7 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…
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…
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…
On the positivity of Fourier transform of the stretched Gaußian function
Hanwen Liu
The stretched Gaußian function , as a real function defined on , has found numerous applications in mathematics and…
Topological conjugacy between Schneider's continued fraction map and a shift map on
Hanwen Liu
We prove that Schneider's continued fraction map is topologically conjugate to a shift map defined on , and the topological conjugation $f\colon\mathbb{Q}_p \rightarr…