What we mean
- Self-modification
- An agent changing parts of its own software or workflow.
- Recursive self-improvement
- A proposed process in which improvements increase the ability to make further improvements.
- Evaluation budget
- The compute, model usage and human effort spent producing and checking a result.
- Shadow, in this research proposal
- An unresolved doubt, missing distinction, contradiction, or lesson kept with its context and the conditions that could reopen investigation.
Values we bring to the question
- Measure useful progress rather than activity alone.
- Keep consequential changes observable and open to correction.
Reasoning and the proposed connection
- A coding agent's software can change even when its underlying model weights remain fixed. Workflow improvement and foundational-model improvement require different evidence.
- A higher score is informative only in relation to evaluation quality, failed attempts, and total cost.
- We propose a loop in which a shadow preserves a gap, a connection from another field suggests a prediction, and an experiment can change a concept, tool, or learning method. Recording a gap or producing a new version alone is not the improvement.
- Independent groups could test a revised method under their own conditions and keep or reject it with reasons. Transfer across unfamiliar problems would matter more than repeated success on the motivating example.
- A program-search loop can generate useful changes while depending on people to choose its task and evaluator. For Leviathan, improving a method should include checking whether its evaluation still represents the intended purpose.
Where the reasoning stops
The cited work concerns limited tasks and research settings. More generated code, longer runs or a single benchmark improvement cannot establish an unrestricted feedback loop.
The strongest objection
An apparent improvement may exploit an evaluation, consume a larger budget, or shift work to uncounted people. A system selecting its own questions and tests could reinforce its blind spots; a successful revision may still fail on unfamiliar tasks or in another community.
Read the evidence
Each source has a specific role in the stated claim. Its findings, review date, and access limits are recorded below. Our proposed architecture and experiments require their own tests; an editorial revision does not mean the source was reviewed again.
R-AG-04 · Supports this claim
Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agents
Jenny Zhang, Shengran Hu, Cong Lu, Robert Lange and Jeff Clune · Preprint
Read: Selected sections · Primary source reviewed
Published: 2025-05-29 · Reviewed: 2026-09-30
Agent code improves on coding benchmarks while underlying model weights remain fixed.
- What it reports
- An agent modifies its own software and selects changes using coding evaluations, improving on two benchmarks. An archive of different past solutions helps the search.
- Limits
- The underlying model weights stay fixed. Bounded coding experiments do not establish open-ended improvement of model training, unlimited recursive improvement, or an AGI timetable.
Review scope and version
Read: Selected sections.
arXiv v3: 12 March 2026
Read alongside the METR cost framework: measured gains, total expenditure and independent evaluation answer different questions.
Related source links
R-AG-05 · Limits the inference
Expenditure Horizon: Measuring Optimization Ability, with an Application to NanoGPT
Tom Cunningham, Manish Shetty, Vincent Cheng and Nate Rush; METR · Research report
Read: Selected sections · Primary source reviewed
Published: 2026-07-21 · Reviewed: 2026-09-30
Comparisons need to include experimental compute, model use and human effort.
- What it reports
- The report proposes comparing human and agent optimization at equal expenditure, illustrated with NanoGPT. It counts experimental compute and human effort alongside model usage.
- Limits
- The human comparison is estimated, the agent results are preliminary, and the study covers one optimization problem. It does not directly measure the returns from human–AI collaboration.
Review scope and version
Read: Selected sections.
Research report
More generated code or a higher benchmark score alone does not establish faster research or economic advantage.
Link to this source noteR-AG-09 · Supports part of this claim
AlphaEvolve: A coding agent for scientific and algorithmic discovery
Alexander Novikov and co-authors · Research white paper
Read: Selected sections · Primary source reviewed; no independent reproduction
Published: 2025-06-16 · Reviewed: 2026-10-04
AlphaEvolve provides a bounded program-search example using supplied evaluators. It does not establish open-ended improvement of every capability.
- What it reports
- An evolutionary pipeline combines LLM-generated code with supplied evaluators, including evolving search algorithms. Reported results include a 48-multiplication algorithm for two 4-by-4 complex matrices and optimizations to Google's computational infrastructure.
- Limits
- The main boundary is availability of automated evaluators. The paper describes self-improvement feedback as modest and occurring over months. It does not demonstrate unrestricted recursive improvement, ethical goal selection or Leviathan's architecture. Results and deployments were not independently reproduced here.
Review scope and version
Read: Selected sections.
arXiv:2506.13131v1; white paper submitted 16 June 2025
Read v1 task definition, code search, evaluation, selected results and discussion. Reported code and deployments were not reproduced; supplied evaluators constrain the demonstrated discovery process.
Related source links
What could change our view?
Gains that disappear on held-out tasks or at equal total cost would weaken the practical case. Repeated improvements that transfer, remain stable and survive external checks would strengthen it.
The next question
At the same total budget, does a method revised through the proposed shadow–hypothesis–experiment loop outperform an unchanged method and a strong ordinary review process on held-out tasks? Count failed searches, verification, and recovery. Test whether an independent group can use or challenge the revision. Leviathan has not yet demonstrated this learning loop or an open-ended RSI result.
Revision record
Added bounded self-improvement evidence and a cost-based comparison framework; separated demonstrated changes from future trajectories.
Added a proposed path from a recorded doubt to an experiment and evaluated method revision, including transfer across tasks or groups. Preserved the bounded findings and cost conditions; no new self-improvement result is claimed.
Made the RSI research direction explicit across concepts, tools, organization, and learning methods. Added a full proposed shadow-to-experiment loop and comparisons involving independent transfer. Bounded empirical findings and cost conditions remain unchanged; no new improvement result is claimed.
Reviewed selected primary-source sections proposed in the external assessment and added scoped connections, access limits and research questions. Interlat retains its existing source ID; its reviewed preprint is distinguished from the final conference text. No experiment was reproduced, claim status promoted or governance rule adopted.
This note records an editorial position. Independent people and groups can bring another interpretation, a useful method, or an objection to the framing. Explore it with your own assistant if helpful and choose what to share. Cite C04 and the relevant revision when contributing; the history explains why our account changed.