Expressive Sparse Matrix Decompression From N:M:P Metadata
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Solution Overview
Problem
Existing neural network matrix representations require significant storage space and computational resources due to the inclusion of zero values, which do not impact the computation results, and existing sparse matrix representations either lose expressivity or require excessive metadata.
Innovation Solution
Implementing expressive sparse matrix representations with limited metadata by compressing dense matrices into N:M:P sparse matrices, where N nonzero values are preserved out of M consecutive elements using P available positions and reduced metadata, allowing for efficient storage and computation through formats like 4:8:4, checkerboard, and 4:8:2b schemes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If dense matrix representation is used, then computational accuracy is maintained, but storage space requirements increase
Solution Approach 1:
The patent extracts only the necessary information (nonzero values and their positions) from the dense matrix representation, discarding redundant zero values. This creates a sparse matrix representation that maintains computational accuracy for nonzero elements while significantly reducing storage space requirements.
Solution Approach 2:
The patent changes the representation parameters from storing all M values (dense) to storing only N nonzero values with their positions (sparse). This parameter change transforms the storage requirement from O(M) to O(N), reducing storage space while maintaining accuracy for the essential nonzero elements.
2Quantity of substance
If sparse matrix representation is used, then storage space is reduced, but expressivity is lost
Solution Approach 1:
The patent adds a position dimension to the sparse representation by storing not only the N nonzero values but also their corresponding positions in the original M-element sequence. This dimensional addition (storing position information) restores expressivity by enabling precise reconstruction of the original matrix pattern while maintaining storage savings.
3Adaptability or versatility
If more metadata is used in sparse representation, then expressivity is improved, but device complexity increases
Solution Approach 1:
The patent uses partial metadata by storing only the position information necessary to reconstruct the sparse matrix, rather than storing complete information about all possible matrix configurations. This partial metadata approach provides sufficient expressivity for the intended applications while minimizing the complexity and storage overhead of the metadata structure.
Data Source
AI summary
Disclosed are systems and techniques for decompressing an expressive sparse matrix representation with limited metadata. The techniques include receiving a sparse matrix and metadata corresponding to the sparse matrix. The sparse matrix is a compressed representation of a dense matrix. The sparse matrix contains a first number (N) of elements to retain from the dense matrix which comprises at least a second number (M) of elements. The metadata corresponding to the sparse matrix is based on a third number (P) of positions and a format determined during compression of the dense matrix. The techniques include generating an uncompressed matrix based on the sparse matrix and the metadata corresponding to the sparse matrix.