Graph neural networks are recognized for their strong performance across various applications, with the backpropagation algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has limitations that challenge its biological plausibility and affect the efficiency, scalability and parallelism of training neural networks for graph-based tasks. While several non-BP training algorithms, such as the direct feedback alignment, have been successfully applied to fully-connected and convolutional network components for handling Euclidean data, directly adapting these non-BP frameworks to manage non-Euclidean graph data in GNN models presents significant challenges. These challenges primarily arise from the violation of the i.i.d. assumption in graph data and the difficulty in accessing prediction errors for all samples (nodes) within the graph. To overcome these obstacles, in this paper we propose DFA-GNN, a novel forward learning framework tailored for GNNs with a case study of semi-supervised learning. The proposed method breaks the limitations of BP by using a dedicated forward training mechanism. Specifically, DFA-GNN extends the principles of DFA to adapt to graph data and unique architecture of GNNs, which incorporates the information of graph topology into the feedback links to accommodate the non-Euclidean characteristics of graph data. Additionally, for semi-supervised graph learning tasks, we developed a pseudo error generator that spreads residual errors from training data to create a pseudo error for each unlabeled node. These pseudo errors are then utilized to train GNNs using DFA. Extensive experiments on 10 public benchmarks reveal that our learning framework outperforms not only previous non-BP methods but also the standard BP methods, and it exhibits excellent robustness against various types of noise and attacks.

翻译：图神经网络因其在各种应用中的卓越性能而受到广泛认可，其中反向传播算法在大多数GNN模型的开发中起着核心作用。然而，尽管BP算法具有高效性，但其存在局限性，这些局限性挑战了其生物合理性，并影响了基于图任务的神经网络在训练效率、可扩展性和并行性方面的表现。虽然直接反馈对齐等非BP训练算法已成功应用于处理欧几里得数据的全连接和卷积网络组件，但将这些非BP框架直接应用于管理GNN模型中的非欧几里得图数据仍面临重大挑战。这些挑战主要源于图数据中独立同分布假设的违背，以及难以获取图中所有样本（节点）的预测误差。为克服这些障碍，本文提出DFA-GNN——一种专为GNN设计的新型前向学习框架，并以半监督学习为例进行案例研究。该方法通过采用专门的前向训练机制，突破了BP算法的限制。具体而言，DFA-GNN扩展了DFA原理以适应图数据及GNN的独特架构，将图拓扑信息融入反馈链路以适配图数据的非欧几里得特性。此外，针对半监督图学习任务，我们开发了一种伪误差生成器，通过传播训练数据的残差误差为每个未标记节点生成伪误差。这些伪误差随后被用于基于DFA的GNN训练。在10个公开基准数据集上的大量实验表明，我们的学习框架不仅超越了先前的非BP方法，也优于标准BP方法，并且对各类噪声与攻击表现出卓越的鲁棒性。