发表机构
McGill University; Arizona State University; BosonLabs（麦吉尔大学; 亚利桑那州立大学; 玻色实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究固定删除策略诱导的排列目标何时具有更简单结构，识别位置可加性与后缀局部化两种独立归约，并改进近似率，实验验证结构可预测未见排序。
AI 中文摘要
给定一组固定的待处理删除请求，在每次请求后从头重新训练代价高昂，因此一种预设的逐请求策略会顺序处理它们。最终模型可能依赖于请求的顺序。我们不预设排序规则，而是研究由固定策略诱导的排列目标，并询问它何时具有更简单的结构。我们识别出两种独立的归约：位置可加性将目标表示为请求-位置成本，将优化简化为分配问题，并且在共享位置分布下简化为排序；后缀局部化则消除对远处前缀的依赖，同时保留幸存请求之间的交互。在共享仿射更新下，我们刻画了阻碍可加性的二次交互，证明了这两种归约的独立性，并表明后缀条件分配将近似率从O(p^L)改进到O(p^(2L))。实验在执行的策略目标中恢复了这两种结构。受控的阻尼牛顿扫描显示，更强的收缩将目标转向更短、更依赖后缀的依赖关系，而两种全网络策略表现出不同的位置和后缀内部结构。从紧凑执行集识别的结构也能预测未见过的排序。这些结果将删除排序框架化为识别由执行更新诱导的计算结构。
英文摘要
Given a fixed set of pending deletion requests, retraining from scratch after each request is prohibitive, so a prescribed request-wise policy processes them sequentially. The resulting terminal model can depend on their order. Rather than prescribing an ordering rule, we study the permutation objective induced by the fixed policy and ask when it admits simpler structure. We identify two independent reductions: position additivity represents the objective by request--position costs, reducing optimization to assignment and, with a shared positional profile, sorting; suffix localization removes dependence on the distant prefix while retaining interactions among the surviving requests. Under shared affine updates, we characterize the quadratic interactions that obstruct additivity, prove the reductions' independence, and show that suffix-conditioned assignment improves the approximation rate from O(p^L) toO(p^(2L)). Experiments recover both structures in executed objectives. A controlled damped-Newton sweep shows that stronger contraction shifts the objective toward shorter, more suffix-specific dependence, while two full-network policies exhibit distinct positional and within-suffix structure. Structures identified from compact execution sets also predict unseen orders. These results frame deletion ordering as identifying the computational structure induced by the executed updates.
