79 citations · 89 across the 10 of their papers we have counts for
10 papers
-sphere covering and approximating nuclear -norm
Jiewen Guan, Simai He, Bo Jiang +1
The spectral -norm and nuclear -norm of matrices and tensors appear in various applications albeit both are NP-hard to compute. The former sets a foundation of -spher…
Approximating Tensor Norms via Sphere Covering: Bridging the Gap Between Primal and Dual
Simai He, Haodong Hu, Bo Jiang +1
The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunate…
Complexity and computation for the spectral norm and nuclear norm of order three tensors with one fixed dimension
Haodong Hu, Bo Jiang, Zhening Li
The recent decade has witnessed a surge of research in modelling and computing from two-way data (matrices) to multiway data (tensors). However, there is a drastic phase transition…
LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions
Zhening Li, Gabriel Poesia, Omar Costilla-Reyes +2
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thu…
Extreme ratio between spectral and Frobenius norms of nonnegative tensors
Shengyu Cao, Simai He, Zhening Li +1
One of the fundamental problems in multilinear algebra, the minimum ratio between the spectral and Frobenius norms of tensors, has received considerable attention in recent years.…
MolScribe: Robust Molecular Structure Recognition with Image-To-Graph Generation
Yujie Qian, Jiang Guo, Zhengkai Tu +3
Molecular structure recognition is the task of translating a molecular image into its graph structure. Significant variation in drawing styles and conventions exhibited in chemical…
On decompositions and approximations of conjugate partial-symmetric complex tensors
Taoran Fu, Bo Jiang, Zhening Li
Conjugate partial-symmetric (CPS) tensors are the high-order generalization of Hermitian matrices. As the role played by Hermitian matrices in matrix theory and quadratic optimizat…
On orthogonal tensors and best rank-one approximation ratio
Zhening Li, Yuji Nakatsukasa, Tasuku Soma +1
As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an matrix with is and is (up to scalar scaling…
Approximation Algorithms for Optimization of Real-Valued General Conjugate Complex Forms
Taoran Fu, Bo Jiang, Zhening Li
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate…
Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations
Bo Jiang, Zhening Li, Shuzhong Zhang
In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions…