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Meta$^n$: Recursive Self-Improvement through Emergent Depth

NeurIPS 2026 · Multi-agent systems and games › LLM agents · approach: Self-evolving language agent learning · 0 citations (OpenAlex)

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Proposes Meta^n, a framework that applies one fixed meta-operation Ω recursively to its own outputs to build a convergence-sized stack of code-writing meta-layers (pre-process plus helper library), evaluated on eight benchmark families with Gemma 4 31B and GPT-5.2.

Problem

Existing self-improving LLM agents improve answers or hold their improvement mechanism fixed; self-editing systems cap realized meta-depth at roughly 2.5 because a driver layer must stay frozen for stability.

Approach

Keep the meta-operation Ω fixed and recurse on its input: each layer is generated from traces plus the code of all earlier layers, so information grows strictly with depth; layers are composed as wrappers (pre-process context threaded inward plus a merged helper library), and an evolutionary archive searches over layer chains.

Key results

• On CO-Bench with Gemma, archive-best reaches 0.851 ± 0.014 vs OpenEvolve 0.814 ± 0.022 and Gödel Agent 0.451 ± 0.023.
• On ARC-AGI-2 under GPT-5.2, archive-best reaches 0.331 ± 0.010 while OpenEvolve scores 0.003 and Gödel Agent 0.054 (dev score).
• Ablation: removing recursion drops CO-Bench (Gemma) from 0.845 to 0.714; removing inter-layer context accounts for about 72% of the recursion gain.

Surprising findings

• Removing the inter-layer context string explains most of the recursion gain, more than the callable code library.
• AlgoTune: the agentic variant underperforms its single-shot sibling on the seed run, as the extra context over-constrains the pre-optimized kernel.

Limitations

• Same model used at base solver and at every Ω call, so heterogeneous improver/solver setups are untested.
• Gains are small and per-seed ranges overlap on Symptom2Disease; significance not claimed.
• AlgoTune and SWE-Bench show no gain or over-constraint, so benefits depend on headroom above the seed.

Experimental setup

Datasets: CO-Bench Symptom2Disease LawBench AlphaEvolve Math Symbolic Regression AlgoTune ARC-AGI-2 TerminalBench 2.0

Benchmarks: CO-Bench Symptom2Disease LawBench AlphaEvolve Math AlgoTune Symbolic Regression ARC-AGI-2 TerminalBench 2.0

Metrics: mean score archive-best score accuracy F1 speedup

Baselines: OpenEvolve Gödel Agent

Builds on: Self-Refine FunSearch AlphaEvolve OpenEvolve Gödel Agent Darwin Gödel Machine

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