揭示大模型推理中能力边界的本质，实现动态可控的性能扩展。
LLM Capability Limits: Static Emergence and Dynamic Boundary Control
- 提出继承性结构能力 $\ ext{D}_\ ext{J}$ 和资源索引有限实现 $\ ext{F}_s$ 模型
- 相同算力下，后续模型仅在凸包保持前驱时才能提升任务表现
- 为长序列任务评估提供信息半径指标，适合系统级模型优化研究者
大模型在推理阶段的能力涌现存在部署边界：额外计算只能实现已由当前信息架构支持的决策。证据、工具、记忆和可执行语义可改变后续计算所继承的类别。本文通过继承性结构能力 $\ ext{D}_\ ext{J}$ 和资源索引有限实现 $\ ext{F}_s(\ ext{J},M)$ 形式化该边界。在固定预算下，定理1给出精确决策表示：后继模型在且仅当其闭凸有限包保留前驱时，才可改进所有有界损失任务。因此，终端能力可扩展，而同预算能力严格下降。同一对象还支持有限切片恢复与开放评估的工作负载尾部信息半径。动态上，贝尔曼值将后继能力类别与其保持的有限策略一并定价。嵌套实现使每个固定资源增量在饱和时消失，从而持久正向后继价值主导该增量。由此理论将涌现转化为边界、兼容性、度量与控制问题。
原文摘要 · Abstract (English)
Test-time emergence in LLM systems has a deployment boundary: additional computation can realize decisions already supported by the deployed information--execution structure, while evidence, tools, memory, and executable semantics can change the class inherited by later computation. We formalize this boundary through inherited structural capability $\mathcal{D}_{\mathcal{J}}$ and resource-indexed finite realization $\mathcal{F}_s(\mathcal{J},M)$. At a common budget, Theorem 1 gives an exact decision representation: a successor improves every bounded-loss task exactly when its closed convex finite envelope retains the predecessor's. Terminal capability can therefore expand while same-budget capability strictly reverses. The same object yields finite-slice recovery and a workload-tail information radius for open-ended evaluation. Dynamically, Bellman value prices the successor capability class together with the finite policies it preserves. Nested realization makes every fixed extra resource increment vanish at saturation, allowing persistent positive successor value to dominate that increment. The resulting theory turns emergence into a boundary, compatibility, measurement, and control problem.
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