发表机构
School of Astronomy and Space Science; University of Science and Technology of China（天文与空间科学学院; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出将终端对称性作为定向顺序构造的可复用决策资源，提出“传递—细化—验证”方法，经多任务实验，其状态级刷新提升了 AUC，且在 GRN 场景中验证器成本更低。
AI 中文摘要
许多顺序构造任务在完成时呈现精确对称性，但其执行过程仍具有定向性和历史依赖性。我们提出终端对称性的决策资源视角：过程证据提供定向性，终端对应关系将该结构传递到等效结果，已实现状态的证据在转移后细化其当前决策相关性，固定验证器对执行过程进行验证。这种分解产生了“传递—细化—验证”的框架。\n\nthe method（本方法）将该原则实例化为具有固定传递过程结构的 episode（ episode指任务片段）、其状态受限的过程秩、在接受转移后刷新的状态依赖残差秩，以及一个序秩 meet（ meet指集合的交集），其 top-k 集合恰好是两个提议前缀的并集。该 meet 在前缀覆盖下提供完成保证，并在相应前缀信息模型下达到最紧的最坏情况验证器查询界；双状态构造预测了严格的转移后动态—静态分离。在 CAD 装配、小程序和精确填充打包任务中，状态级刷新将任何时间 AUC 分别提高了多达 6.77、21.75 和 8.68 个百分点。在来自官方 GRN OOD 场景的 1135 个目标移除 episode 上，the method 在所有三个尺度下，在对比的 GRN 和 CDGS 风格规划器中达到了最低的平均 capped 验证器成本。状态级信号还可在聚合和调度器组织之间传递。由此，终端对称性成为定向构造的可复用决策资源。
英文摘要
Many sequential construction tasks have exact terminal symmetries even though execution is directed and depends on history. Process evidence supplies order. Terminal correspondence transports it between equivalent outcomes; the realized state updates relevance. These roles define a carrier framework: transport what the outcome preserves; refine what history changes. SymBuild combines transported process and state residual ranks by ordinal rank meet. Its rank threshold sets equal the corresponding unions, yielding a tight worst-case verifier query bound under prefix information. We evaluate SymBuild in three construction domains: computer-aided design (CAD) assembly, Mini-Programs, and exact-fill packing, and its ordinal adaptation in target removal. SymBuild improves the area under the anytime verified success curve by up to 6.77, 21.75, and 8.68 points over Static in the three construction domains. Refresh gains recur beyond SymBuild under alternative aggregation, planning, and learned scoring methods; on Geometric Reasoning Network (GRN) target removal, direct Combined refresh has the lowest mean verifier query score at all three scales and reduces distinct scored states by factors of 6.48-12.22 relative to refreshed population-based search. Together, these results support the carrier framework and demonstrate that SymBuild is an effective, analyzable method for anytime verified construction.
