Sparse Matrix Compression via Global Sparsity Constraints
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Solution Overview
Problem
Current approaches for sparse matrix operations in high-performance computing, particularly in deep learning, face challenges in efficiently utilizing sparsity to reduce computational load and memory overhead, as conventional methods require significant overhead and irregular computations, limiting the realization of processing speed improvements even with high sparsity levels.
Innovation Solution
Applying a global sparsity constraint across submatrices to evenly distribute non-zero values, allowing for compression and efficient processing by skipping zero-value elements, thereby reducing computational load and improving processing speed through fine-grained structured sparsity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional sparse matrix operations are used, then sparsity can be represented, but significant overhead and irregular computations prevent efficient utilization of sparsity
Solution Approach 1:
The patent divides the sparse matrix into multiple submatrices and processes them in parallel using tensor core instructions. This segmentation allows regular computation patterns to be applied to each submatrix independently, eliminating the irregular computations that plague conventional sparse matrix operations while maintaining sparsity benefits.
Solution Approach 2:
The patent transforms the sparse matrix operation into a structured format with controlled sparsity patterns, changing the parameter of sparsity distribution from arbitrary to structured. This enables the use of high-performance dense matrix multiplication instructions while still achieving sparsity benefits through carefully controlled zero-value element distribution.
2Reliability
If zero-value elements are stored and processed, then complete data representation is maintained, but memory overhead and processing time increase significantly
Solution Approach 1:
The patent extracts and removes zero-value elements from the computation by structuring the sparse matrix so that zeros are positioned in a predictable pattern. This allows the computation to proceed using only non-zero elements, eliminating memory overhead for storing and processing zero values while maintaining computational accuracy through the structured sparsity constraint.
Solution Approach 2:
The patent applies a sparsity constraint that allows some zero-value elements to remain in the matrix, accepting partial sparsity rather than complete sparsity. This balanced approach maintains enough data representation for accuracy while significantly reducing memory overhead compared to storing all elements including zeros.
3Productivity
If large dense matrix computation is performed, then high performance is achieved for training and inferencing, but computational cost becomes expensive
Solution Approach 1:
The patent applies different computation strategies to different parts of the matrix based on local sparsity characteristics. By dividing the sparse matrix into submatrices with controlled sparsity patterns, each submatrix can be processed using optimized tensor core instructions, achieving high performance locally while reducing overall computational cost through the structured sparsity approach.
Data Source
AI summary
Approaches in accordance with various embodiments provide for the processing of sparse matrices for mathematical and programmatic operations. In particular, various embodiments enforce sparsity constraints for performing sparse matrix multiply-add instruction (MMA) operations. Deep neural networks can exhibit significant sparsity in the data used in operations, both in the activations and weights. The computational load can be reduced by excluding zero-valued data elements. A sparsity constraint is applied across all submatrices of a sparse matrix, providing fine-grained structured sparsity that is evenly distributed across the matrix. The matrix may then be compressed since a minimum number of elements of the matrix are known to have zero value. Matrix operations are then performed using these matrices.