AI 中文总结
研究层状图神经网络中检查点依赖性与任务级价值，用两个估计量区分相关说法，通过任务零定理和精确框架模型说明差异，经实验验证，表明学习的映射可控制计算但非不可或缺，相关说法应结合检查点干预与重新训练。
AI 中文摘要
层状图神经网络中学习的限制映射常被视为模型发现有用边几何的证据。但该结论不能从参数移动或事后消融得出。我们用两个估计量区分这些说法。检查点依赖性干预固定预测器的映射；协议相关替换重新训练去除映射能力、边变化或持久边分配的匹配族。任务零定理表明了这些说法为何会不同。精确框架模型给出了依赖性变为不可替代任务价值的边界。仅标签训练实现了预测的分离，对公共NSD、DNSD和定向层状神经网络实现的审计恢复了真实图上可替换和不可替换的传输机制。所有五个DNSD基准都表现出固定检查点依赖性。重新训练后，破坏分配或共享映射控制在四个上恢复了全部性能；在十个官方划分中，罗马帝国相对于连续重新采样分配保留了0.0675的优势，相对于参数匹配的共享映射保留了0.0391的优势。因此，学习的映射可以控制拟合计算而不构成不可或缺的边几何。关于学习传输的说法应将检查点干预与匹配的重新训练结合起来。
英文摘要
Learned restriction maps in sheaf graph neural networks are often treated as proof that the model has discovered useful edge geometry. That conclusion does not follow from parameter movement or from a post-hoc ablation: both can show how one checkpoint is organized while leaving open whether learned transport still helps after the rest of the model adapts. We separate these claims with two estimands. Checkpoint reliance intervenes on the maps of a fixed predictor; protocol-relative replacement retrains matched families that remove map capacity, edge variation, or persistent edge assignment. A task-null theorem shows why the claims can diverge: labels identify only the transported classifier directions, leaving $d^2-d$ invisible degrees of freedom in every full $d\times d$ map. An exact frame model then gives the boundary at which reliance becomes unreplaced task value. Label-only training realizes the predicted separation, while audits of public NSD, DNSD, and Directed Sheaf Neural Network (DSNN) implementations recover both replaceable and unreplaced transport regimes on real graphs. All five DNSD benchmarks exhibit fixed-checkpoint reliance. After retraining, assignment-breaking or shared-map controls recover Full performance on four; Roman-Empire retains a $.0675$ advantage over continually resampled assignment and a $.0391$ advantage over a parameter-matched shared map across ten official splits. Thus, a learned map can govern a fitted computation without constituting indispensable edge geometry. Claims of learned transport should pair checkpoint interventions with matched retraining.
Comments23 pages, 4 figures
