6 papers
Illustrating Hyperbolic Surfaces with Mesh Embeddings
Fabian Lander, Erik Löffelholtz, Diaaeldin Taha +2
Hyperbolic geometry exhibits geometric phenomena, such as fast area growth, that are difficult to visualize faithfully in Euclidean space, and which standard models like the Poinca…
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…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
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…