7 papers
Communicability-Inspired Positional Encoding (CIPE)
Yipeng Zhang, Zhongtian Sun, Pietro Liò +1
Positional encodings (PEs) are essential for Transformers. Yet designing effective PEs for non-Euclidean graphs remains challenging. Such encodings should ideally induce an Attenti…
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
Yuhan Peng, Junwen Dong, Yuzhi Zeng +6
Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (direc…
Full-Spectrum Graph Neural Networks: Expressive and Scalable
Xiaohan Wang, Deyu Bo, Longlong Li +1
It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Wei…
Rhomboid Tiling for Geometric Graph Deep Learning
Yipeng Zhang, Longlong Li, Kelin Xia
Graph Neural Networks (GNNs) have proven effective for learning from graph-structured data through their neighborhood-based message passing framework. Many hierarchical graph clust…
Commutative algebra-enhanced topological data analysis
Chuanshen Hu, Yu Wang, Kelin Xia +2
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space…
KA-GNN: Kolmogorov-Arnold Graph Neural Networks for Molecular Property Prediction
Longlong Li, Yipeng Zhang, Guanghui Wang +1
As key models in geometric deep learning, graph neural networks have demonstrated enormous power in molecular data analysis. Recently, a specially-designed learning scheme, known a…