AI 中文总结
本文提出几何诱导算子族（GIOF）框架，从固定几何生成传播算子并动态选择，在PEMS-BAY和METR-LA上实现最低MAE，较最强基线提升2.4%-8.8%。
AI 中文摘要
潜在表示的几何结构决定了哪些组件应当交互以及信息应如何传播，这使得几何感知的算子设计成为结构化深度表示学习的基本要素。然而，现有的神经架构通常依赖于通用的算子模板或特定于几何的构造，因此需要一个统一的框架，能够直接从固定的结构信息中推导出可容许的算子，同时保持对变化上下文的适应性。我们引入了几何诱导算子族（GIOF），这是一个通用框架，它将固定的几何转换为结构化的传播算子族，并根据当前上下文动态选择该族中的合适成员。GIOF首先将几何衍生的交互通道转换为可复用的生成器基，然后通过上下文相关的选择器和自适应传播尺度进行组合，最后通过稳定的连续时间传播和瓶颈残差层实现所选算子。我们建立了涵盖参数压缩、可辨识性、稳定性、局部性、组合结构和过平滑行为的理论保证，同时受控实验验证了这些机制，并且在PEMS-BAY和METR-LA上的实验在所有报告的局部缺失设置中取得了最低的平均MAE，在30%传感器缺失的情况下，相比最强保留基线提升了2.4%至8.8%。
英文摘要
The geometry of latent representations governs which components should interact and how information should propagate, making geometry-aware operator design a fundamental ingredient of structured deep representation learning. However, existing neural architectures typically rely on generic operator templates or geometry-specific constructions, creating a need for a unified framework that can derive admissible operators directly from fixed structural information while remaining adaptive to changing contexts. We introduce \emph{Geometry-Induced Operator Families} (GIOF), a general framework that converts fixed geometry into a structured family of propagation operators and dynamically selects an appropriate member of this family according to the current context. GIOF first transforms geometry-derived interaction channels into reusable generator bases, then combines them through a context-dependent selector and adaptive propagation scale, and finally realizes the selected operator through stable continuous-time propagation and a bottleneck residual layer. We establish theoretical guarantees covering parameter compression, identifiability, stability, locality, compositional structure, and oversmoothing behavior, while controlled experiments validate these mechanisms and experiments on PEMS-BAY and METR-LA achieve the lowest mean MAE across all reported regional-outage settings, improving over the strongest retained baseline by 2.4\%--8.8\% at 30\% missing sensors.
