提出直接在多输入多输出场景下近似图卷积的新方法。
What Can We Learn From MIMO Graph Convolutions?
- 直接在多输入多输出框架中推导并近似图卷积
- 证明单计算图下对多重集具有唯一性，多图时表征线性无关
- 可融合多种方法优势，适用于各类图神经网络任务
大多数图神经网络（GNNs）使用基于图傅里叶域的通用图卷积近似。尽管GNN通常应用于多输入多输出（MIMO）场景，但其近似仍基于单输入单输出（SISO）情形。本文首次通过卷积定理推导出MIMO图卷积，并直接在MIMO框架中进行近似。我们发现图卷积的核心MIMO特性在于同时作用于多个计算图，或等价地，为每对节点应用不同的特征变换。作为局部近似，我们提出局部化MIMO图卷积（LMGC），它推广了众多线性消息传递神经网络。对于几乎任意边权选择，我们证明：仅使用一个计算图时，LMGC在多重集上是注入的；当使用多个计算图时，所得表示线性无关。实验结果表明，LMGC能有效结合多种方法的优势。
原文摘要 · Abstract (English)
Most graph neural networks (GNNs) utilize approximations of the general graph convolution derived in the graph Fourier domain. While GNNs are typically applied in the multi-input multi-output (MIMO) case, the approximations are performed in the single-input single-output (SISO) case. In this work, we first derive the MIMO graph convolution through the convolution theorem and approximate it directly in the MIMO case. We find the key MIMO-specific property of the graph convolution to be operating on multiple computational graphs, or equivalently, applying distinct feature transformations for each pair of nodes. As a localized approximation, we introduce localized MIMO graph convolutions (LMGCs), which generalize many linear message-passing neural networks. For almost every choice of edge weights, we prove that LMGCs with a single computational graph are injective on multisets, and the resulting representations are linearly independent when more than one computational graph is used. Our experimental results confirm that an LMGC can combine the benefits of various methods.
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