GPU-Based Third-Order Low-Rank Tensor Calculation Method
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Solution Overview
Problem
Conventional CPU-based third-order low-rank tensor calculations are inefficient and cannot meet real-time requirements due to high computation time complexity, which is exacerbated by the exponential increase in tensor size, making them impractical for large-scale tensor data analysis.
Innovation Solution
A GPU-based third-order low-rank tensor calculation method that involves transmitting third-order real value tensor data from a CPU to a GPU, performing Fourier transforms, matrix operations, and inverse Fourier transforms, allowing for parallel processing and significantly improving computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If CPU-based tensor calculation is used, then the system is simple to implement, but the computation time increases exponentially with tensor size
Solution Approach 1:
The patent transitions from CPU-based sequential processing to GPU-based parallel processing, utilizing the dimensional advantage of parallel computation architecture. The GPU's massive number of cores enable simultaneous execution of multiple tensor operations, fundamentally changing the computational dimension from sequential to parallel, thereby resolving the time complexity issue while maintaining implementation feasibility through standardized GPU programming interfaces.
Solution Approach 2:
The patent replaces the traditional CPU mechanical computing system with a GPU-based parallel computing system. This substitution leverages the GPU's architectural advantages (thousands of cores, high memory bandwidth) to perform tensor calculations, replacing the sequential mechanical processing of CPU with parallel computational mechanics, thus achieving exponential speedup for large-scale tensor operations.
2Productivity
If GPU-based parallel computing is used, then computation efficiency is significantly improved, but device complexity increases
Solution Approach 1:
The patent employs GPU technology which serves multiple functions: it can perform both traditional graphics rendering and general-purpose parallel computing (GPGPU). This multi-functionality allows the same hardware device to handle tensor calculations efficiently while maintaining compatibility with existing graphics workloads, thereby improving computation efficiency without proportionally increasing system complexity.
Solution Approach 2:
The patent introduces CUDA programming interface and memory management layers as intermediaries between the host CPU and GPU device. These intermediary software layers abstract the complex GPU parallel programming details, providing high-level APIs that simplify development while leveraging GPU's full computational power, thus achieving high productivity without exposing the full complexity to users.
3Quantity of substance
If tensor size increases, then more data can be processed, but computation time complexity increases exponentially
Solution Approach 1:
The patent segments large-scale tensor data into smaller chunks that can be processed in parallel across multiple GPU cores. By dividing the computational workload into independent segments that can be executed simultaneously, the system maintains linear scaling with data size rather than exponential time complexity, enabling efficient processing of large tensors through parallel segment execution.
Solution Approach 2:
The patent exploits the parallel processing dimension of GPU architecture to handle increased data quantities. Instead of sequentially processing larger tensors on CPU (which leads to exponential time increase), the system distributes tensor elements across thousands of GPU cores, adding a parallel computation dimension that allows data capacity to scale without proportionally increasing computation time.
Data Source
AI summary
The present disclosure provides a GPU-based third-order low-rank tensor calculation method. Operation steps of the method include: transmitting, by a CPU, third-order real value tensor input data DATA1 to a CPU; performing, by the GPU, Fourier transforms on the DATA1, to obtain third-order complex value tensor data DATA2; performing, by the GPU, matrix operations on the DATA2, to obtain third-order complex value tensor data DATA3; performing, by the GPU, inverse Fourier transforms on the DATA3, to obtain third-order real value tensor output data DATA4; and transmitting, by the GPU, the DATA4 to the CPU. In the present disclosure, in the third-order low-rank tensor calculation, a computational task with high concurrent processes is accelerated by using the CPU to improve computational efficiency. Compared with conventional CPU-based third-order low-rank tensor calculation, computational efficiency is significantly improved, and same calculation can be completed by using less time.