Structure-Feature Aligned Graph Learning via Alternating Constrained Optimization

Conventional Graph Neural Networks (GNNs) tightly couple feature transformation with neighborhood aggregation. This dependency makes them susceptible to topological noise and performance degradation in heterophilous graphs, where neighbors may not share the same labels. The authors seek to decouple these processes to improve robustness and classification accuracy.

The paper proposes a two-view framework that separates graph learning into a structure-free feature view and a structure-conditioned GNN view.

1. Feature View: An independent anchor network (an AutoEncoder) learns a structure-agnostic feature prior via a self-supervised reconstruction objective. This prior captures intrinsic node attributes without being influenced by potentially noisy graph topology.
2. Structure View: The authors introduce a Channel-Split Adaptive Gated GNN (CSAG-GNN). This architecture uses a dual-branch approach—combining GCN (spectral smoothing) and GraphSAGE (spatial discrimination)—regulated by a node-wise gating mechanism that dynamically balances the two based on local node needs.
3. Optimization: Instead of joint end-to-end training, which can lead to feature drift, the authors employ a cyclic alternating optimization strategy. This bi-level approach updates the anchor network to refine the feature prior, then updates the GNN to align its intermediate representations with that prior while minimizing the downstream task loss.

By explicitly aligning structural embeddings with a clean feature prior, the model mitigates the propagation of erroneous signals from noisy or heterophilous graph structures. The alternating optimization ensures that the feature prior remains stable, preventing the "mutual drift" often observed in joint training paradigms. Empirical results demonstrate that this approach provides balanced performance gains across both homophilous and heterophilous benchmarks, offering a more robust alternative to standard GNN training.