12 papers
Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianc
Dongzhe Zheng, Christine Allen-Blanchette
Physical fields on meshes require a separation between topology and geometry: conservation laws are topological and should be exact, while geometry, material response, and anisotro…
Topology-Preserving Neural Operator Learning via Hodge Decomposition
Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resol…
HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts
Tao Zhong, Dongzhe Zheng, Christine Allen-Blanchette
Sparse Mixture-of-Experts (MoE) layers route tokens through a handful of experts, and learning-free compression of these layers reduces inference cost without retraining. A subtle…
Picard groups of completed period images and the Deng-Robles problem
Badre Mounda, Dongzhe Zheng
A basic problem in the geometry of degenerating period maps is to determine whether their completed images admit an intrinsic algebraic description. For polarized variations of Hod…
Mirror Duality in a Spencer-Type Complex: Analytic and Riemann-Roch Perspectives
Dongzhe Zheng
We introduce and analyze a Spencer-type elliptic complex on the space of differential forms valued in symmetric powers of an adjoint bundle, $Ω^\bullet(X)\otimes \mathrm{Sym}^\bul…
The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture
Dongzhe Zheng
This paper proposes a new theoretical perspective for studying the Hodge conjecture through an analytical framework based on constraint geometry. Our theory begins with a key obser…