# A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models

arXiv: https://arxiv.org/abs/2601.21207 · HTML: https://mlsanity.com/paper/2601.21207/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [A Sheaf-Theoretic Construction of Shape Space](https://mlsanity.com/paper/2204.09020/) (2022)

## Abstract (arXiv)

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such domains, integrate local features, and generate representations for diverse real-world applications. However, the distribution and diffusion behavior of GDL and TDL features during training remains an open and underexplored problem. Motivated by this gap, we introduce a cellular sheaf theoretic framework for modeling and analyzing the local consistency and harmonicity of node features and edge weights in graph-based architectures. By tracking local feature alignments and agreements through sheaf structures, the framework offers a topological perspective on feature diffusion and aggregation. Furthermore, a multiscale extension inspired by topological data analysis (TDA) is proposed to capture hierarchical feature interactions in graph models. This approach enables a joint characterization of GDL and TDL architectures based on their underlying geometric and topological structures and the learned signals defined on them, providing insights for future studies on conventional tasks such as node classification, substructure detection, and community detection.