42 lines
1.6 KiB
Markdown
42 lines
1.6 KiB
Markdown
---
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title: "Recursive Self-Optimization"
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type: concept
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tags: []
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---
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## Definition
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递归自我优化是一种通过迭代自我修改构建稳定生成能力的计算框架——系统的目标不是直接产出最优输出，而是在生成器空间（Generator Space）中通过不断的"生成-优化-更新"循环收敛到稳定不动点。
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## Formalization
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给定：
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- $\mathcal{I}$：意图空间（Intention Space）
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- $\mathcal{G} \subseteq \mathcal{P}^{\mathcal{I}}$：生成器空间，每个生成器 $G: \mathcal{I} \to \mathcal{P}$
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- $O: \mathcal{P} \times \Omega \to \mathcal{P}$：优化算子
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- $M: \mathcal{G} \times \mathcal{P} \to \mathcal{G}$：元生成算子
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系统演化：
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```
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P = G(I)
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P* = O(P, Ω)
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G' = M(G, P*)
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```
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自映射 $\Phi: \mathcal{G} \to \mathcal{G}$ 定义为：
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$$\Phi(G) = M\big(G, O(G(I), \Omega)\big)$$
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迭代序列 $G_{n+1} = \Phi(G_n)$。
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## Key Insight
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系统的收敛目标不是某个特定的输出 $P^*$，而是生成器序列 $\{G_n\}$ 的极限行为。当 $\Phi$ 满足收缩性条件时：
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$$G^* = \lim_{n \to \infty} \Phi^n(G_0)$$
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这就是**稳定生成能力**（Stable Generative Capability）。
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## Sources
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- [[a-formalization-of-recursive-self-optimizing-generative-systems]]
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## Connections
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- [[Generator Space]] ← defines_the_space ← [[Recursive Self-Optimization]]
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- [[Fixed-Point Semantics]] ← formalizes_convergence ← [[Recursive Self-Optimization]]
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- [[Self-Improving AI]] ← is_applied_instance ← [[Recursive Self-Optimization]]
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- [[Self-Improving-Skill]] ← concrete_implementation ← [[Recursive Self-Optimization]]
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