4 papers
On Topology of Compact Hessian Manifolds
Hanwen Liu
We investigate the global topological constraints and structural properties of compact Hessian manifolds. By establishing novel fibration and splitting theorems, we confirm Chern's…
Hausdorff Dimension of Union of Lines Covering a Curve: Applications to Mathematical Physics
Hanwen Liu
We prove that for any nonlinear , the union of lines covering its graph has a Hausdorff dimension of at least , and this dimension bound is sharp. We t…
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…
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…