Poincar\'e Ball

The Poincaré ball, a hyperbolic geometric model, is increasingly used in machine learning to represent hierarchical data structures and address limitations of Euclidean spaces. Current research focuses on applying Poincaré embeddings within various neural network architectures, including graph neural networks and Gaussian neural networks, to improve tasks like semantic segmentation, orbit classification, and sequential recommendation. This approach leverages the Poincaré ball's ability to naturally embed hierarchical relationships, leading to improved model accuracy and calibration, particularly in complex or high-dimensional datasets. The resulting advancements have implications for diverse fields, from plasma physics to natural language processing and Bayesian inference.