4 papers
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…
Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry
Deniz Kucukahmetler, Maximilian Jean Hemmann, Julian Mosig von Aehrenfeld +4
Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecaste…
Immersive Visualization of Flat Surfaces Using Ray Marching
Fabian Lander, Diaaeldin Taha
We present an effective method for visualizing flat surfaces using ray marching. Our approach provides an intuitive way to explore translation surfaces, mirror rooms, unfolded poly…
Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
Diaaeldin Taha, James Chapman, Marzieh Eidi +2
Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological me…