Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNs

2026-06-01

AI Summary

Existing pre-propagation graph neural networks (PPGNNs) struggle to consistently outperform simpler models due to the absence of a joint node-channel adaptive filtering mechanism. This work addresses this limitation by introducing, from a graph filtering perspective, the first node-channel jointly adaptive filtering paradigm. Specifically, it employs a mixture-of-experts architecture that combines a learnable library of Chebyshev filter experts with a three-dimensional gating tensor to dynamically select diffusion bases. This approach fills a critical gap in flexible filter design for PPGNNs and eliminates the need for dataset-specific aggregators. Evaluated across 11 homophilic and heterophilic benchmark datasets, the proposed method surpasses strong baselines on 9 of them, achieves top performance on all 3 large-scale datasets, and yields an average improvement of 1.53 percentage points in test accuracy.

Abstract

Pre-propagation graph neural networks (PPGNNs) push all graph-dependent computation into a preprocessing step and train only on the resulting dense hop features, which makes them highly scalable. A puzzle in this regime is that more complex hop aggregators do not reliably outperform simpler ones: on many benchmarks, a plain MLP-based aggregator matches or beats hop-attention variants. We revisit this behavior from a graph-filter perspective. Over a precomputed diffusion basis, existing PPGNNs differ mainly in how filter coefficients are shared across nodes and feature channels, rather than simply in raw aggregator capacity. MLP-based architectures learn channel-dependent filters that are largely shared across nodes, while hop-attention-based architectures learn node-dependent mixtures that are largely shared across channels. This reveals a missing regime in standard PPGNN designs: joint node- and channel-adaptive filtering under the pre-propagation computational contract. We propose FilterMoE, a mixture-of-experts PPGNN in which a small bank of learnable Chebyshev filter experts is routed jointly over nodes and channels by a 3D gating tensor. Across eleven homophilic and heterophilic benchmarks, FilterMoE outperforms strong PPGNN baselines on nine datasets and ranks first on all three large-scale benchmarks, improving the average test score by 1.53 points. These results establish joint node-channel filter routing as a robust alternative to dataset-specific hop-aggregator selection.

Problem

• pre-propagation GNNs
• graph filtering
• node-channel adaptation
• hop aggregation
• scalable graph learning

Innovation

• pre-propagation GNNs
• graph filtering
• mixture-of-experts
• node-channel adaptation
• Chebyshev filters