Edge-Splitting MLP: Node Classification on Homophilic and Heterophilic Graphs without Message Passing

TL;DR

ES-MLP addresses the challenge of node classification on graphs with varying homophily by fusing Graph-MLP’s neighborhood-aware training with ES-GNN’s edge-splitting into a two-channel, no-inference-edge architecture. It learns task-relevant and task-irrelevant embeddings, applying a neighborhood contrastive loss and an irrelevance regularization to achieve robust performance without relying on edges at inference time. Across seven real-world datasets and a CSBM synthetic dataset, ES-MLP matches or surpasses baselines on both homophilic and heterophilic graphs, while offering significant inference-time speedups and resilience to edge-noise. The work demonstrates practical impact for scalable, robust graph learning and suggests future directions toward incorporating graph directionality and further optimizing edge-splitting dynamics.

Abstract

Message Passing Neural Networks (MPNNs) have demonstrated remarkable success in node classification on homophilic graphs. It has been shown that they do not solely rely on homophily but on neighborhood distributions of nodes, i.e., consistency of the neighborhood label distribution within the same class. MLP-based models do not use message passing, \eg Graph-MLP incorporates the neighborhood in a separate loss function. These models are faster and more robust to edge noise. Graph-MLP maps adjacent nodes closer in the embedding space but is unaware of the neighborhood pattern of the labels, i.e., relies solely on homophily. Edge Splitting GNN (ES-GNN) is a model specialized for heterophilic graphs and splits the edges into task-relevant and task-irrelevant, respectively. To mitigate the limitations of Graph-MLP on heterophilic graphs, we propose ES-MLP that combines Graph-MLP with an edge-splitting mechanism from ES-GNN. It incorporates the edge splitting into the loss of Graph-MLP to learn two separate adjacency matrices based on relevant and irrelevant feature pairs. Our experiments on seven datasets with six baselines show that ES-MLP is on par with homophilic and heterophilic models on all datasets without using edges during inference. We show that ES-MLP is robust to multiple types of edge noise during inference and that its inference time is two to five times faster than that of commonly used MPNNs. The source code is available at https://github.com/MatthiasKohn/ES-MLP.

Figures (10)

• Figure 1: The pipeline of ES-MLP. Node features are first projected into two different subspaces $R$ and $IR$. A separate forward pass is performed to obtain embeddings $Z_R$ and $Z_{IR}$. Both embeddings are then used for edge splitting to divide the original graph edges into two sets and for the neighborhood contrastive loss. The task-relevant representation $Z_R$ is then used for the prediction task and task-irrelevant representation $Z_{IR}$ is used to calculate the Irrelevant Consistency Loss.
• Figure 2: Test accuracies for the CSBM datasets (left). The scores are averaged over 5 runs. The probability for intra-class edges is on the x-axis and the probability for inter-class edges is on the y-axis. The adjusted homophily ratios $\mathcal{H}_{adj}$ for the CSBM datasets (right).
• Figure 3: Test accuracies of the robustness analysis on the Cora and Amazon datasets. Left to right: Results on Cora with uniform edge-noise, Cora with categorical edge-noise, Amazon with Uniform edge-noise, and Amazon with categorical edge-noise. Our ES-MLP, as it does not require edges at test time, remains constant on all datasets. Graph-MLP, not shown for brevity, also remains constant.
• Figure 4: Results for the edge-noise experiment on Cora with uniform (left) and categorical (right) noise.
• Figure 5: Hyperparameter sensitivity analysis on the neighborhood contrastive loss weight $\alpha_{NC}$ hyperparameter