Sparse Matrix Partitioning for Crossbar-Based Nonzero Computation
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Solution Overview
Problem
Sparse matrix-vector multiplication operations in computational science and deep learning applications result in significant computational costs due to the large number of zero elements in sparse matrices, leading to wasted energy and resources.
Innovation Solution
Partitioning sparse matrices into denser sub-matrices, where only columns with nonzero elements are assigned to crossbar devices, reducing the number of crossbar devices needed and minimizing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sparse matrices are processed using conventional matrix-vector multiplication methods, then computational completeness is maintained, but computational cost and energy consumption increase significantly
Solution Approach 1:
The patent segments the sparse matrix into multiple sub-matrices, where each sub-matrix corresponds to a specific crossbar device. This segmentation allows the computation to be distributed across multiple devices, processing only the non-zero elements in each sub-matrix, thereby reducing the overall computational burden and energy consumption compared to processing the entire sparse matrix as a single unit.
Solution Approach 2:
The patent extracts and processes only the non-zero elements of the sparse matrix by partitioning it into sub-matrices that contain exclusively non-zero elements. This extraction principle eliminates the need to perform multiplications with zero elements, directly reducing computational cost and energy consumption while maintaining computational completeness.
2Reliability
If all columns of sparse matrix are assigned to crossbar devices, then complete matrix-vector multiplication is achieved, but number of crossbar devices and device complexity increase
Solution Approach 1:
The patent extracts only the columns containing non-zero elements from the sparse matrix and assigns them to crossbar devices. This extraction eliminates the need to allocate crossbar devices for columns that would only perform zero multiplications, thereby reducing the number of required devices and system complexity while preserving computational accuracy for all non-zero contributions.
Solution Approach 2:
The patent applies local quality by creating sub-matrices with different characteristics - each sub-matrix is tailored to contain only non-zero elements specific to its corresponding crossbar device. This localized optimization ensures that each device processes only relevant data, reducing overall system complexity while maintaining global computational accuracy.
Data Source
AI summary
According to examples, an apparatus may include a processor and a non-transitory computer readable medium having instructions that when executed by the processor, may cause the processor to partition a matrix of elements into a plurality of sub-matrices of elements. Each sub-matrix of the plurality of sub-matrices may include elements from a set of columns of the matrix of elements that includes a nonzero element. The processor may also assign elements of the plurality of sub-matrices to a plurality of crossbar devices to maximize a number of nonzero elements of the matrix of elements assigned to the crossbar devices.