A tensor is multi-dimensional generalization of a vector and a matrix in high-dimensional space. Tensor decomposition can represent a high-order tensor into many low-dimensional factors, which can reduce computation and storage complexity during data processing. Canonical Polyadic (CP) decomposition is one of the most widely used decomposition frameworks, which decomposes a N-order tensor into N factor matrices via operating Matricized Tensor Times Khatri-Rao Product (MTTKRP) computation. However, the MTTKRP is the computational bottleneck for algorithms computing CP decomposition of incomplete tensors due to intermediate product of feature matrices. To reduce the computation complexity of MTTKRP, this paper presents Hyperparameter-CSF (HP-CSF). Its main idea is to increase the balance of load at thread-level and set up an allocation rule for parallel deployment. Compared to state-of-the-art works, our method achieves 100.7% speedup across NVIDIA Geforce RTX 4090 on a range of sparse tensors.

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HP-CSF: An GPU Optimization Method for CP Decomposition of Incomplete Tensors

  • Guanxiong Liu,
  • Hao Wu

摘要

A tensor is multi-dimensional generalization of a vector and a matrix in high-dimensional space. Tensor decomposition can represent a high-order tensor into many low-dimensional factors, which can reduce computation and storage complexity during data processing. Canonical Polyadic (CP) decomposition is one of the most widely used decomposition frameworks, which decomposes a N-order tensor into N factor matrices via operating Matricized Tensor Times Khatri-Rao Product (MTTKRP) computation. However, the MTTKRP is the computational bottleneck for algorithms computing CP decomposition of incomplete tensors due to intermediate product of feature matrices. To reduce the computation complexity of MTTKRP, this paper presents Hyperparameter-CSF (HP-CSF). Its main idea is to increase the balance of load at thread-level and set up an allocation rule for parallel deployment. Compared to state-of-the-art works, our method achieves 100.7% speedup across NVIDIA Geforce RTX 4090 on a range of sparse tensors.