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math.DG2025
On Two Dimensional Flat Hessian Potentials
Hanwen Liu
A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential fun…
cs.LG2025
How Particle-System Random Batch Methods Enhance Graph Transformer: Memory Efficiency and Parallel Computing Strategy
Hanwen Liu, Yixuan Ma, Shi Jin +1
Attention mechanism is a significant part of Transformer models. It helps extract features from embedded vectors by adding global information and its expressivity has been proved t…
math.DG2025
On Compact Hessian Manifolds
Hanwen Liu
We study compact Hessian manifolds. We prove vanishing of their Euler characteristics. For compact hyperbolic affine manifolds, we deduce that topologically they are periodic mappi…