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cs.LG2026
IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry
Ying Yan, Liwei Hu, Xiaoming Zhang
Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Theref…
cs.LG2026
Geodesic Gradient Descent: A Generic and Learning-rate-free Optimizer on Objective Function-induced Manifolds
Liwei Hu, Guangyao Li, Wenyong Wang +2
Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian…