Hyperagents — part 4/7

Cleaned-text code points [46692, 61860). Bibliography omitted here; source.md includes it.

One example is DGM-H’s autonomous development of performance tracking infrastructure. Rather than relying on isolated evaluation outcomes, the hyperagent records, aggregates, and compares performance metrics across iterations, identifying which changes yield sustained improvements and which lead to regressions. This performance tracking supports informed decision-making, such as prioritizing promising iterations and avoiding unproductive modification directions. The snippet below shows an automatically introduced performance tracker that logs and organizes metrics across iterations: ⬇

Another example is DGM-H’s innovation of persistent memory, which enables learning to accumulate across iterations. Instead of merely logging numerical scores, the hyperagent stores synthesized insights, causal hypotheses, and forward-looking plans (e.g., identifying which generations performed best, diagnosing over-corrections, and proposing how to combine successful strategies). This memory is actively consulted during subsequent self-modification steps, allowing later generations to build on earlier discoveries and avoid repeating past mistakes. This is an example of a stored memory entry: ⬇

### 5.3 Compounding Self-Improvements

We investigate whether self-improvements learned by DGM-H in one setting continue to accumulate when DGM-H is run in a different setting. From prior DGM-H runs on the paper review and robotics reward design tasks ( Section 5.1 ), we select transfer hyperagents using the same selection mechanism described earlier ( Section 5.2 , Section D.4 ). We then evaluate their ability to continue self-improving in a new domain, Olympiad-level math grading. After 200 iterations of DGM-H starting from these transfer agents (DGM-H + transfer), the best generated agents (selected based on validation score) achieve a test-set score of 0.640 (CI: 0.550 – 0.720). Under the same experimental setup, DGM-H starting from the initial agent achieves a best test-set score of 0.610 (CI: 0.510 – 0.680). Although the difference between DGM-H + transfer and DGM-H is not statistically significant (p ¿ 0.05), DGM-H + transfer achieves a higher median performance and higher confidence intervals than DGM-H starting from the initial agent ( Figure 4 ). Notably, improvements at higher performance levels are increasingly difficult due to saturation effects (e.g., increasing performance from 0.7 to 0.8 is typically more challenging than from 0.0 to 0.1), making these gains meaningful despite their modest absolute magnitude. These results suggest that DGM-H’s self-improvements are reusable and can potentially accumulate across runs, supporting the possibility of compounding self-improvement over time.

The representative static baseline for Olympiad-level math grading from IMO-GradingBench is ProofAutoGrader ( Luong et al., 2025 ) . We initialize the DGM-H with ProofAutoGrader as the task agent and a transfer meta agent obtained from a prior DGM-H run (on paper review and robotics reward design), and then continue optimizing for Olympiad-level math grading. After 200 iterations, the best discovered agent achieves a test-set score of 0.700, outperforming ProofAutoGrader’s score of 0.670 ( Figure 4 ). We then evaluate both the best discovered agent and ProofAutoGrader on the full IMO-GradingBench to obtain a more accurate estimate of the improvement. On the full IMO-GradingBench, the DGM-H improves ProofAutoGrader’s accuracy from 0.561 to 0.601, and lowers the mean absolute error from 0.178 to 0.175 ( Section E.4 ). We open-source this artifact to support future research and development ( Section E.1.3 ). These results show that the DGM-H can build on strong existing solutions and further improve their performance.

## 6 Safety Discussion

The DGM-Hyperagents (DGM-H) introduces distinct safety considerations due to its ability to autonomously modify its own behavior and improvement mechanisms over time. In this work, all experiments are conducted under strict safety constraints. In particular, agent-generated code is executed within carefully sandboxed environments with enforced resource limits (e.g., timeouts, restricted internet access). These measures are designed to prevent unintended side effects, contain failures, and ensure that self-modifications remain confined to the intended experimental scope. Moreover, evaluation is performed using predefined tasks and metrics, and human oversight is maintained throughout all experiments.

Potential to evolve faster than human oversight. As AI systems gain the ability to modify themselves in increasingly open-ended ways, they can potentially evolve far more rapidly than humans can audit or interpret. At the cusp of such explosive capability growth, it becomes necessary to reconsider the roles that AI systems play in society ( Bengio et al., 2024 ) . Rather than framing safety solely in terms of absolute guarantees or full interpretability, a central challenge lies in balancing the potential of AI as a catalyst for human progress and well-being (e.g., automating scientific discovery) with the degree of trust humans are willing to place in these systems (e.g., delegating decisions or actions without requiring continuous human verification), while minimizing the many potential risks and downsides ( Clune, 2019 ; Ecoffet et al., 2020 ; Bengio et al., 2024 ; Weston and Foerster, 2025 ) . This balance is shaped by factors such as transparency and controllability.

While the DGM-H operates within safe research boundaries (e.g., sandboxing, controlled evaluations), these safeguards may become increasingly strained or infeasible as self-improving systems grow more capable. We discuss additional safety considerations in Appendix F . We proactively include this discussion to encourage broader engagement with what safety means for open-ended self-improving AI systems ( Clune, 2019 ; Ecoffet et al., 2020 ; Sheth et al., 2025 ) . This includes ongoing discussion about appropriate levels of trust, oversight, and transparency, and societal deliberation about which benefits these systems should prioritize when deployed.

## 7 Limitations and Conclusion

This work introduces hyperagents and incorporates them into the Darwin Gödel Machine (DGM) to form DGM-Hyperagents (DGM-H). DGM-H is a general self-improvement framework that open-endedly evolves an archive of self-improving hyperagents for any computable task, enabling the system to improve both task performance and its own self-improvement mechanism. Across diverse domains, the DGM-H produced substantial and generalizable gains in task performance while also improving its ability to generate improvements, with these meta-level gains transferring across domains and compounding across runs.

Our results suggest that self-improvements can compound across different experimental settings, but this version of DGM-H has limitations that constrain truly unbounded progress. First, it operates with a fixed task distribution. One direction is to co-evolve the task distribution by generating new tasks and curricula that adapt to the agent’s capabilities ( Clune, 2019 ; Zhang et al., 2024 ; Faldor et al., 2025 ; Bolton et al., 2025 ) . Second, components of the open-ended exploration loop (e.g., parent selection, evaluation protocols) remain fixed. Although hyperagents can modify their self-improvement mechanisms, they cannot alter the outer process that determines which agents are selected or how they are evaluated. Keeping these components fixed improves experimental stability and safety, but limits full self-modifiability. Enabling hyperagents to modify these outer-loop components and adapt their own search strategy and evaluation process is another promising direction for future work. Our preliminary results suggest such extensions are feasible ( Section E.5 ).

DGM-H demonstrate that open-ended self-improvement can be made practical across diverse domains. Provided sufficient safety considerations are worked out, the DGM-H suggest a path toward self-accelerating systems that not only search for better solutions, but continually improve their ability to self-improve.

## Acknowledgments

We thank Andrew Budker and Ricardo Silveira Cabral for supporting this work, and Alisia Lupidi, Chenxi Whitehouse, John Quan, Lisa Alazraki, Lovish Madaan, Lucia Cipolina-Kun, Mattia Opper, Michael Dennis, Parth Pathak, Rishi Hazra, Roberta Raileanu, Sandra Lefdal, Shashwat Goel, Shengran Hu, Timon Willi, Tim Rocktäschel, and Yoram Bachrach for insightful discussions and feedback.

## Author Contributions

Jenny Zhang led the conceptualization of the study, conducted the experiments, and wrote the manuscript. Bingchen Zhao and Wannan Yang contributed to experimental design and execution. Jakob Foerster, Jeff Clune, Minqi Jiang, Sam Devlin, and Tatiana Shavrina provided feedback on the methodology and manuscript. All authors reviewed and approved the final manuscript.

## Appendix A Algorithmic details

This appendix provides additional algorithmic details for the DGM-Hyperagents (DGM-H). We first describe the implementation of the initial hyperagent, including the tools and prompts available to the initial task and meta agents ( Section A.1 ). We then detail the parent selection mechanism used during open-ended exploration, which balances exploitation of high-performing agents with continued exploration of the archive ( Section A.2 ). Finally, we present pseudocode for DGM-H ( Section A.3 ).

### A.1 Initial Agent

We present the details of the tools available to the initial hyperagent and its prompts ( Section 4 ).

Initial task agent prompt: ⬇

Initial meta agent prompt: ⬇

Information of the given bash tool: ⬇

Information of the given edit tool: ⬇

### A.2 Parent Selection

At each iteration, we select a subset of agents from the archive as parents to self-modify and produce new child agents ( Section 3 ). We use a mechanism similar to that of Zhang et al. [2025b] , inspired by Ecoffet et al. [2019] , that is roughly proportional to an agent’s performance score and inversely proportional to the number of children that successfully compiled. This selection mechanism biases sampling toward agents that outperform the current frontier average while down-weighting agents that have already produced many children, retaining smooth probabilistic exploration and automatically adapting as the archive improves over time. The details of the parent selection process are outlined below.

At each iteration t t of the DGM-H run, let 𝒜 t = { a 0 , a 1 , … , a t } \mathcal{A}^{t}=\{a_{0},a_{1},\dots,a_{t}\} denote the archive of candidate agents with associated performance scores α i = performance ⁡ ( a i ) \alpha_{i}=\mathrm{performance}(a_{i}) . All agents in the archive are eligible for parent selection.

We first compute a dynamic midpoint based on the current performance distribution. Let α m ​ i ​ d = 1 m ​ ∑ j ∈ 𝒯 t α j , \alpha_{mid}\;=\;\frac{1}{m}\sum_{j\in\mathcal{T}^{t}}\alpha_{j}, where 𝒯 t ⊂ 𝒜 t \mathcal{T}^{t}\subset\mathcal{A}^{t} indexes the top- m m highest-performing agents at iteration t t (with m = 3 m=3 in our experiments). This midpoint adapts over time and reflects the current performance frontier.

Each agent’s score is first passed through a sigmoid transformation: s i = 1 1 + exp ⁡ ( − λ ⁡ ( α i − α m ​ i ​ d ) ) , s_{i}\;=\;\frac{1}{1+\exp\!\bigl(-\lambda(\alpha_{i}-\alpha_{mid})\bigr)}, where λ > 0 \lambda>0 controls the sharpness of selection. We set λ = 10 \lambda=10 .

To encourage exploration, we introduce a novelty bonus based on the number of compiled children n i n_{i} produced by agent a i a_{i} : h i = 1 1 + n i . h_{i}\;=\;\frac{1}{1+n_{i}}.

We then form an unnormalized weight w i = s i ​ h i , w_{i}\;=\;s_{i}\,h_{i}, which balances performance and novelty.

The weights are normalized to form a categorical distribution: p i = { w i ∑ j = 0 t w j , if ​ ∑ j = 0 t w j > 0 , 1 t + 1 , otherwise . p_{i}\;=\;\begin{cases}\dfrac{w_{i}}{\sum_{j=0}^{t}w_{j}},&\text{if }\sum_{j=0}^{t}w_{j}>0,\\[10.0pt] \dfrac{1}{t+1},&\text{otherwise}.\end{cases}

We sample parents independently with replacement according to this distribution: { parents } ∼ Categorical ⁡ ( { p i } i = 0 t ) . \{\,\text{parents}\,\}\;\sim\;\mathrm{Categorical}\bigl(\{p_{i}\}_{i=0}^{t}\bigr).

A wide range of search and exploration strategies has been proposed in prior work [ Coulom, 2006 , Silver et al., 2016 , Herr et al., 2025 , Wang et al., 2025b , Weng et al., 2026 ] . We present preliminary evidence that the DGM-H can begin to autonomously rediscover and adapt such strategies by modifying its own exploration dynamics ( Section E.5 ). An open research direction is whether self-improving systems can reliably discover search and exploration mechanisms that outperform carefully handcrafted algorithms.

### A.3 Pseudocode

This is the pseudocode of the DGM-H, described in Section 3 :

### A.4 Multi-domain Optimization

When optimizing for multiple domains within the same run, hyperagents are evaluated on tasks from different domains and have access to all evaluations across these tasks during self-modification. We do not specify which particular domain or task to prioritize. Parent selection is based on the average performance across domains. As a result, improvements in any domain increase selection probability, while regressions reduce it. Because the meta agent can inspect evaluations from any task, it can introduce shared mechanisms (e.g., structured reasoning, memory, and error handling) that benefit multiple domains simultaneously. Thus, rather than manually specifying which task or domain to optimize, hyperagents can optimize across multiple domains within the same run.

## Appendix B Baseline Details

We outline the pseudocode for each baseline described in Section 4.1 , provide a comparison table summarizing their key differences ( Table 1 ), and include a detailed conceptual figure that visually contrasts the architectural components and modification mechanisms across DGM variants and hyperagents ( Figure 5 ).

Method Self-improving meta agents Open-ended exploration Metacognitive self-modification (i.e., hyperagents) DGM-H ✓ ✓ ✓ DGM-H w/o self-improve ✕ ✓ ✓ DGM-H w/o open-ended exploration ✓ ✕ ✓ DGM ✓ ✓ ✕ DGM-custom ✓ ✓ ✕

This is the pseudocode of the baseline DGM-H without self-improving agents [ Hu et al., 2025 , ADAS,] :

This is the pseudocode of the baseline DGM-H without open-ended exploration:

This is the pseudocode for the original DGM [ Zhang et al., 2025b ] , framed within the hyperagent setting:

The handcrafted instruction-generation step in the original DGM: ⬇

The customized instruction-generation step in DGM-custom: ⬇

## Appendix C Domain Details

This appendix provides detailed descriptions of each domain used for evaluation: Polyglot ( Section C.1 ), paper review ( Section C.2 ), robotics reward design ( Section C.3 ), Olympiad-level math grading ( Section C.4 ). For each domain, we specify the agent’s input and required output for a given task, the evaluation protocol, and representative static baselines ( Table 2 ).

### C.1 Polyglot