  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.
