Meta^n: Recursive Self-Improvement through Emergent Depth
Summary
This paper introduces Meta^n, a method for recursive self-improvement in LLM agents by applying a fixed meta-operation to expand reasoning depth, outperforming prior approaches on benchmarks like ARC-AGI-2.
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Paper page - Meta^n: Recursive Self-Improvement through Emergent Depth
Source: https://huggingface.co/papers/2608.24735
Abstract
Meta^n recursively applies a fixed meta-operation to growing inputs, building deeper reasoning layers that improve self-improving LLM agents without destabilizing the system.
Self-improving LLM agentsrefine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We presentMeta^n, which keeps themeta-operationfixed and recurses on its input instead. That operation,Ω, is applied repeatedly to its own products, reading the traces of thesolver stackbelow together with the code that produced them, then writing the next layer as astrategic pre-processand a library of callable helpers. BecauseΩnever changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and anevolutionary archivesearches overlayer chains. Across two backbones,Meta^noutperforms prior self-improving agents on all eight benchmark families. The sharpest case isARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain fromrecursioncomes from theconditioningeach layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n
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