Geometry aware operators improve learning with missing sensor data
Geometry-Aware Operator Families for Structured Representation Learning
Machine Learning
Summary
Understanding the shapes and connections in data helps decide how parts of a computer program should share information. Existing methods either use very general tools or tools designed for one specific shape but don’t adapt well to changes. The authors created a new toolset called Geometry-Induced Operator Families that turns fixed shapes into flexible operators that can adjust depending on what’s happening right now. They proved this method is stable and effective, then tested it on traffic sensor data where some sensors were missing, achieving better accuracy than previous methods.
What this means in practice
- •For traffic management teams: Improve traffic prediction accuracy when some traffic sensors fail, by dynamically adapting to sensor data geometry and context.
- •For industrial sensor network operators: Maintain robust monitoring despite missing or faulty sensors by using geometry-aware operator families to better propagate information.
Authors
Zuyuan Zhang, Fei Xu Yu, Tian Lan
Abstract
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.