Recursive Self-Improvement

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Overview

Recursive self-improvement asks how AI systems can use their own experience to make future versions more capable, efficient, or safe. Approaches include revising agent prompts, tools, memory, and code; evolving training data or models; and using search, world models, or learned evaluators to guide changes. Most demonstrated progress comes from bounded tasks with external or held-out checks, such as coding, reasoning, robotics, and scientific research benchmarks. A central challenge is ensuring that gains persist beyond the feedback used to produce them, without benchmark overfitting, unsafe regressions, or goal drift.

Latest papers

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84 papers40 papers in the last four weeks, up 167% on the four weeks before. 0.2% of all new papers.

Aug 19, 2026

What is Missing from AI Post-Training AI: An Empirical Analysis

Large language model (LLM) agents can now post-train an LLM end-to-end, raising the prospect of recursive self-improvement (RSI). Yet this progress is measured by aggregate benchmark scores, which cannot tell whether an agent executes a fixed plan well or strategically revises the plan when it fails. We separate these two capabilities: execution-level capability, iterating within an established training strategy, and strategy-level capability, revising that strategy as experimental evidence accumulates. Analyzing 1,338 post-training trajectories of frontier agents, we find that agents reliably execute post-training but lock into a default strategy, which follows the agent rather than the task, and only 2.1% of transitions between adjacent training runs ever change strategy. We then test whether the agent lacks experience, reasoning, or the decision to switch. (1) Experience improves execution but not the strategy. (2) Additional reasoning compute yields front-loaded gains on easier tasks but refines, rather than revises, the committed strategy. (3) Human review before training changes which strategy the agent locks into, not whether it locks in, whereas a single mid-run instruction outperforms the agent's own continuation by up to 17.44 points under the same budget. In conclusion, what the agent lacks is the decision to reopen a committed strategy and try another one. Realizing RSI therefore calls for interaction protocols and training signals that make strategy revision an explicit, rewarded decision.

Joy Jia Yin Lim, Xin Huang, Hao Peng +5

Tsinghua University · University of Electronic Science and Technology of China · Renmin University of China

AI Agent EvaluationLLM Agent Self-ImprovementLLM AgentsLLM Post-TrainingRecursive Self-Improvement
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Aug 14, 2026

The Dynamics of Intelligence Explosions

AI is increasingly being used to help with AI R&D. Under certain conditions this feedback loop might be able to produce an intelligence explosion, with rapidly escalating AI capabilities. I explore the mathematics of the most explosive possibilities, with an eye to understanding what drives the dynamics. I show that singular growth (towards a vertical asymptote) is harder to achieve than would be expected from recent economics-inspired modelling, and that there is an important but neglected class of growth rates that are faster than exponential but don't lead to a vertical asymptote. I draw out the generation time (the time to go around the feedback loop) as a neglected parameter that plays a pivotal role in determining the behaviour of any intelligence explosion --- one cannot have singular growth unless the generation time rapidly approaches zero.

Toby Ord

Oxford Martin AI Governance Initiative, at Oxford University

Recursive Self-Improvement
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Aug 13, 2026

AQuA: Recursively Self-Improving Quantitative Trading Research Agents

We study recursive self-improvement at the level of quantitative-investment research: whether an autonomous system can use evidence from earlier experiments to improve the hypotheses and candidates proposed in later iterations. We present AQuA, which comprises two separate language-model-driven research systems: one for symbolic factor discovery and one for trainable model development. Each system records experimental results and uses them to guide subsequent proposals. Each operates in a fixed sandbox, which fixes the data splits, feature and label definitions, and evaluator while allowing the model to act only through constrained factor expressions or configuration diffs. The factor system, a manager-mediated multi-agent pipeline, discovers and combines factors into a signal that reaches a combined validation information coefficient of about 0.1900.190 on a crypto universe. The model system, a config-driven loop over a hybrid time-series architecture, reaches a per-stock information coefficient of +0.0843+0.0843 on US equities and converts it into a threshold long/short strategy with a held-out Sharpe of up to +2.50+2.50 at a two-leg cost. The strategy is positive in every year from 2021 to 2025.

Jiacheng Guo, Suozhi Huang, Yunlong Gao +5

Princeton University · Ant Group · Stanford University

Quantitative FinanceAutomated Algorithm DiscoverySelf-Improving AgentsRecursive Self-ImprovementAutonomous ExperimentationAutonomous Research Agents+1
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Aug 7, 2026

Mendel Gödel Machine: Recursive Self-Improving Coding Agents via Comparative Evolution

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.

Changzhi Liu, Yilun Liu, Sikuan Yan +2

University of Electronic Science and Technology of China · Ludwig Maximilian University of Munich · Munich Center for Machine Learning

Coding AgentsGenetic ProgrammingLLM Agent Self-ImprovementRecursive Self-Improvement
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Aug 4, 2026

PAST-Bench: Benchmarking the Foundations of Recursive Self-Improvement in Personal Agents

Recursive self-improvement requires agents to turn accumulated experience into better future behavior. Personal AI agents offer a concrete setting for studying this capability because they retain preferences, task histories, tool routines, and learned skills across sessions. Yet whether retained experience actually improves them over time has not been systematically tested. We introduce PAST-Bench, a benchmark designed to isolate this question. Each agent runs through ordered sequences of fresh-session tasks under matched conditions that turn retained experience on and off. It spans 26 scenarios and 204 episodes across memory, procedural reuse, information gathering, and update. We report both later-task gains and whether those gains follow the intended save, retrieve, and update pathway. Across seven base models and four agent frameworks, improvement is real but uneven across capabilities. Agents with the same headline gain can differ markedly in whether that gain is supported by evidence of the intended pathway. Guided by these findings, we develop Hermes+, which extends Hermes with five targeted interventions across stages of the agent loop. Hermes+ raises the average gain from retained experience and provides clearer pathway evidence, with its strongest improvement on tasks requiring outdated state to be replaced, although the effect remains capability- and model-dependent. Together, PAST-Bench and Hermes+ provide an evaluation and diagnostic foundation for studying how persistent agents can progress from retaining experience to systematically improving through it. Code: https://github.com/Gen-Verse/PAST-Bench

Shuhan Xue, Zixin Ding, Yichen Shen +6

LLM Agent MemoryLong-Horizon Agent EvaluationMemory Agent BenchmarksSelf-Improving AgentsRecursive Self-Improvement
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Jul 30, 2026

Frontis-MA1: Training an AI4AI Model towards Recursive Self-Improvement in Machine Learning Engineering

Recursive self-improvement (RSI) requires AI systems that improve the process of building AI (i.e., AI4AI); machine learning engineering (MLE) offers a concrete, executable testbed for studying this capability. We introduce OpenMLE, an open full-stack system for RSI research in MLE, spanning verifiable task environments with execution feedback (OpenMLE-Gym), operator learning (OpenMLE-RL), and long-horizon search (OpenMLE-Evo). On this stack we post-train Frontis-MA1 (35B) as a meta-evolution agent for MLE, aligning post-training and inference around four atomic program-evolution operators (Draft, Improve, Debug, Crossover): the same operators are trained via execution-grounded SFT and RL on data deduplicated against all evaluation benchmarks, then composed into long-horizon search, coupling learning and evolution in a single loop. On MLE-Bench Lite under a 12-hour per-task budget on one RTX 4090 capped at 12 GB VRAM, Frontis-MA1 (35B) improves Medal Average from 39.39% to 60.61% over its base model with OpenMLE-Evo, and reaches 71.21% with OpenMLE-Evo-Max (benchmark-independent experience priors and asynchronous search), exceeding GPT-5.5 + Codex and approaching GPT-5.6 Sol and the 2.8T Kimi K3. On held-out NatureBench Lite, both components transfer: with the framework fixed, swapping in the trained model raises Match-SOTA from 50% to 70%; with the model fixed, swapping in OpenMLE-Evo raises it from 20% to 50%. We release the model weights and the full OpenMLE stack to enable reproducible research on executable AI4AI toward RSI. Code: https://github.com/FrontisAI/OpenRSI

Junlin Yang, Che Jiang, Yu Fu +21

Horizon Research, Frontis.AI

Evolutionary OptimizationSelf-Improving AgentsRecursive Self-Improvement
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Jul 28, 2026

RSIBench-Data: Benchmarking Data-Centric Research for Recursive Self-Improvement

Recursive self-improvement requires turning evidence of model failures into better models. Data-centric post-training research entails diagnosing capability gaps, designing and validating training-data strategies, and learning from checkpoint feedback. Can LLM agents automate this loop? Existing benchmarks entangle research decisions with optimization, serving, evaluation, and systems implementation, obscuring agents' research capability. We introduce RSIBench-Data, a controlled benchmark of LLM agents as data-centric researchers with a fixed post-training stack. Agents iteratively revise training-data strategies for a fixed target model; training and serving use Tinker-backed services, official evaluation runs through Harbor and E2B sandboxes, and budgets are fixed across agents. We evaluate four frontier agents on six benchmarks across software engineering, terminal use, scientific question answering, and mathematics. Agents demonstrate core data-centric research capabilities: in 58.33% of settings, they improve upon the first valid attempt by refining strategies from feedback. However, improvement is inconsistent. Among searches continuing after the best observed score, 78.26% end with a lower-scoring final attempt, while the rest only recover the same peak. A strong candidate may therefore appear early or midway through a run even as later revisions fail. Trajectory analysis identifies four patterns in stronger runs: accurate hypotheses, validation-grounded supervision, behavior-aligned data, and preservation of strong checkpoints. These findings suggest that current agents can make useful data-centric discoveries but cannot yet translate feedback into consistent improvements. RSIBench-Data provides a measurable, auditable testbed for the research capabilities required for recursive self-improvement. We open-source our code at https://github.com/evolvent-ai/RSIBench-Data.

Fanqing Meng, Lingxiao Du, Qiguang Chen +4

1Evolvent AI · 2National University of Singapore

LLM Agent EvaluationLLM Agent Self-ImprovementAI Agent BenchmarksLLM Post-TrainingRecursive Self-Improvement
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Jul 23, 2026

AREX: Towards a Recursively Self-Improving Agent for Deep Research

Deep research requires agents to find answers that jointly satisfy multiple constraints. Discovering such answers is costly, whereas verifying a candidate can often be decomposed into tractable constraint-wise checks. This discovery--verification asymmetry suggests that a research agent should do more than simply search longer: it should recursively improve its current answer by verifying intermediate results and using the partially verified state to guide subsequent refinement. We introduce AREX, a family of Recursively Self-Improving (RSI) deep research agents. AREX alternates between an inner research loop that gathers evidence and constructs a provisional answer, and an outer self-improvement loop that audits the answer constraint-wise, identifies unresolved claims, and launches targeted follow-up research. To sustain RSI over long horizons, AREX learns an autonomous context-update tool that compresses growing interaction history into a compact improvement state preserving verified evidence and unresolved constraints, without relying on an external model. We train AREX on verified synthetic tasks and high-quality trajectories through agentic mid-training and long-horizon reinforcement learning. To mitigate sparse final rewards during long horizon learning, we emphasize key steps where decisive evidence is acquired or erroneous research directions are corrected. We instantiate a dense 4B model and a 122B-A10B Mixture-of-Experts model. Across BrowseComp, WideSearch, DeepSearchQA, Humanity's Last Exam (HLE), and other reasoning and tool-use benchmarks, AREX substantially outperforms comparable-scale baselines and remains competitive with models using substantially more activated parameters.

Shuqi Lu, Chaofan Li, Kun Luo +21

Beijing Academy of Artificial Intelligence (BAAI)

Agentic RLDeep Research AgentsSelf-Improving AgentsRecursive Self-ImprovementMemory-Augmented Agents
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Jul 15, 2026

Cura 1T: Healthcare Foundation Model via Recursive Self-Improvement

Healthcare spans high-stakes communication, expert reasoning, and workflow execution, yet specialized language models that cover these use cases together remain limited. A healthcare model must handle patient consultation, clinical reasoning over text and images, interactive diagnosis, and electronic health record (EHR) tool use. These capabilities fail in different ways, and a narrow update for one task can degrade another. We present Cura 1T, a healthcare foundation model trained through recursive self-improvement (RSI). In each RSI round, the RSI harness runs the current model on healthcare benchmarks, evaluates the trajectories to locate capability gaps, and refines the training mixture by synthesizing training data. On 6 healthcare benchmarks, Cura 1T scores highest on MedAgentBench, HealthBench Professional, HealthBench Hard, MedXpertQA text, and AgentClinic, and second on MedXpertQA multimodal. It preserves performances on out-of-domain reasoning and agentic benchmarks including AIME, GPQA-Diamond, and τ2τ^2-Bench.

Haolin Chen, Leon Qi, Steve Brown +7

actAVA AI Team

Medical VLMsLLM Agent TrainingLanguage Model Self-ImprovementMedical LLMsRecursive Self-Improvement
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Jul 8, 2026

Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops

AI systems increasingly participate in their own improvement: revising their outputs, adapting their own harnesses during deployment, training on data they generate, and, increasingly, conducting AI research itself. This literature is described under a vocabulary ("self-refine," "self-reward," "self-play," "self-evolve") that conflates fundamentally different ambitions. We survey 1,250 arXiv papers (2024-2026) along two axes: what the system improves -- its behavior in deployment, its policy through training, its evaluator, or the research process itself -- and the degree of loop closure (human-in-the-loop to fully closed). The taxonomy separates bounded self-refinement -- convergent, evaluable, and already industrial practice -- from open-ended recursive self-improvement (RSI), which remains bounded by grounding requirements, collapse dynamics, and compute constraints on every measured axis. Its distinctive feature is a dedicated category for self-evaluation: every improvement loop is a claim that some signal can substitute for human judgment. We survey the evaluator design space -- judges, process reward models, verifiers, rubrics, meta-evaluation -- order the signals into a verification hierarchy from formal verifiers (strongest) to intrinsic self-assessment (weakest), and observe that demonstrated self-improvement strength tracks this hierarchy, that its failure modes (self-confirming loops, model collapse, diversity collapse) follow from its violations, and that the "research direction-setting" bottleneck keeping humans in the loop sits at the top of that hierarchy. We connect the technical literature to the theory of RSI limits and to the safety and governance questions raised by frontier-lab accounts of closing the loop, and identify governance-grade measurement of self-improvement as the field's most underpopulated niche.

Mingguang Chen, Licheng Wang, Bo Qu

University of California, Riverside (UCR) · AlphaAvatar · Illinois Institute of Technology (IIT)

LLM Self-RefinementHuman-in-the-Loop EvaluationSelf-Improving AgentsLanguage Model Self-ImprovementRecursive Self-ImprovementAutonomous Research Agents
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Jul 6, 2026

MetaSkill-Evolve: Recursive Self-Improvement of LLM Agents via Two-Timescale Meta-Skill Evolution

Recent LLM agents tackle increasingly long-horizon, open-ended tasks, and external skills, reusable procedural knowledge supplied to the agent, further extend this capability. However, a fixed, hand-authored skill is rarely optimal, and cannot adapt to the diversity of tasks an agent encounters. Self-improving agents address this by rewriting their own skill files from execution traces, yielding meaningful gains on challenging benchmarks. Yet such self-evolution remains non-recursive: it improves only the task skill (what the agent does) while the improvement procedure (how it improves) is authored once and held fixed. We introduce MetaSkill-Evolve, a two-timescale framework that makes agentic skill improvement recursive: every branch carries both a task skill ss and a branch-local meta-skill m=(ψ,σ,α,π,ε)m=(ψ,σ,α,π,\varepsilon) whose five components parameterise the Analyzer, Retriever, Allocator, Proposer, and Evolver agents of the improvement pipeline. Task skills evolve on a fast loop while the meta-skill evolves on a slower one under the same pipeline applied to itself, with no additional model or objective. With all five pipeline agents sharing a single frozen backbone, MetaSkill-Evolve outperforms no-skill, static-skill, and single-level evolution baselines on three agentic benchmarks (OfficeQA, SealQA, ALFWorld), improving held-out test accuracy over the raw backbone by +23.54, +16.09, and +1.92 points respectively.

Zefeng Wang, Minxi Yan, Jinhe Bi +3

LMU Munich · The Chinese University of Hong Kong · MCML +1

LLM Agent Self-ImprovementLLM Agent Skill LearningRecursive Self-Improvement
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Jul 5, 2026

Self-Reference in Large Language Models: The Introspection Threshold for Recursive Self-Improvement

The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann's complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in Large Language Models (LLMs) requires a functional analogue: introspection -- the system's capacity to simulate its own operations and target modifications. Grounded in Kleene's Second Recursion Theorem, we demonstrate the theoretical existence of such introspective programs. However, an empirical review reveals that while current LLMs exhibit quasi-introspection (e.g., partial metacognition), they fall short of true introspection due to structural bottlenecks: a lack of complete self-access, the feedforward nature of the Transformer, and computational class constraints that prevent fixed-point iteration. We conclude by outlining architectural paths to cross this complexity threshold and discussing the associated safety implications.

Jiang Zhang, Bing Yuan, Qian Zhang

School of Systems Science, Beijing Normal University · Swarma Research

Language Model IntrospectionLanguage Model Self-ImprovementRecursive Self-ImprovementMetacognition in Language Models
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Jun 26, 2026

Algorithmic Unverifiability of Safety for Fixed and Recursively Self-Improving Systems

Existing impossibility results for AI verification concern a fixed system. Self-modifying systems (agents that rewrite their own code, recursive self-improvement loops) raise a different question: can a safety property that holds now be certified, in advance, to keep holding after the system rewrites itself? We model one step of self-modification as a total computable transformation of code, and preservation as 'safe now and safe after the step'. If the transformation depends only on behaviour, preservation is Rice's theorem one level up; if it reads the code, as self-modification does, preservation is no longer semantic, yet at least as hard as the halting problem, by the same s-m-n reduction carried out inside a class of behaviourally identical programs. One step is never harder than the property; persistence along the whole trajectory can be one arithmetical level higher. No tower of supervisors lowers the problem; every total supervisor errs on a set of systems it cannot locate. Every faithful scheme certifying on finite behavioural evidence admits, for properties not settled by any finite set of inputs, an evolution trace it certifies at every stage while the property is violated. Statically, we record the classical limits (Rice, Goedel, Trakhtenbrot) and add the resource face: over succinctly described finite environments, verifying a policy against an adversary is coNP-complete and synthesising one PSPACE-complete. These limits do not say self-modifying systems are unsafe; they locate where algorithmic guarantees break, at the expressivity a general system needs: Turing-completeness and unrestricted self-modification. What survives is exact: a monitor detects the first violation of a safety property, and no sound procedure certifies all safe systems; certification requires restricting rewrites by design; and a frozen reference keeps the question well posed.

Jose Pascual Gumbau Mezquita

Universitat Jaume I, Castelló de la Plana, Spain

Formal VerificationSelf-Improving AgentsAI SafetyRecursive Self-Improvement
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Jun 24, 2026

The Red Queen Gödel Machine: Co-Evolving Agents and Their Evaluators

Self-improving agents are state-of-the-art on agentic coding benchmarks, yet their search methods assume a stationary evaluation criterion. This ignores a central feature of evolution: species adapt as their environments change with them. We introduce the Red Queen Gödel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. This allows learned evaluators to improve alongside the agents they guide. On DeepSWE, the RQGM improves over its fixed-evaluator baseline by adding a complementary agent-as-a-judge code-review signal: a co-evolved reviewer grades coder patches to guide search. At low reasoning effort, the RQGM coder passes 82.1% of held-out tasks against the baseline's 75.0%, and nearly matches the GPT-6 Astra model at high effort. In scientific paper writing and reviewing, and Olympiad-level proof writing and grading, co-evolved evaluators provide an evaluation criterion. Anchored to human IMO grades, a co-evolved grader writes its own milestone rubric and exceeds static baselines at a 3x lower search cost, driving the prover to the best mean score. Since the RQGM can modify the search objective across epochs, it can regularize the search. For example, the RQGM reduces self-preference bias via an additional adversarial objective to discover reviewers equally stringent on AI and human work. Guided by these calibrated reviewers, co-evolved writers reach 1.78x-1.86x higher acceptance rates than the baseline under an agent-as-a-judge panel. The RQGM enables self-improving systems where agents and evaluators recursively bootstrap each other beyond static evaluation.

Alex Iacob, Andrej Jovanović, William F. Shen +12

University of Cambridge · Flower Labs · NVIDIA +2

Evolutionary OptimizationAI Agent EvaluationSelf-Improving AgentsAutomated Peer ReviewRecursive Self-Improvement
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Jun 17, 2026

Recursive Self-Evolving Agents via Held-Out Selection

LLM agents are increasingly improved without weight updates by evolving a natural-language artifact, such as reflections, workflows, playbooks, cheatsheets, or optimized prompts, that conditions a frozen policy. Such methods are typically reported as wins on the single benchmark where they help. We study them apples-to-apples and surface a sharper picture. We introduce RSEA, a Recursive Self-Evolving Agent that carries a compact three-layer natural-language state: an imperative strategy, reusable skills, and a procedural playbook. Across generations, RSEA rewrites all three layers from its own trajectories and commits a candidate only if it does not regress on a disjoint held-out split, using a strict keep-better gate. Across four diverse benchmarks, ALFWorld, GAIA, (τ)-bench, and WebShop, and six faithful baselines, ReAct, Reflexion, GEPA, AWM, ACE, and Dynamic Cheatsheet, all evaluated on one shared local backbone, we find three main results. First, no artifact universally wins. RSEA is the strongest single-pass method on ALFWorld, reaching 69.3% compared with 64.6% for ReAct (McNemar (p=0.015)), and reaches 79.4% with retry, the best overall result. However, concrete-workflow induction, represented by AWM, is best on the strong-backbone tool-use tasks. Second, unguarded context evolution is high-variance and unsafe. Dynamic Cheatsheet, which curates context online without a held-out gate, is near-best on ALFWorld at 70.7%, yet collapses on WebShop, with a score of 0.14 compared with 0.43 for ReAct. Third, RSEA's strict held-out selection is what makes recursive self-evolution monotone-safe: it never significantly underperforms the base agent on any benchmark and falls back to vanilla ReAct when evolved context would hurt.

Michael Nguyen, Quoc Nguyen, Paul Vuong

School of Information Technology Monash University Malaysia

LLM Agent EvaluationLLM Agent Workflow OptimizationLLM Agent Self-ImprovementRecursive Self-ImprovementSelf-Evolving Agents
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Jun 10, 2026

From AGI to ASI

Over the last decade, building human-level artificial general intelligence has moved from far-fetched speculation to being a concrete next-decade target for many of the largest AI organisations. Achieving this goal would have profound and far-reaching impacts on human society, which raises many complex questions for the decade ahead. This report investigates how AI itself might continue to develop in a post-AGI world along the continuum of machine intelligence. The endpoint of this continuum, Universal AI, is theoretically well understood, which provides some formal grounding for the main focus of this report: the transition from human-level AGI to artificial general superintelligence, which can intuitively be understood as a system that is more intelligent and cognitively capable than large organisations of humans. After characterizing ASI, the report discusses four potential pathways from AGI to ASI: scaling AGI, AI paradigm shifts, recursive improvement, and ASI emerging from large-scale multi-agent collectives. The report then discusses possible frictions and bottlenecks along these pathways. Determining whether the impact of these frictions will be negligible or substantial raises a number of concrete open research questions. Due to large uncertainties for predicting ASI progress, it cannot be ruled out that AI progress might continue to accelerate over the next years. This could imply that the image of a single transformative step change, caused by the introduction of human-level AGI into our society, could be inaccurate. More apt might be the prospect of a series of transformative societal changes caused by AI-enabled progress and breakthroughs across many areas of science and technology. Preparing for this prospect requires a massively interdisciplinary endeavour of global scope and interest.

Tim Genewein, Matija Franklin, Alexander Lerchner +11

Google DeepMind · University of Waterloo (work conducted while at Google DeepMind) · Australian National University +1

Self-Improving AgentsRecursive Self-ImprovementArtificial General Intelligence
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Jun 8, 2026

From 0-to-1 to 1-to-N: Reproducible Engineering Evidence for MetaAI Recursive Self-Design

Recursive self-design refers to AI-assisted modification of the mechanisms by which an AI system is built, evaluated, and improved. This paper treats MetaAI not as a mature paradigm, but as a working term for a human-seeded, AI-expanded development pattern in which the design space itself becomes a target of modification. We propose an operational evidence framework with four criteria: inspectable target system, meta-level modifier, feedback-directed selection, and recursive continuation. We then map public systems, including Darwin Goedel Machine (DGM), STOP, Goedel Agent, and ShinkaEvolve, against these criteria. DGM provides the most direct currently reported evidence: its published results show improvement from 20% to 50% on SWE-bench Verified and from 14.2% to 30.7% on full Polyglot after 80 iterations, with ablations suggesting that both open-ended exploration and self-improvement contribute. Finally, we provide MetaAI-Mini, a reproducible HumanEval-based protocol and codebase. Because no completed model run is included in this build, MetaAI-Mini is reported as a protocol rather than as an experimental result.

Dun Li, Jiatao Li, Hongzhi Li

Department of Computing, The Hong Kong Polytechnic University, Hong Kong SAR, China · Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China · College of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247100, China

LLM Agent Self-ImprovementSelf-Improving AgentsRecursive Self-ImprovementSelf-Evolving Agents
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Apr 9, 2026

A Relative-Computability Theory of Self-Improving Agents

Agents increasingly modify the procedures by which they solve tasks and improve themselves. Autonomy over improvement, gains in practical capability, and enlargement of computational reach are distinct properties. We develop an oracle-relative model with mutable solvers, evaluators, and improvers. Uniform simulation keeps every total decision procedure produced by effective self-revision over AA within C(A)={D:D≤TA}\mathcal{C}(A)=\{D:D\leq_T A\}; oracle joins account for additional access, while the relativized limit lemma separates limiting answers from effective completion. A worked model of Boolean rule acquisition makes the distinction constructive. For a known finite-dimensional feature language, we characterize exactly which answers a query history determines, obtain a sharp teacher-query bound, and give a terminating protocol that permits revisions to the query proposer. The learned solver can dispense with the teacher on every input while remaining in the same computability layer. However, uniformly constructing the required feature-span specification from arbitrary effective feature programs is already as hard as the relative halting problem. We also give a conditional criterion for strict ascent and distinguish it from finite behavioral evidence. The framework thus separates acquisition, certification, and computability ascent, identifying both a positive route to verified support removal and the assumptions on which it depends.

Chien-Ping Lu

Self-Improving AgentsRecursive Self-Improvement
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Mar 29, 2026

What Does a System Modify When It Modifies Itself?

When a cognitive system modifies its own functioning, what exactly does it modify: a low-level rule, a control rule, or the criterion that evaluates its revisions? Cognitive science describes executive control, metacognition, and hierarchical learning, while artificial intelligence modifies policies, parameters, and learning mechanisms, but the two fields lack common criteria for comparing these transformations. We propose a minimal analytical model distinguishing functional rules Phi_t = {R0, ..., Rk}, modification mechanisms Mt, and evaluation criteria Nt. It separates two independent dimensions: the depth of the modified target and whether the modification is blind or reflexive. Internal representational access AtR and endogenous causal control AtC are further distinguished from external inspectability and modifiability by a designer. Four regimes are defined by the target of modification: action without organizational modification, modification of low-level rules, modification of control rules or mechanisms, and revision of the evaluation criterion. Each is related to cognitive phenomena and artificial systems while making explicit the system boundary on which attribution of endogenous self-modification depends. The comparison yields a conditional crossed-opacities hypothesis: humans often have richer endogenous self-description at abstract and strategic levels than at implementation levels, whereas current artificial systems may be externally inspectable and modifiable at operational levels without corresponding self-representation or endogenous control. The framework also identifies three difficulties - viability, evaluation of revisions to evaluation criteria, and continuity of identity - and proposes two empirical discriminants for identifying the target of a modification and the causal role of self-representation.

Florentin Koch

École Polytechnique, Palaiseau, France

Recursive Self-Improvement
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Mar 24, 2026

A Theory of LLM Information Susceptibility

Large language models (LLMs) are increasingly deployed as optimization modules in agentic systems, yet the fundamental limits of such LLM-mediated improvement remain poorly understood. Here we propose a theory of LLM information susceptibility, centred on the hypothesis that when computational resources are sufficiently large, the intervention of a fixed LLM does not increase the performance susceptibility of a strategy set with respect to budget. We develop a multi-variable utility-function framework that generalizes this hypothesis to architectures with multiple co-varying budget channels, and discuss the conditions under which co-scaling can exceed the susceptibility bound. We validate the theory empirically across structurally diverse domains and model scales spanning an order of magnitude, and show that nested, co-scaling architectures open response channels unavailable to fixed configurations. These results clarify when LLM intervention helps and when it does not, demonstrating that tools from statistical physics can provide predictive constraints for the design of AI systems. If the susceptibility hypothesis holds generally, the theory suggests that nested architectures may be a necessary structural condition for open-ended agentic self-improvement.

Zhuo-Yang Song, Hua Xing Zhu

School of Physics, Peking University, Beijing 100871, China · Center for High Energy Physics, Peking University, Beijing 100871, China

Large Language Model-Guided OptimizationLanguage Model ScalingRecursive Self-Improvement
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Mar 24, 2026

Polaris: A Gödel Agent Framework for Small Language Models through Experience-Abstracted Policy Repair

Gödel agent realize recursive self-improvement: an agent inspects its own policy and traces and then modifies that policy in a tested loop. We introduce Polaris, Gödel agent for compact models that performs policy repair via experience abstraction, turning failures into policy updates through a structured cycle of analysis, strategy formation, abstraction, and minimal code patch repair with conservative checks. Unlike response level self correction or parameter tuning, Polaris makes policy level changes with small, auditable patches that persist in the policy and are reused on unseen instances within each benchmark. As part of the loop, the agent engages in meta reasoning: it explains its errors, proposes concrete revisions to its own policy, and then updates the policy. To enable cumulative policy refinement, we introduce experience abstraction, which distills failures into compact, reusable strategies that transfer to unseen instances. On MGSM, DROP, GPQA, and LitBench (covering arithmetic reasoning, compositional inference, graduate-level problem solving, and creative writing evaluation), a 7-billion-parameter model equipped with Polaris achieves consistent gains over the base policy and competitive baselines.

Aditya Kakade, Vivek Srivastava, Shirish Karande

TCS Research, India

Small Language ModelsSelf-Improving AgentsRecursive Self-Improvement
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Mar 19, 2026

Hyperagents

Self-improving AI systems aim to reduce reliance on human engineering by learning to improve their own learning and problem-solving processes. Existing approaches to self-improvement rely on fixed, handcrafted meta-level mechanisms, fundamentally limiting how fast such systems can improve. The Darwin Gödel Machine (DGM) demonstrates open-ended self-improvement in coding by repeatedly generating and evaluating self-modified variants. Because both evaluation and self-modification are coding tasks, gains in coding ability can translate into gains in self-improvement ability. However, this alignment does not generally hold beyond coding domains. We introduce hyperagents, self-referential agents that integrate a task agent (which solves the target task) and a meta agent (which modifies itself and the task agent) into a single editable program. Crucially, the meta-level modification procedure is itself editable, enabling metacognitive self-modification, improving not only the task-solving behavior, but also the mechanism that generates future improvements. We instantiate this framework by extending DGM to create DGM-Hyperagents (DGM-H), eliminating the assumption of domain-specific alignment between task performance and self-modification skill to potentially support self-accelerating progress on any computable task. Across diverse domains, the DGM-H improves performance over time and outperforms baselines without self-improvement or open-ended exploration, as well as prior self-improving systems. Furthermore, the DGM-H improves the process by which it generates new agents (e.g., persistent memory, performance tracking), and these meta-level improvements transfer across domains and accumulate across runs. DGM-Hyperagents offer a glimpse of open-ended AI systems that do not merely search for better solutions, but continually improve their search for how to improve.

Jenny Zhang, Bingchen Zhao, Wannan Yang +5

University of British Columbia · Vector Institute · University of Edinburgh +4

Self-Improving AgentsRecursive Self-ImprovementSelf-Evolving Agents
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Mar 6, 2026

SAHOO: Safeguarded Alignment for High-Order Optimization Objectives in Recursive Self-Improvement

Recursive self-improvement is moving from theory to practice: modern systems can critique, revise, and evaluate their own outputs, yet iterative self-modification risks subtle alignment drift. We introduce SAHOO, a practical framework to monitor and control drift through three safeguards: (i) the Goal Drift Index (GDI), a learned multi-signal detector combining semantic, lexical, structural, and distributional measures; (ii) constraint preservation checks that enforce safety-critical invariants such as syntactic correctness and non-hallucination; and (iii) regression-risk quantification to flag improvement cycles that undo prior gains. Across 189 tasks in code generation, mathematical reasoning, and truthfulness, SAHOO produces substantial quality gains, including 18.3 percent improvement in code tasks and 16.8 percent in reasoning, while preserving constraints in two domains and maintaining low violations in truthfulness. Thresholds are calibrated on a small validation set of 18 tasks across three cycles. We further map the capability-alignment frontier, showing efficient early improvement cycles but rising alignment costs later and exposing domain-specific tensions such as fluency versus factuality. SAHOO therefore makes alignment preservation during recursive self-improvement measurable, deployable, and systematically validated at scale.

Subramanyam Sahoo, Aman Chadha, Vinija Jain +1

MARS 4.0 Fellowship, Cambridge AI Safety Hub(CAISH), University of Cambridge · AWS Generative AI Innovation Center, Amazon Web Services, USA · Stanford University +2

LLM Safety AlignmentLLM Self-RefinementRecursive Self-Improvement
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Oct 11, 2025

SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification

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.

Xuening Wu, Shenqin Yin, Yanlan Kang +4

Fudan University · University of California, San Diego · Tongji University

Automated Machine LearningSelf-Improving AgentsSequential Hypothesis TestingRecursive Self-Improvement
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