Recently, graph prompt learning has garnered increasing attention in adapting pre-trained GNN models for downstream graph learning tasks. However, existing works generally conduct prompting over all graph elements (e.g., nodes, edges, node attributes, etc.), which is suboptimal and obviously redundant. To address this issue, we propose exploiting sparse representation theory for graph prompting and present Graph Sparse Prompting (GSP). GSP aims to adaptively and sparsely select the optimal elements (e.g., certain node attributes) to achieve compact prompting for downstream tasks. Specifically, we propose two kinds of GSP models, termed Graph Sparse Feature Prompting (GSFP) and Graph Sparse multi-Feature Prompting (GSmFP). Both GSFP and GSmFP provide a general scheme for tuning any specific pre-trained GNNs that can select some desired attributes for prompting by employing sparsity-guided prompt learning. A simple yet effective algorithm has been designed for solving GSFP and GSmFP models. Experiments on 16 widely-used benchmark datasets validate the effectiveness and advantages of the proposed GSFPs.

Multi-modal object Re-IDentification (ReID) has gained considerable attention with the goal of retrieving specific targets across cameras using heterogeneous visual data sources. At present, multi-modal object ReID faces two core challenges: (1) learning robust features under fine-grained local noise caused by occlusion, frame loss, and other disruptions; and (2) effectively integrating heterogeneous modalities to enhance multi-modal representation. To address the above challenges, we propose a robust approach named Uncertainty-Guided Graph model for multi-modal object ReID (UGG-ReID). UGG-ReID is designed to mitigate noise interference and facilitate effective multi-modal fusion by estimating both local and sample-level aleatoric uncertainty and explicitly modeling their dependencies. Specifically, we first propose the Gaussian patch-graph representation model that leverages uncertainty to quantify fine-grained local cues and capture their structural relationships. This process boosts the expressiveness of modal-specific information, ensuring that the generated embeddings are both more informative and robust. Subsequently, we design an uncertainty-guided mixture of experts strategy that dynamically routes samples to experts exhibiting low uncertainty. This strategy effectively suppresses noise-induced instability, leading to enhanced robustness. Meanwhile, we design an uncertainty-guided routing to strengthen the multi-modal interaction, improving the performance. UGG-ReID is comprehensively evaluated on five representative multi-modal object ReID datasets, encompassing diverse spectral modalities. Experimental results show that the proposed method achieves excellent performance on all datasets and is significantly better than current methods in terms of noise immunity. Our code is available at https://github.com/wanxixi11/UGG-ReID.

Existing Graph Attention Networks (GATs) generally adopt the self-attention mechanism to learn graph edge attention, which usually return dense attention coefficients over all neighbors and thus are prone to be sensitive to graph edge noises. To overcome this problem, sparse GATs are desirable and have garnered increasing interest in recent years. However, existing sparse GATs usually suffer from high training complexity and are also not straightforward for inductive learning tasks. To address these issues, we propose to learn sparse GATs by exploiting spiking neuron (SN) mechanism, termed Graph Spiking Attention (GSAT). Specifically, it is known that spiking neuron can perform inexpensive information processing by transmitting the input data into discrete spike trains and return sparse outputs. Inspired by it, this work attempts to exploit spiking neuron to learn sparse attention coefficients, resulting in edge-sparsified graph for GNNs. Therefore, GSAT can perform message passing on the selective neighbors naturally, which makes GSAT perform compactly and robustly w.r.t graph noises. Moreover, GSAT can be used straightforwardly for inductive learning tasks. Extensive experiments on both transductive and inductive tasks demonstrate the effectiveness, robustness and efficiency of GSAT.

Graph Attention (GA) which aims to learn the attention coefficients for graph edges has achieved impressive performance in GNNs on many graph learning tasks. However, existing GAs are usually learned based on edges' (or connected nodes') features which fail to fully capture the rich structural information of edges. Some recent research attempts to incorporate the structural information into GA learning but how to fully exploit them in GA learning is still a challenging problem. To address this challenge, in this work, we propose to leverage a new Replicator Dynamics model for graph attention learning, termed Graph Replicator Attention (GRA). The core of GRA is our derivation of replicator dynamics based sparse attention diffusion which can explicitly learn context-aware and sparse preserved graph attentions via a simple self-supervised way. Moreover, GRA can be theoretically explained from an energy minimization model. This provides a more theoretical justification for the proposed GRA method. Experiments on several graph learning tasks demonstrate the effectiveness and advantages of the proposed GRA method on ten benchmark datasets.

Graph convolutional networks (GCNs) have been widely studied to address graph data representation and learning. In contrast to traditional convolutional neural networks (CNNs) that employ many various (spatial) convolution filters to obtain rich feature descriptors to encode complex patterns of image data, GCNs, however, are defined on the input observed graph G(X,A) and usually adopt the single fixed spatial convolution filter for graph data feature extraction. This limits the capacity of the existing GCNs to encode the complex patterns of graph data. To overcome this issue, inspired by depthwise separable convolution and DropEdge operation, we first propose to generate various graph convolution filters by randomly dropping out some edges from the input graph A . Then, we propose a novel graph-dropping convolution layer (GDCLayer) to produce rich feature descriptors for graph data. Using GDCLayer, we finally design a new end-to-end network architecture, that is, a graph-dropping convolutional network (GDCNet), for graph data learning. Experiments on several datasets demonstrate the effectiveness of the proposed GDCNet.

Existing GNNs usually conduct the layer-wise message propagation via the 'full' aggregation of all neighborhood information which are usually sensitive to the structural noises existed in the graphs, such as incorrect or undesired redundant edge connections. To overcome this issue, we propose to exploit Sparse Representation (SR) theory into GNNs and propose Graph Sparse Neural Networks (GSNNs) which conduct sparse aggregation to select reliable neighbors for message aggregation. GSNNs problem contains discrete/sparse constraint which is difficult to be optimized. Thus, we then develop a tight continuous relaxation model Exclusive Group Lasso GNNs (EGLassoGNNs) for GSNNs. An effective algorithm is derived to optimize the proposed EGLassoGNNs model. Experimental results on several benchmark datasets demonstrate the better performance and robustness of the proposed EGLassoGNNs model.

The main aspect powering GNNs is the multi-layer network architecture to learn the nonlinear representation for graph learning task. The core operation in GNNs is the message propagation in which each node updates its information by aggregating the information from its neighbors. Existing GNNs usually adopt either linear neighborhood aggregation (e.g. mean, sum) or max aggregator in their message propagation. 1) For linear aggregators, the whole nonlinearity and network's capacity of GNNs are generally limited because deeper GNNs usually suffer from the over-smoothing issue due to their inherent information propagation mechanism. Also, linear aggregators are usually vulnerable to the spatial perturbations. 2) For max aggregator, it usually fails to be aware of the detailed information of node representations within neighborhood. To overcome these issues, we re-think the message propagation mechanism in GNNs and develop the new general nonlinear aggregators for neighborhood information aggregation in GNNs. One main aspect of our nonlinear aggregators is that they all provide the optimally balanced aggregator between max and mean/sum aggregators. Thus, they can inherit both i) high nonlinearity that enhances network's capacity, robustness and ii) detail-sensitivity that is aware of the detailed information of node representations in GNNs' message propagation. Promising experiments show the effectiveness, high capacity and robustness of the proposed methods.

Graph representation and learning is a fundamental problem in machine learning area. Graph Convolutional Networks (GCNs) have been recently studied and demonstrated very powerful for graph representation and learning. Graph convolution (GC) operation in GCNs can be regarded as a composition of feature aggregation and nonlinear transformation step. Existing GCs generally conduct feature aggregation on a full neighborhood set in which each node computes its representation by aggregating the feature information of all its neighbors. However, this full aggregation strategy is not guaranteed to be optimal for GCN learning and also can be affected by some graph structure noises, such as incorrect or undesired edge connections. To address these issues, we propose to integrate elastic net based selection into graph convolution and propose a novel graph elastic convolution (GeC) operation. In GeC, each node can adaptively select the optimal neighbors in its feature aggregation. The key aspect of the proposed GeC operation is that it can be formulated by a regularization framework, based on which we can derive a simple update rule to implement GeC in a self-supervised manner. Using GeC, we then present a novel GeCN for graph learning. Experimental results demonstrate the effectiveness and robustness of GeCN.