Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

Pre-propagation graph neural networks (PPGNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch training without inter-node dependencies, avoids repeated sparse matrix--matrix multiplications, and better matches modern accelerators optimized for dense compute. However, their expressivity remains unclear, and empirical results show a gap between PPGNNs and their message-passing counterparts on commonly used graph benchmarks, especially heterophilic ones. In this paper, we propose a suite of robust graph diffusion operators for preprocessing and a few-shot hidden-state re-propagation scheme during training. Our methods improve the validation and test accuracy of PPGNNs, enabling them to match the accuracy of message-passing GNNs while maintaining training efficiency.

Graph Neural Networks (GNNs) have demonstrated impressive performance in learning representations from graph-structured data. However, their message-passing mechanism inherently relies on the assumption of label consistency among connected nodes, limiting their applicability to low-homophily settings. Moreover, since message passing operates as a hierarchical diffusion process, GNNs face challenges in capturing long-range dependencies. As network depth increases, the structural noise along heterophilic edges tends to be amplified, resulting in over-smoothing. This issue becomes especially prominent in highly heterophilic graphs, where the propagation of inconsistent semantics across the topology continually exacerbates misaggregation. To address this issue, we propose a novel framework named Layer Embedding Deep Fusion Graph Neural Network (LEDF-GNN). Specifically, we design a Layer Embedding Deep Fusion (LEDF) operator that nonlinearly fuses multi-layer embeddings to capture inter-layer dependencies and effectively alleviate deep propagation degradation. Meanwhile, to mitigate structural heterophily, LEDF-GNN employs a Dual-Topology Parallel Strategy (DTPS) that simultaneously leverages the original and reconstructed topologies, allowing for adaptive structure-semantics co-optimization under diverse homophily conditions. Extensive semi-supervised classification experiments on the citation and image benchmarks demonstrate that, under both homophilic and heterophilic settings, LEDF-GNN consistently outperforms state-of-the-art baselines, validating its effectiveness and generalization capability across diverse graph types.

Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.