Cost-Sensitive Neighborhood Aggregation for Heterophilous Graphs: When Does Per-Edge Routing Help?

TL;DR

This paper introduces CSNA, a GNN layer that adaptively routes messages based on learned pairwise distances, improving performance in adversarial heterophily but not in informative heterophily, with a diagnostic for heterophily regimes.

Contribution

The paper proposes CSNA, a novel cost-sensitive GNN layer that distinguishes heterophily regimes and adaptively routes messages, providing insights into when per-edge routing is beneficial.

Findings

CSNA performs well on adversarial heterophily datasets.

CSNA underperforms on informative heterophily datasets.

The cost function acts as a diagnostic for heterophily regimes.

Abstract

Recent work distinguishes two heterophily regimes: adversarial, where cross-class edges dilute class signal and harm classification, and informative, where the heterophilous structure itself carries useful signal. We ask: when does per-edge message routing help, and when is a uniform spectral channel sufficient? To operationalize this question we introduce Cost-Sensitive Neighborhood Aggregation (CSNA), a GNN layer that computes pairwise distance in a learned projection and uses it to soft-route each message through concordant and discordant channels with independent transformations. Under a contextual stochastic block model we show that mean aggregation can reverse the label-aligned signal direction under heterophily, and that cost-sensitive weighting with $w_+/w_- > q/p$ preserves the correct sign. On six benchmarks with uniform tuning, CSNA is competitive with state-of-the-art methods on adversarial-heterophily datasets (Texas, Wisconsin, Cornell, Actor) but underperforms on informative-heterophily datasets (Chameleon, Squirrel) -- precisely the regime where per-edge routing has no useful decomposition to exploit. The pattern is itself the finding: the cost function's ability to separate edge types serves as a diagnostic for the heterophily regime, revealing when fine-grained routing adds value over uniform channels and when it does not. Code is available at https://github.com/eyal-weiss/CSNA-public .