In critical web applications such as e-commerce and recommendation systems, multimodal graphs integrating rich visual and textual attributes are increasingly central, yet their large scale introduces substantial computational burdens for training Graph Neural Networks (GNNs). While Graph Condensation (GC) offers a promising solution by synthesizing smaller datasets, existing methods falter in the multimodal setting. We identify a dual challenge causing this failure: (1) conflicting gradients arising from semantic misalignments between modalities, and (2) the GNN's message-passing architecture pathologically amplifying this gradient noise across the graph structure. To address this, we propose Structurally-Regularized Gradient Matching (SR-GM), a novel condensation framework tailored for multimodal graphs. SR-GM introduces two synergistic components: first, a gradient decoupling mechanism that resolves inter-modality conflicts at their source via orthogonal projection; and second, a structural damping regularizer that acts directly on the gradient field. By leveraging the graph's Dirichlet energy, this regularizer transforms the topology from a noise amplifier into a stabilizing force during optimization. Extensive experiments demonstrate that SR-GM significantly improves accuracy and accelerates convergence compared to baseline methods. Ablation studies confirm that addressing both gradient conflict and structural amplification in tandem is essential for achieving superior performance. Moreover, the condensed multimodal graphs exhibit strong cross-architecture generalization and promise to accelerate applications like Neural Architecture Search. This research provides a scalable methodology for multimodal graph-based learning in resource-constrained environments.

Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such cases, we observe that the performance of GC deteriorates significantly, while existing robust graph learning technologies offer only limited effectiveness. Through both empirical investigation and theoretical analysis, we reveal that GC is inherently an intrinsic-dimension-reducing process, synthesizing a condensed graph with lower classification complexity. Although this property is critical for effective GC performance, it remains highly vulnerable to adversarial perturbations. To tackle this vulnerability and improve GC robustness, we adopt the geometry perspective of graph data manifold and propose a novel Manifold-constrained Robust Graph Condensation framework named MRGC. Specifically, we introduce three graph data manifold learning modules that guide the condensed graph to lie within a smooth, low-dimensional manifold with minimal class ambiguity, thereby preserving the classification complexity reduction capability of GC and ensuring robust performance under universal adversarial attacks. Extensive experiments demonstrate the robustness of \ModelName\ across diverse attack scenarios.

Conventionally, we use a deterministic setting to select the node, e.g., the fixed grid However, these methods are unable to learn a new structure with a significantly reduced node size. We use the MSE [37] as the matching function Match() for simplicity. SGDD still be linear to the number of nodes in the original graph. We report the running time of the SGDD in the two datasets: Ogbn-arxiv, and Y elpChi. As shown in the Tab. 5, our approach achieves a similar running time to GCond when the We report the dataset statistics in Tab. 6. Citeseer-L: We use the Citeseer in the link prediction setting, named Citeseer-L.

Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have attracted increasing concerns.

Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a dependency severely restricts their reusability and generalization across various tasks and architectures. In this work, we revisit the goal of ideal GC from the perspective of GNN optimization consistency, and then a generalized GC optimization objective is derived, by which those traditional GC methods can be viewed nicely as special cases of this optimization paradigm. Based on this, Pre-trained Graph Condensation (PreGC) via optimal transport is proposed to transcend the limitations of task- and architecture-dependent GC methods. Specifically, a hybrid-interval graph diffusion augmentation is presented to suppress the weak generalization ability of the condensed graph on particular architectures by enhancing the uncertainty of node states. Meanwhile, the matching between optimal graph transport plan and representation transport plan is tactfully established to maintain semantic consistencies across source graph and condensed graph spaces, thereby freeing graph condensation from task dependencies. To further facilitate the adaptation of condensed graphs to various downstream tasks, a traceable semantic harmonizer from source nodes to condensed nodes is proposed to bridge semantic associations through the optimized representation transport plan in pre-training. Extensive experiments verify the superiority and versatility of PreGC, demonstrating its task-independent nature and seamless compatibility with arbitrary GNNs.

Graph Neural Networks (GNNs) have demonstrated remarkable results in various real-world applications, including drug discovery, object detection, social media analysis, recommender systems, and text classification. In contrast to their vast potential, training them on large-scale graphs presents significant computational challenges due to the resources required for their storage and processing. Graph Condensation has emerged as a promising solution to reduce these demands by learning a synthetic compact graph that preserves the essential information of the original one while maintaining the GNN's predictive performance. Despite their efficacy, current graph condensation approaches frequently rely on a computationally intensive bi-level optimization. Moreover, they fail to maintain a mapping between synthetic and original nodes, limiting the interpretability of the model's decisions. In this sense, a wide range of decomposition techniques have been applied to learn linear or multi-linear functions from graph data, offering a more transparent and less resource-intensive alternative. However, their applicability to graph condensation remains unexplored. This paper addresses this gap and proposes a novel method called Multi-view Graph Condensation via Tensor Decomposition (GCTD) to investigate to what extent such techniques can synthesize an informative smaller graph and achieve comparable downstream task performance. Extensive experiments on six real-world datasets demonstrate that GCTD effectively reduces graph size while preserving GNN performance, achieving up to a 4.0\ improvement in accuracy on three out of six datasets and competitive performance on large graphs compared to existing approaches. Our code is available at https://anonymous.4open.science/r/gctd-345A.

Recent research on deep graph learning has shifted from static to dynamic graphs, motivated by the evolving behaviors observed in complex real-world systems. However, the temporal extension in dynamic graphs poses significant data efficiency challenges, including increased data volume, high spatiotemporal redundancy, and reliance on costly dynamic graph neural networks (DGNNs). To alleviate the concerns, we pioneer the study of dynamic graph condensation (DGC), which aims to substantially reduce the scale of dynamic graphs for data-efficient DGNN training. Accordingly, we propose DyGC, a novel framework that condenses the real dynamic graph into a compact version while faithfully preserving the inherent spatiotemporal characteristics. Specifically, to endow synthetic graphs with realistic evolving structures, a novel spiking structure generation mechanism is introduced. It draws on the dynamic behavior of spiking neurons to model temporally-aware connectivity in dynamic graphs. Given the tightly coupled spatiotemporal dependencies, DyGC proposes a tailored distribution matching approach that first constructs a semantically rich state evolving field for dynamic graphs, and then performs fine-grained spatiotemporal state alignment to guide the optimization of the condensed graph. Experiments across multiple dynamic graph datasets and representative DGNN architectures demonstrate the effectiveness of DyGC. Notably, our method retains up to 96.2% DGNN performance with only 0.5% of the original graph size, and achieves up to 1846 times training speedup.

Federated graph learning is a widely recognized technique that promotes collaborative training of graph neural networks (GNNs) by multi-client graphs. However, existing approaches heavily rely on the communication of model parameters or gradients for federated optimization and fail to adequately address the data heterogeneity introduced by intricate and diverse graph distributions. Although some methods attempt to share additional messages among the server and clients to improve federated convergence during communication, they introduce significant privacy risks and increase communication overhead. To address these issues, we introduce the concept of a condensed graph as a novel optimization carrier to address FGL data heterogeneity and propose a new FGL paradigm called FedGM. Specifically, we utilize a generalized condensation graph consensus to aggregate comprehensive knowledge from distributed graphs, while minimizing communication costs and privacy risks through a single transmission of the condensed data. Extensive experiments on six public datasets consistently demonstrate the superiority of FedGM over state-of-the-art baselines, highlighting its potential for a novel FGL paradigm.