https://arxiv.org/api/gFlbO9lqp/cPz/CO4bykC2bWWi0 2026-09-26T16:11:45Z 30 6 0 http://arxiv.org/abs/2608.07645v1 2026-08-07T16:46:44Z

Self-improving coding agents that iteratively rewrite their own source code have demonstrated impressive performance on coding tasks. However, existing solutions generally derive self-modification from a single failure trajectory at a time, overlooking rich comparative signals available in the agent's expanding archive of past attempts. According to Mendelian principles of controlled inheritance, we introduce Mendel Gödel Machine (MGM). In addition to the general single-trajectory clonal mutation, MGM includes two new types of self-modification that better utilizes evidences accumulated: the reaction-norm mutation edits an agent based on its trajectories on multiple tasks simultaneously, and the cross-lineage hybridization edits an agent using the trajectory of a reference agent from another lineage on the same task. Under an additive fitness landscape model, we prove theoretically and demonstrate via controlled surrogate simulation that the new strategies facilitate a faster and better convergence over single-trajectory baselines. Experiments on SWE-bench and Polyglot confirm MGM's consistent improvement in performance, efficiency, and generalizability.

2026-08-07T16:46:44Z Project Page at https://reallcz.github.io/MGM; Code at https://github.com/RealLcz/MGM Changzhi Liu Yilun Liu Sikuan Yan Volker Tresp Yunpu Ma http://arxiv.org/abs/2606.26294v2 2026-06-29T17:13:25Z

Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains. However, their search methods generally assume a stationary evaluation criterion: a fixed verifier, benchmark, or labeled dataset that remains valid as the agent improves. This ignores a central feature of evolution: species adapt as their environments change with them. We aim to bring the same principle to recursive self-improvement, making evaluation part of the improvement loop and opening search to evolving evaluators, adversarial objectives, and dynamic utilities that may surpass static benchmarks. We introduce the Red Queen Godel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. The RQGM makes this possible through controlled utility evolution: search is organized into epochs with a fixed within-epoch evaluation criterion, while the utility can be updated at epoch boundaries, so self-improvement guarantees hold per epoch as the objective evolves across them. We begin by showing that even on verifiable coding tasks, the RQGM improves test pass rate over the prior SOTA by adding a complementary agent-as-a-judge code-review signal. This signal is cheaper and the RQGM uses 1.35x-1.72x fewer tokens. We then turn to scientific paper writing and reviewing, and Olympiad-level proof writing and grading, where the RQGM improves performance over prior self-improving agents: co-evolved writers reach 1.78x-1.86x higher acceptance rates under a diverse agent-as-a-judge panel, while co-evolved graders reach 9% higher ground-truth accuracy. In paper reviewing, the strongest baseline reviewer over-accepts AI-generated papers at up to 1.91x the human rate. The RQGM corrects this by introducing an adversarial objective that discovers reviewers equally stringent on AI and human work.

2026-06-24T18:38:26Z 13 pages main text + 21 pages appendix (38 pages total, incl. references); 11 figures (7 main text + 4 appendix); 10 tables (2 main text + 8 appendix). Preliminary preprint; work in progress. Keywords: self-improving agents, learned evaluation, multi-agent systems, auto-mated scientific discovery, controlled utility evolution, co-evolutionary search, autoresearch Alex Iacob Andrej Jovanović William F. Shen Daniel Burkhardt Meghdad Kurmanji Nurbek Tastan Lorenzo Sani Niccolò Alberto Elia Venanzi Ambroise Odonnat Zeyu Cao Bill Marino Xinchi Qiu Nicholas D. Lane http://arxiv.org/abs/2601.14401v1 2026-01-20T19:05:21Z

This article introduces Recursivism as a conceptual framework for analyzing contemporary artistic practices in the age of artificial intelligence. While recursion is precisely defined in mathematics and computer science, it has not previously been formalized as an aesthetic paradigm. Recursivism designates practices in which not only outputs vary over time, but in which the generative process itself becomes capable of reflexive modification through its own effects. The paper develops a five-level analytical scale distinguishing simple iteration, cumulative iteration, parametric recursion, reflexive recursion, and meta-recursion. This scale clarifies the threshold at which a system shifts from variation within a fixed rule to genuine self-modification of the rule itself. From this perspective, art history is reinterpreted as a recursive dynamic alternating between internal recursion within movements and meta-recursive transformations of their generative principles. Artificial intelligence renders this logic technically explicit through learning loops, parameter updates, and code-level self-modification. To distinguish Recursivism from related notions such as generative art, cybernetics, process art, and evolutionary art, the article proposes three operational criteria: state memory, rule evolvability, and reflexive visibility. These concepts are examined through case studies including Refik Anadol, Sougwen Chung, Karl Sims, and the Darwin-Godel Machine. The article concludes by examining the aesthetic, curatorial, and ethical implications of self-modifying artistic systems.

2026-01-20T19:05:21Z Preprint under review Florentin Koch http://arxiv.org/abs/2510.10232v2 2026-09-17T11:32:17Z

Recursive self-modification is increasingly central in AutoML, neural architecture search, and adaptive optimization, yet no existing framework ensures that such changes are made safely. Godel machines offer a principled safeguard by requiring formal proofs of improvement before rewriting code; however, such proofs are unattainable in stochastic, high-dimensional settings. We introduce the Statistical Godel Machine (SGM), the first statistical safety layer for recursive edits. SGM replaces proof-based requirements with statistical confidence tests (e-values, Hoeffding bounds), admitting a modification only when superiority is certified at a chosen confidence level, while allocating a global error budget to bound cumulative risk across rounds.We also propose Confirm-Triggered Harmonic Spending (CTHS), which indexes spending by confirmation events rather than rounds, concentrating the error budget on promising edits while preserving familywise validity.Experiments across supervised learning, reinforcement learning, and black-box optimization validate this role: SGM certifies genuine gains on CIFAR-100, rejects spurious improvement on ImageNet-100, and demonstrates robustness on RL and optimization benchmarks.Together, these results position SGM as foundational infrastructure for continual, risk-aware self-modification in learning systems.Code is available at: https://github.com/gravitywavelet/sgm-anon.

2025-10-11T14:09:37Z Xuening Wu Shenqin Yin Yanlan Kang Xinhang Zhang Qianya Xu Zeping Chen Wenqiang Zhang http://arxiv.org/abs/2505.22954v3 2026-03-12T23:47:40Z

Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The Gödel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin Gödel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, high-quality agents and allows the parallel exploration of many different paths through the search space. Empirically, the DGM automatically improves its coding capabilities (e.g., better code editing tools, long-context window management, peer-review mechanisms), increasing performance on SWE-bench from 20.0% to 50.0%, and on Polyglot from 14.2% to 30.7%. Furthermore, the DGM significantly outperforms baselines without self-improvement or open-ended exploration. All experiments were done with safety precautions (e.g., sandboxing, human oversight). The DGM is a significant step toward self-improving AI, capable of gathering its own stepping stones along paths that unfold into endless innovation.

2025-05-29T00:26:15Z Code at https://github.com/jennyzzt/dgm Jenny Zhang Shengran Hu Cong Lu Robert Lange Jeff Clune http://arxiv.org/abs/cs/0302012v2 2003-11-27T10:01:42Z

Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam's razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse's thesis of the computer-generated universe.

2003-02-10T14:17:33Z 23 pages, updated refs, added Goedel machine overview, corrected computing history timeline. To appear in B. Goertzel and C. Pennachin, eds.: Artificial General Intelligence Juergen Schmidhuber