Graph neural networks (GNNs) are recognized for their strong performance across various applications, with the backpropagation (BP) 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-backpropagation (non-BP) training algorithms, such as the direct feedback alignment (DFA), 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 independent and identically distributed (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.

Graph Matching has recently emerged as an attractive technique applied to various computer vision tasks. Graph Matching based multi-label image classification, in particular, treats each image as a bag of instances and reformulates the classification task as an instance-label matching selection problem, achieving state-of-the-art results on diverse benchmarks. However, the generalization and scalability of such learned model cannot be well guaranteed due to its manually predetermined graph structure and high-dimension embedding of dense connections between instances and labels. To address these limitations, in this work, we propose a novel${T}$ransformer Driven${M}$atching${S}$election framework for Multi-Label Image${C}$lassification (C-TMS), where instance structural relationships, class-wise global dependencies, and the co-occurrence possibility of varying instance-label assignments are simultaneously taken into consideration in a unified and adaptive manner. Moreover, the parallelization capability of the Transformer enables efficient computation, making our model scalable to large-scale datasets. Specifically, we first represent instances and labels as nodes in the visual space and label space respectively, and then compute the hidden representation of each node in its individual space, by attending a self-attention strategy over its entire neighborhood. Subsequently, the cross-attention is adopted to excavate the correct assignments between instances and labels, and further interprets how classifying each label depends on the instances within an image and its interaction with other labels. Finally, an asymmetric focal loss is designed to optimize the instance-label correspondence, and read out image-level category confidences. Extensive experiments conducted on various multi-label image datasets demonstrate the superiority of our proposed method.

Graph convolutional networks (GCNs) are widely believed to perform well in the graph node classification task, and homophily assumption plays a core rule in the design of previous GCNs. However, some recent advances on this area have pointed out that homophily may not be a necessity for GCNs. For deeper analysis of the critical factor affecting the performance of GCNs, we first propose a metric, namely, neighborhood class consistency (NCC), to quantitatively characterize the neighborhood patterns of graph datasets. Experiments surprisingly illustrate that our NCC is a better indicator, in comparison to the widely used homophily metrics, to estimate GCN performance for node classification. Furthermore, we propose a topology augmentation graph convolutional network (TA-GCN) framework under the guidance of the NCC metric, which simultaneously learns an augmented graph topology with higher NCC score and a node classifier based on the augmented graph topology. Extensive experiments on six public benchmarks clearly show that the proposed TA-GCN derives ideal topology with higher NCC score given the original graph topology and raw features, and it achieves excellent performance for semi-supervised node classification in comparison to several state-of-the-art (SOTA) baseline algorithms.