层神经网络是否使用和乐性？一项测量-干预-控制研究
Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study
浏览论文内容
中文总结 AI 辅助
以层神经网络为测试平台，对训练后的三角循环积进行与基无关测量，通过神经层传播等方法区分几何变化等，在不同实验设置下观察其效果，研究层神经网络是否使用和乐性及相关特性。
中文摘要 AI 辅助
几何架构通常由诸如旋转等内部机制来解释，但仅任务性能无法表明这些机制是否驱动预测。我们以层神经网络（SNN）为测试平台，首次对训练后的三角循环积进行了与基无关的测量，区分了旋转、茎空间面积和方向。在自定义的高同质性图宇宙机制中，神经层传播（NSP）将三角计数的三角加权平均二维SO(2)循环旋转从0.010弧度提高到0.388弧度，而社区检测比较在0.029弧度时结束。在训练集大小实验中，用恒等替换所有学习到的SO(2)传输会大幅增加测试误差，证明训练后对完整学习连接的敏感性。然而，图摘要岭预测器更准确，对角映射也有改进，固定度图的旋转增加但未超过训练均值预测器。这项测量-干预-控制研究区分了几何变化、连接敏感性和三角特定计算的证据。
英文摘要
Geometric architectures are often motivated by internal mechanisms, but accuracy alone does not show whether predictions use them. In Sheaf Neural Networks (SNNs), edge transports form a connection whose cycle products define holonomy. We ask whether training changes triangle holonomy, whether predictions rely on the learned connection, and whether holonomy drives triangle counting. We use basis-independent loop readouts with identity interventions and shortcut controls. On high-homophily GraphUniverse graphs, triangle counting increases the mean SO(2) triangle rotation in Neural Sheaf Propagation (NSP) from 0.010 to 0.388 radians, while community detection ends at 0.029 radians. With more data, learned SO(2)--NSP outperforms Identity NSP, and replacing its transports after training increases error further. However, ridge regression is more accurate, diagonal maps improve without continuous rotation, and fixed-degree models develop rotation without improved counting. Thus, NSP can learn and rely on a nontrivial connection, but our experiments do not show that triangle holonomy drives its predictions.
发表机构
- KTH Royal Institute of Technology（瑞典皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。
