Meta^n：經由湧現深度實現的遞迴自我改進

摘要

自我改進的LLM代理會完善答案，而非產生這些答案的過程。加入元層級的系統會將該層級固定不動；自我編輯的系統則必須保留部分自身編輯機制不予更動才能保持穩定，這使其所能達到的元深度上限約為二。我們提出Meta^n，將元操作固定不變，轉而對其輸入進行遞迴。該操作Ω被反覆應用於其自身的產出：讀取下方解算器堆疊的軌跡及產生這些軌跡的程式碼，然後將下一層撰寫為策略性前置處理程序與可呼叫的輔助函式庫。由於Ω從不改變，系統不會因此失去穩定性；又因輸入嚴格遞增，每一層都比前一層立於更高的視角進行推理。深度由收斂決定而非事先固定，且演化式存檔會對層級鏈進行搜尋。在兩個主幹模型上，Meta^n在全部八個基準測試家族中皆優於先前的自我改進代理。最突出的案例是ARC-AGI-2——該基準專為抵抗技能記憶而設計——Meta^n是其中唯一得分高於零的方法。消融實驗顯示，遞迴帶來的大部分增益源於每一層傳遞至下一層的條件設定，且儘管沒有任何提示加以規定，不同層級的角色仍會隨深度而湧現。程式碼見 https://github.com/minnesotanlp/meta-n

English

Self-improving LLM agents refine 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 present Meta^n, which keeps the meta-operation fixed and recurses on its input instead. That operation, Ω, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because Ω never 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 an evolutionary archive searches over layer chains. Across two backbones, Meta^n outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each 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