论文标题
部分可观测时空混沌系统的无模型预测
Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model
论文作者
论文摘要
图形神经网络（GNNS），尤其是图形卷积神经网络（GCNN），已成为机器学习和信号处理中的关键仪器，用于处理图形结构化数据。本文提出了一个分析框架，以研究GCNN对概率图扰动的敏感性，从而直接影响图形移动算子（GSO）。我们的研究建立了紧张的预期GSO误差界，这些误差界限与误差模型参数明确链接，并揭示了GSO扰动与GCNN每一层的产生差异之间的线性关系。这种线性表明，只要GSO误差保持界限，无论扰动量表如何，只要GSO误差保持界限，单层GCNN仍保持稳定性。对于多层GCNN，系统的输出差异对GSO扰动的依赖性被证明是线性的递归。最后，我们用图形同构网络（GIN）和简单的图形卷积网络（SGCN）来体现框架。实验验证了我们的理论推导和方法的有效性。
Graph Neural Networks (GNNs), particularly Graph Convolutional Neural Networks (GCNNs), have emerged as pivotal instruments in machine learning and signal processing for processing graph-structured data. This paper proposes an analysis framework to investigate the sensitivity of GCNNs to probabilistic graph perturbations, directly impacting the graph shift operator (GSO). Our study establishes tight expected GSO error bounds, which are explicitly linked to the error model parameters, and reveals a linear relationship between GSO perturbations and the resulting output differences at each layer of GCNNs. This linearity demonstrates that a single-layer GCNN maintains stability under graph edge perturbations, provided that the GSO errors remain bounded, regardless of the perturbation scale. For multilayer GCNNs, the dependency of system's output difference on GSO perturbations is shown to be a recursion of linearity. Finally, we exemplify the framework with the Graph Isomorphism Network (GIN) and Simple Graph Convolution Network (SGCN). Experiments validate our theoretical derivations and the effectiveness of our approach.
