Sparse Matrix Encoding With Limited Metadata for Neural Networks
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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 contribute to the computation, and existing sparse matrix representations either require excessive metadata or lose expressivity.
Innovation Solution
The system compresses dense matrices into fully-expressive sparse matrices with limited metadata by selecting N nonzero values out of M consecutive elements, using formats like 4:8:4, checkerboard, to reduce metadata requirements while maintaining expressivity, and employs hardware-efficient compression sequences to maximize importance values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If dense matrices are used to store neural network weights, then all values including zeros are preserved, but storage space and computational bandwidth are wasted on zero values that do not contribute to computation
Solution Approach 1:
The patent extracts only the nonzero values from the dense matrix and stores them in the sparse matrix, along with their positions. This extraction eliminates the storage of zero values while preserving all computationally relevant information, directly resolving the contradiction between maintaining computation accuracy and reducing storage space.
2Quantity of substance
If traditional sparse matrix representations are used to reduce storage space, then zero values are discarded, but excessive metadata is required to track nonzero value positions
Solution Approach 1:
The patent applies local quality by using different metadata bit lengths for different position encodings. Specifically, it uses 2 bits for the first metadata value (encoding 4 possible positions) and 1 bit for the second metadata value (encoding 2 possible positions), rather than using uniform metadata length. This optimized local encoding reduces total metadata storage while maintaining the ability to represent all nonzero value positions.
3Adaptability or versatility
If more metadata bits are allocated per nonzero value, then more dense matrices can be expressed, but storage space increases and hardware efficiency decreases
Solution Approach 1:
The patent changes the parameter of metadata bit allocation from uniform to variable. By using 2 bits for the first metadata value and 1 bit for the second metadata value, it creates a variable-length encoding scheme that adapts to the specific sparsity pattern. This parameter change achieves full expressivity for the targeted sparsity levels while minimizing storage space and optimizing for hardware efficiency.
Data Source
AI summary
Disclosed are systems and techniques for compressing a dense matrix into a fully-expressive sparse matrix representation with limited metadata. The techniques include generating a sparse matrix with corresponding metadata based on a dense matrix. Generating the sparse matrix with corresponding metadata includes identifying a first number (M) of elements to compress, a second number (N) of elements to retain, and a third number (B) indicating the number of bits each metadata value uses; determining a metadata value for each of N elements of the dense matrix; packing a first metadata value having more than B bits into a second metadata value having B bits; and generating the sparse matrix containing the N elements of the dense matrix. The techniques include storing the sparse matrix and the corresponding metadata, wherein the corresponding metadata comprises the second metadata value.