4 papers
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 the…
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…
Accelerating Low-Rank Factorization-Based Semidefinite Programming Algorithms on GPU
Qiushi Han, Zhenwei Lin, Hanwen Liu +4
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough accelerati…