AI 中文总结
该研究形式化了语言为核心的智能的限制，提出动态边界控制框架，通过DeepSeek V4-Flash实验验证其可提升大语言模型的推理性能，组织了大语言模型的涌现限制。
AI 中文摘要
以语言为核心的智能受限于其符号记录所纳入的区分项、语言-解释器-环境复合体可执行的映射，以及有限资源下可实现的可能性。我们通过有效接口φ、可执行支持Π_{φ,H}、实现轮廓M和资源索引族F_s(J,M)对这些限制进行形式化，它们诱导出四个嵌套的能力层级：当前可达性、预算可实现性、渐近可实现性和结构能力，每个层级均有字面形式和风险等价形式。在有限任务空间中，通用有界损失优势由闭凸化风险包络的包含性表征；定向缺陷和资源变换量化近似模拟与实现负担。分解R^*_{s,J,M}=R^*_J+C_s(J,M)将结构限制与有限资源补偿缺口分离。我们开发了对这些边界的动态控制：目标风险识别出必须改变的最低能力层级；奥卡姆式控制在继承的结构可能性内运作；查顿式包容控制可产生超出继承决策类的终点结构新颖性；结构内计算的收益递减与持续的结构丰富价值形成切换阈值，切换成本则产生滞后性。匹配DeepSeek V4-Flash的实验证据显示：思维使指针追踪从0/16提升至14/16，精确观测与记忆孪生体维持在0.5的基线，恢复决定性记忆将性能从0.5提升至1.0，可执行支持决定推理能否生效。该框架通过结构能力、有限可实现性、边界控制和递归元控制组织了大语言模型的涌现限制。
英文摘要
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.
