Graph neural networks improve learning with adaptive aggregation types
Graph Representation Learning via Adaptive Expectile Aggregation
Machine Learning
Summary
Graph neural networks (GNNs) often combine information from connected nodes by averaging, but averaging can miss important signals, especially when connected nodes differ a lot. The authors propose a new method called ExpectileGCN that learns how to mix information by focusing more on either smaller or larger values instead of just averaging. This new approach adapts automatically and helps GNNs make better predictions on various graph types, including those where neighbors are quite different. The authors also provide mathematical guarantees and show that this method is more robust when data is noisy or connections are disturbed.
What this means in practice
- •For machine learning engineers: Improve graph-based prediction models in social networks by using adaptive neighborhood aggregation that captures varied neighbor importance.
- •For cybersecurity analysts: Enhance network anomaly detection models by using expectile aggregation to better differentiate between normal and anomalous patterns in complex graphs.
Authors
Tianyi Zhu, Wei Lan
Abstract
Graph neural networks (GNNs) rely critically on neighborhood aggregation, yet conventional mean aggregation may fail to capture class-relevant distributional information, particularly in heterophilic graphs. We propose ExpectileGCN, an adaptive graph aggregation framework that introduces a learnable expectile level to capture neighborhood information beyond the mean. The proposed operator continuously adjusts aggregation between minimum- and maximum-type behaviors, with mean aggregation as a special case. A differentiable approximation based on sigmoid smoothing and fixed-point iterations enables end-to-end optimization. Theoretically, we establish stability properties and transductive generalization guarantees for ExpectileGCN. We further investigate its classification risk under heterophilic neighborhood models. For informative neighborhoods, we show that expectile aggregation can exploit class-dependent scale differences to achieve a classification advantage over mean aggregation. Under a local asymptotic regime with diminishing per-neighbor label informativeness, we establish that this advantage can persist in terms of limiting classification risk. Experiments on homophilic and heterophilic benchmark graphs demonstrate strong predictive performance and improved robustness under feature corruption and structural perturbations.