发表机构
Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对满足加性守恒约束的精确支撑生成，揭示了无通信并行与顺序采样在内存需求上的指数-对数差距，并提出了最优选择速率定律，表明在线记忆可替代前置协调。
AI 中文摘要
许多人工智能系统在局部做出决策，即使每个实际输出都必须遵守加性守恒定律，例如恰好选择固定数量的项目。这种约束在统计上可能是不可见的：平衡的固定预算输出的小子集看起来越来越独立，然而无通信的坐标并行生成需要指数级数量的预共享计划，而顺序精确采样器只需要对数级内存。我们研究在中间机制下以加性守恒定律为条件的乘积测度，在该机制中，一个计划在固定顺序遍历之前被选择，每个计划都是一个有界状态随机执行器，其支撑完全合法，并且计划定律的混合在总变差上逼近目标分布。我们的主要结果确定了最优渐近选择器速率，直至常数因子，与守恒差游走的被杀光谱轮廓一致。由此产生的协调成本随活状态宽度呈反幂次下降，其指数由内在守恒秩而非字母表大小决定；该定律扩展到非中心预算和异质局部分数。其逆命题由状态与资源总和之间的障碍驱动，而速率匹配构造将差异控制编译为精确支撑的有限状态计划。补充结果刻画了块并行计划的复杂性以及可编程输出顺序的益处。这些结果共同精确地展示了在线记忆如何在精确支撑生成中替代前置协调。
英文摘要
Many AI systems make decisions locally, even when every realized output must obey an additive conservation law, such as selecting exactly a fixed number of items. This constraint can be statistically invisible: small subsets of a balanced fixed-budget output look increasingly independent, yet communication-free coordinate-parallel generation needs exponentially many pre-shared plans, while a sequential exact sampler needs only logarithmic memory. We study product measures conditioned on additive conservation laws in the intermediate regime where one plan is selected before a fixed-order pass, every plan is a bounded-state stochastic executor whose support is entirely legal, and the mixture of plan laws approximates the target distribution in total variation. Our main result identifies the optimal asymptotic selector rate, up to constant factors, with the killed spectral profile of the conservation-difference walk. The resulting coordination cost decreases as an inverse power of live-state width, with an exponent determined by intrinsic conservation rank rather than alphabet size; the law extends to noncentral budgets and heterogeneous local scores. The converse is driven by a state-versus-resource-sum obstruction, while a rate-matching construction compiles discrepancy control into exact-support finite-state plans. Complementary results characterize block-parallel plan complexity and the benefit of programmable output order. Together, these results show precisely how online memory substitutes for front-loaded coordination in exact-support generation.
