7 papers
Intrinsic Low-Tucker-Rank Theory and Unified Tensor CUR Decomposition for High-Dimensional Hyperinterpolation
Maolin Che, Yimin Wei, Chong Wu
High-dimensional hyperinterpolation is severely hampered by the curse of dimensionality, as its coefficient tensors grow exponentially with the ambient dimension. Existing research…
How many integrals should be evaluated at least in two-dimensional hyperinterpolation?
Maolin Che, Congpei An, Yimin Wei +1
This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techni…
Effective algorithms for tensor train decomposition via the UTV framework
Yuchao Wang, Maolin Che, Yimin Wei
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for const…
ELFATT: Efficient Linear Fast Attention for Vision Transformers
Chong Wu, Maolin Che, Renjie Xu +2
The attention mechanism is the key to the success of transformers in different machine learning tasks. However, the quadratic complexity with respect to the sequence length of the…
sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation
Renjie Xu, Chong Wu, Maolin Che +3
We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomp…
Efficient randomized algorithms for the fixed Tucker-rank problem of Tucker decomposition with adaptive shifts
Maolin Che, Yimin Wei, Chong Wu +1
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast rand…