We propose a framework for the definition of neural models for graphs that do not rely on backpropagation for training, thus making learning more biologically plausible and amenable to parallel implementation. Our proposed framework is inspired by Gated Linear Networks and allows the adoption of multiple graph convolutions. Specifically, each neuron is defined as a set of graph convolution filters (weight vectors) and a gating mechanism that, given a node and its topological context, generates the weight vector to use for processing the node’s attributes. Two different graph processing schemes are studied, i.e., a message-passing aggregation scheme where the gating mechanism is embedded directly into the graph convolution, and a multi-resolution one where neighboring nodes at different topological distances are jointly processed by a single graph convolution layer. We also compare the effectiveness of different alternatives for defining the context function of a node, i.e., based on hyperplanes or on prototypes, and using a soft or hard-gating mechanism. We propose a unified theoretical framework allowing us to theoretically characterize the proposed models’ expressiveness. We experimentally evaluate our backpropagation-free graph convolutional neural models on commonly adopted node classification datasets and show competitive performances compared to the backpropagation-based counterparts.

我们提出了一个用于定义图神经模型的框架，该框架不依赖于反向传播进行训练，从而使学习在生物学上更加合理并且适合并行实现。我们提出的框架受到门控线性网络的启发，并允许采用多个图卷积。具体来说，每个神经元被定义为一组图卷积滤波器（权重向量）和一个门控机制，给定节点及其拓扑上下文，生成权重向量以用于处理节点的属性。研究了两种不同的图处理方案，即一种消息传递聚合方案，其中门控机制直接嵌入到图卷积中，另一种是多分辨率方案，其中不同拓扑距离的相邻节点由单个图卷积层联合处理。我们还比较了定义节点上下文函数的不同替代方案的有效性，即基于超平面或原型，并使用软门控或硬门控机制。我们提出了一个统一的理论框架，使我们能够从理论上描述所提出模型的表达能力。我们在常用的节点分类数据集上通过实验评估了我们的无反向传播图卷积神经模型，并显示出与基于反向传播的模型相比具有竞争力的性能。