Cooperative Sheaf Neural Networks
Andr\'e Ribeiro, Ana Luiza Ten\'orio, Juan Belieni, Amauri H. Souza, Diego Mesquita
TL;DR
This paper introduces Cooperative Sheaf Neural Networks (CSNNs), a novel approach that enables cooperative information diffusion on directed graphs, improving over existing sheaf diffusion methods by allowing selective attention to distant nodes.
Contribution
We propose the concept of cellular sheaves over directed graphs and develop CSNNs, enabling cooperative behavior and selective attention in sheaf-based graph neural networks.
Findings
CSNNs outperform prior sheaf diffusion methods in experiments.
CSNNs enable nodes to attend selectively to distant nodes.
Theoretical analysis shows CSNNs mitigate oversquashing.
Abstract
Sheaf diffusion has recently emerged as a promising design pattern for graph representation learning due to its inherent ability to handle heterophilic data and avoid oversmoothing. Meanwhile, cooperative message passing has also been proposed as a way to enhance the flexibility of information diffusion by allowing nodes to independently choose whether to propagate/gather information from/to neighbors. A natural question ensues: is sheaf diffusion capable of exhibiting this cooperative behavior? Here, we provide a negative answer to this question. In particular, we show that existing sheaf diffusion methods fail to achieve cooperative behavior due to the lack of message directionality. To circumvent this limitation, we introduce the notion of cellular sheaves over directed graphs and characterize their in- and out-degree Laplacians. We leverage our construction to propose Cooperative…
Peer Reviews
Decision·ICLR 2026 Poster
The work is well motivated, addressing a clear limitation of sheaf neural networks in modeling cooperation patterns between nodes. The proposed solution has solid theretical grounds. Synthetic results clearly confirm the ability to mitigate oversquashing, and an extensive evaluation on real-world datasets shows competitive performance wrt the state of the art.
Experimental results on the classical datasets for heterophilic analysis (Table 2) show very marginal improvements (considering the high variance, most likely none of these is significant). This is not a novelty, and questions the appropriateness of these datasets as benchmarks (as Platonov et al already pointed out). I encourage the authors to briefly discuss this aspect, so as to direct further research towards more appropriate evaluation benchmarks.
- The motivation, goal, and methodology are well formulated. - The paper reads well, it has a nice structure, and the necessary background knowledge is well presented.
There are strong claims regarding (1) consistently outperforming SNNs and cooperative GNNs (both in introduction and in the experiments, see Results in Section 6.2), and (2) about not soccumbing to oversquashing (abstract). Looking at the results, it doesn't appear to improve substantially with respect to the competitors, so I would advise to reconsider the strength of the claims, which may lead to high expectations in the experiments. Additionally, the introduction of a sheaf structure general
Clear theoretical guarantees linked to long-range neighbors and over-squashing. Empirical performance is compelling
Scalability of sheaf-based models on large-scale graphs remains to be tested.
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Taxonomy
TopicsAdvanced Graph Neural Networks · Functional Brain Connectivity Studies · Complex Network Analysis Techniques