reported coding benchmarks, HGM shows stronger estimation alignment, improves performance and efficiency, and transfers to unseen tasks and another backbone.

4 EXPERIMENTAL RESULTS

  • The evaluation covers CMP estimation, self-improvement versus DGM and SICA, and automatic agent design versus a leading human-designed system across SWE-bench Verified, SWE-bench Lite, and Polyglot.Experiments use HGM-Async and, in comparisons with DGM and SICA, the same initial agent.Source: §4 · p. 7

4.1 METAPRODUCTIVITY-PERFORMANCE MISMATCH

  • The experiments use SWE-Verified-60 and Polyglot to compare estimated metaproductivity with empirical CMP, excluding target-related evaluations to reduce leakage.Empirical CMP is the maximum empirical mean task performance within a node’s clade, excluding the clade root.Source: §4.1 · p. 8
  • HGM’s CMP estimator has weighted Pearson correlations of 0.778 on SWE-Verified-60 and 0.626 on Polyglot, and unweighted correlations of 0.512 and 0.8783, respectively.These correlations exceed those of DGM and SICA, whose reported Pearson correlations are 0.285 and 0.444 on SWE-Verified-60, and 0.383 and 0.274 on Polyglot, respectively.Source: §4.1 · p. 8, Table 1 · p. 8

4.2 EVALUATING HGM SELF-IMPROVING CAPABILITY

  • HGM achieves the highest task performance on both benchmarks and uses the fewest CPU-hours for 800 evaluations, running 6.86 times faster than DGM and 1.65 times faster than SICA on Polyglot, and 2.38 times faster than DGM on SWE-Verified-60.The best-belief agent scores 56.7% on SWE-Verified-60 and 30.5% on Polyglot.Source: §4.2 · p. 9, Table 2 · p. 9

4.3.1 OPTIMIZATION ON FULL SWE-BENCH VERIFIED

  • After 8000 evaluations, HGM discovers an agent that solves 61.4% of full SWE-Bench Verified tasks, surpassing the best human-designed GPT-5-mini agent on that benchmark.The paper cautions that leaderboard scores do not necessarily indicate superior general coding ability because agents may overfit to the benchmark.Source: §4.3.1 · p. 9

4.3.2 GENERALIZATION TO SWE-BENCH LITE

  • On SWE-Lite, HGM’s SWE-Verified agent scores 40.1% on filtered unseen tasks and 49.0% on the standard benchmark, versus 34.8% and 44.0% for its initial ancestor.The HGM agent also exceeds the SWE-agent + GPT-5-mini baseline, which scores 39.6% filtered and 47.6% standard.Source: Table 3 · p. 10, §4.3.2 · p. 10
  • HGM’s GPT-5-mini-optimized agent maintains strong SWE-Lite performance when evaluated with GPT-5, with results comparable to human-engineered agents.The paper reports that it exceeds all other officially checked SWE-Bench Lite submissions and is one task behind the best-performing model on the selected filtered set.Source: Table 4 · p. 10, §4.3.2 · p. 10

5 RELATED WORKS

Related work traces self-improvement from early self-modifying systems and coding agents to methods that alter their own scaffolding. HGM differs from prior coding-agent approaches by directing modifications with metaproductivity estimates rather than assuming benchmark scores measure future improvement potential.

5 RELATED WORKS

  • The Gödel machine accepts code rewrites only when it can prove an expected-utility improvement, while earlier methods include hindsight-based undoing and fitness-monotonic execution.The Success-Story Algorithm preserves modifications associated with greater reward intake per unit time; Fitness-Monotonic Execution favors models with higher ancestral performance.Source: §5 · p. 11
  • Coding agents extend LLMs with conventional computing environments, and later systems such as DGM and SICA modify their own repositories and validate changes through execution-grounded tasks.ChatDev first illustrated coding-agent bug fixing, followed by frameworks including SWE, OpenHands, MetaGPT, and AgentLess.Source: §5 · p. 11
  • DGM and SICA treat higher coding-benchmark scores as evidence of greater self-improvement capacity, whereas HGM guides modifications using estimates of metaproductivity.The paper frames its tree-search problem as distinct from finite-arm methods and reservoir-based infinite-armed bandits because expansions create structured candidate leaves.Source: §5 · p. 11

6 CONCLUSION

The paper identifies the Metaproductivity–Performance Mismatch and introduces Clade-Metaproductivity (CMP) to measure agents’ self-improvement potential through their lineages. Under stated assumptions, a CMP oracle can implement the Gödel Machine, and HGM estimates CMP to guide search, with reported transfer across datasets and models.

6 CONCLUSION

  • Under Assumption 1, a CMP oracle is sufficient to implement the Gödel Machine in the self-improving coding-agent search problem.The stated setting concerns utility measured by the final agent’s evaluation performance.Source: §6 · pp. 11–12
  • HGM approximates CMP and uses Thompson sampling with adaptive scheduling to guide search through self-modified agents.The authors report that it produces higher-quality agents than prior self-improving frameworks while reducing wall-clock time.Source: §6 · p. 12
  • The results suggest that clade-based measures of improvement potential are more effective for self-improvement than immediate performance alone.The authors frame this as a perspective focused on the long-term generative potential of agent lineages.Source: §6 · p. 12

A GÖDEL MACHINE WITH CMP ORACLE

The section formalizes a setting in which a CMP oracle can reproduce the Gödel Machine’s decision behavior. It maps the Gödel Machine’s parent–child choice to coding-agent search, with assumptions that constrain the utility, evaluation, and budget.

A GÖDEL MACHINE WITH CMP ORACLE

  • A CMP oracle suffices to imitate the Gödel Machine in the specified setting, where access to CMP provides the true Q value for choosing whether to accept a modification.The proof identifies the oracle’s choice with maximizing the Gödel POMDP’s Q value; the resulting policy is optimal by the Bellman Optimality Equation.Source: A GÖDEL MACHINE WITH CMP ORACLE · pp. 15–16
  • The objective depends only on the final agent, with no intermediate rewards, and agent utility is measured on tasks under repeatable trials.The environment and evaluation metric remain fixed, and each agent–task evaluation is independent of evaluation time or prior events.Source: A GÖDEL MACHINE WITH CMP ORACLE · p. 15
  • The result assumes the prover knows the utility function, the computation budget is finite and known, proofs consume no budget, and each self-modification costs one budget unit.The original Gödel Machine’s time-aware setting is set aside for this fixed-environment setup.Source: A GÖDEL MACHINE WITH CMP ORACLE · p. 15
  • In the Gödel POMDP, the policy accepts or rejects a parent–child modification, then selects a final agent using its score function.The final score is restricted to select one of the observed parent or child agents, after which the agent is evaluated by utility.Source: A GÖDEL MACHINE WITH CMP ORACLE · pp. 15–16
  • The coding-agent setting is represented as an Extended MDP, and each Gödel POMDP policy maps to one that chooses between the two special nodes while ignoring the rest of the tree.The adapted CMP is defined over the extended state and agent; the proof relates it to the Gödel POMDP’s Q value.Source: A GÖDEL MACHINE WITH CMP ORACLE · p. 16

B ALGORITHM

HGM alternates between expanding agents in a self-modification tree and evaluating agents on benchmark tasks, using sampled scores to choose candidates. Its asynchronous execution has an early evaluation bias, and the algorithm initializes with parallel expansions to address a separate early-search bias.

B ALGORITHM

  • To avoid an early-search bias toward expansions that finish first, HGM initially expands the initial agent five times with each process in parallel.The authors explain that early evaluation choices otherwise concentrate on the few expansions already completed.Source: B ALGORITHM · p. 17
  • The asynchronous process favors agents with fewer evaluations for further evaluation, but this bias is barely observed after more than 50 evaluations.The authors report that many agents succeeded on their first ten evaluated tasks, while accuracy dropped quickly as evaluations increased.Source: B ALGORITHM · p. 17
  • HGM samples clade and agent success scores to select nodes for expansion or evaluation, then returns an agent selected by its evaluated performance.Expansion creates a child through self-modification; evaluation allocates a benchmark task to the selected agent.Source: B ALGORITHM · p. 17

C.1 INITIAL AGENTS

The paper’s initial agents are adapted from DGM’s official implementation, with task-specific differences between SWE-bench and Polyglot. The agent used in the later experiment is further simplified and given longer execution limits.

C.1 INITIAL AGENTS

  • The initial agents derive from DGM’s official implementation, with API support, timeout, and LLM-interaction-length changes, and a one-hour execution limit.The agent runs a loop of LLM queries with file-editing and bash-command tools.Source: §C.1 · p. 18
  • The Polyglot initial agent adds test commands for different programming languages, while the SWE-bench agent has functions to summarize existing tests and run tests with reports.Source: §C.1 · p. 18
  • For Section 4.3, the initial agent removes the file-editing tool and extends the time limit to five hours for self-modification and task evaluation.The stated aim is to reduce premature elimination of stronger agents due to time constraints.Source: §C.1 · p. 18

C.2 OTHER DETAILS

The Polyglot experiments used a mixed-quantized Qwen3-Coder model for self-modification and cost approximately $5,000 across the three methods.

C.2 OTHER DETAILS

  • The Polyglot experiments used Qwen3-Coder-480B-A35B-Instruct for self-modification.The model was an int4 and int8 mixed-quantized version generated by AutoRound.Source: §C.2 · p. 18
  • The model was generated by AutoRound in an int4 and int8 mixed-quantized version.Source: §C.2 · p. 18
  • Producing the experimental results cost approximately $5,000 USD across all three methods.Source: §C.2 · p. 18

D EMPIRICAL CMP AND ITS ESTIMATION

This appendix describes the empirical CMP calculation and estimator used for correlation analysis, then presents a comparison of baseline and HGM policies.

D EMPIRICAL CMP AND ITS ESTIMATION

E BASELINES

F DISCOVERED AGENTS

The discovered agents illustrate iterative self-modification and nested edit records, including how successive changes can shape later modifications.

F DISCOVERED AGENTS

  • One discovered agent performs multiple self-modifications during a single expansion step through iterative refinement.The authors describe this repetitive modification as self-motivated and as producing successive levels of meta-improvement.Source: F DISCOVERED AGENTS · p. 21
  • Nested diff files record edits to earlier edits, representing how self-modifications influence subsequent modifications.The authors say this format can inspire long-sighted self-improvement, although its semantics are difficult to parse manually.Source: F DISCOVERED AGENTS · pp. 21, 23
  • The example agent’s test run passed 29 tests in 3.58 seconds.Source: F DISCOVERED AGENTS · pp. 23, 25

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