Sparse Matrix Tiling for Parallel Processing Efficiency
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Solution Overview
Problem
Conventional compressed formats for sparse matrices are not optimized for highly parallel processors, leading to increased latencies and reduced processing efficiency due to uneven workload distribution and inefficient data access during matrix multiplication operations.
Innovation Solution
A tree structure is created to index nonzero elements in sparse matrices, allowing for recursive division into regions with balanced nonzero elements, enabling efficient access and distribution across multiple processing elements, and reducing data access during matrix operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional compressed formats (CSR/CSC) are used for sparse matrices, then storage efficiency is improved, but processing efficiency on parallel processors deteriorates due to uneven workload distribution and inefficient data access
Solution Approach 1:
The sparse matrix is divided into multiple rectangular tiles that partition the nonzero elements into balanced groups. Each tile contains a subset of nonzero elements with approximately equal counts, enabling even distribution across processing elements. The tiling strategy segments the matrix along both row and column dimensions to optimize for both row-based and column-based operations.
Solution Approach 2:
The invention introduces a two-dimensional tiling structure instead of conventional one-dimensional row or column-based compression. By organizing nonzero elements into 2D tiles with metadata specifying both row and column ranges, the format enables efficient access patterns in multiple dimensions simultaneously, resolving the contradiction between storage efficiency and parallel processing efficiency.
2Ease of operation
If nonzero elements are organized along entire rows (CSR format), then row-based access is simplified, but column access efficiency deteriorates and workload distribution becomes uneven
Solution Approach 1:
The matrix is segmented into rectangular tiles that span multiple rows and columns, rather than organizing all nonzero elements along entire rows. Each tile's metadata specifies row ranges and column ranges, enabling efficient column-based access within tile boundaries while maintaining row-based access simplicity.
Solution Approach 2:
Different regions of the matrix are organized into tiles with properties optimized for their specific access patterns. Each tile maintains local compactness and can be accessed efficiently in either row or column direction, providing locally optimized access patterns throughout the matrix.
3Quantity of substance
If conventional compressed formats are used, then storage compactness is improved, but parallel processing workload distribution deteriorates due to uneven nonzero element distribution
Solution Approach 1:
The sparse matrix is partitioned into multiple tiles that collectively distribute nonzero elements evenly across the matrix structure. The tiling algorithm ensures that each tile contains a balanced number of nonzero elements, which can then be assigned to different processing elements for uniform workload distribution during parallel operations.
Solution Approach 2:
The invention changes the organizational parameters of sparse matrix storage by introducing tile dimensions and metadata structures that track both row and column ranges. This parameter change enables the system to achieve both storage compactness and balanced workload distribution by controlling how nonzero elements are grouped and indexed.
Data Source
AI summary
One embodiment sets forth a technique for performing one or more matrix multiplication operations based on a first matrix and a second matrix. The technique includes receiving data associated with the first matrix from a first traversal engine that accesses nonzero elements included in the first matrix via a first tree structure. The technique also includes performing one or more computations on the data associated with the first matrix and the data associated with the second matrix to produce a plurality of partial results. The technique further includes combining the plurality of partial results into one or more intermediate results and storing the one or more intermediate results in a first buffer memory.