Compressed Sparse Matrix Transpose via Pattern Numbers
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Solution Overview
Problem
Conventional methods for matrix operations in artificial neural networks are inefficient in terms of data storage and processing power, particularly when dealing with sparse matrices, as they require decompression and recompression during transposition, which is data-intensive and computationally costly.
Innovation Solution
The method involves representing a compressed sparse matrix as a set of compressed sparse submatrices in a logical space, using pattern numbers as metadata instead of indices, and generating a compressed transpose without decompressing the matrix, utilizing a look-up table to directly determine the transpose, thereby reducing data storage and processing requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional methods are used for transposing compressed sparse matrices, then the transposition operation can be performed, but decompression and recompression are required which increases data storage requirements and computational cost
Solution Approach 1:
The compressed sparse matrix is divided into multiple compressed sparse submatrices arranged in a logical space. Each submatrix can be independently transposed using pattern numbers, avoiding the need to decompress and recompress the entire matrix. This segmentation enables efficient transposition while maintaining compression and reducing computational overhead.
2Loss of time
If conventional methods are used for transposing compressed sparse matrices, then the transposition operation can be performed, but decompression and recompression are required which increases computational cost
Solution Approach 1:
Pattern numbers are pre-computed and stored for each compressed sparse submatrix, representing the transposition pattern without requiring actual decompression. During transposition operations, these pre-computed pattern numbers are directly utilized to rearrange submatrices, eliminating the need for time-consuming decompression and recompression processes and reducing computational energy consumption.
3Quantity of substance
If pattern numbers are used instead of indices, then data storage is reduced and processing is simplified, but a different data representation scheme is required
Solution Approach 1:
The patent transforms the traditional index-based metadata representation into a pattern number-based representation. Each compressed sparse submatrix is assigned a pattern number that encodes its transposition characteristics. This parameter change reduces metadata storage requirements and simplifies processing operations, as pattern numbers directly indicate how submatrices should be rearranged during transposition without requiring complex index calculations.
Data Source
AI summary
Many computing systems process data organized in a matrix format. For example, artificial neural networks (ANNs) perform numerous computations on data organized into matrices using conventional matrix arithmetic operations. One such operation, which is commonly performed, is the transpose operation. Additionally, many such systems need to process many matrices and/or matrices that are large in size. For sparse matrices that hold few significant values and many values that can be ignored, transmitting and processing all the values in such matrices is wasteful. Thus, techniques are introduced for storing a sparse matrix in a compressed format that allows for a matrix transpose operation to be performed on the compressed matrix without having to first decompress the compressed matrix. By utilizing the introduced techniques, more matrix operations can be performed than conventional systems.