Sparse Matrix Tree Structure for GPU Load Balancing
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Solution Overview
Problem
Conventional compressed formats for sparse matrices are not optimized for highly parallel processors like GPUs, leading to increased latencies and reduced processing efficiency due to inefficient access patterns and imbalance in workload distribution.
Innovation Solution
A tree structure is used to represent a sparse matrix, allowing for efficient access and distribution of non-empty regions across multiple processing elements. This structure recursively divides the matrix into regions with similar numbers of nonzero elements, improving load balancing 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 to store sparse matrices, then storage efficiency is improved by omitting zero elements, but processing efficiency on parallel processors deteriorates due to inefficient access patterns and unbalanced workload distribution
Solution Approach 1:
The patent segments the sparse matrix into multiple tiles, where each tile is a submatrix containing a balanced number of nonzero elements. This segmentation enables parallel processors to work on independent tiles simultaneously, improving processing efficiency while maintaining storage efficiency through the compressed format.
Solution Approach 2:
The patent introduces a hierarchical structure with multiple levels of tiles, adding a dimensional aspect to the traditional flat CSR/CSC representation. This hierarchical organization allows for better load balancing and more efficient memory access patterns on parallel processors.
2Quantity of substance
If conventional compressed formats are used, then memory usage is reduced by storing only nonzero elements, but access latency increases due to inefficient data retrieval patterns
Solution Approach 1:
By dividing the sparse matrix into tiles with balanced nonzero element counts, the patent enables sequential or predictable access patterns during computation, reducing access latency while maintaining compact storage of only nonzero elements.
Solution Approach 2:
The patent performs preliminary organization of nonzero elements into balanced tiles during matrix storage, so that during subsequent operations, data can be accessed in an optimized sequence, reducing retrieval latency without increasing memory usage.
3Ease of operation
If rows are organized independently in CSR format, then row-based operations are simplified, but column lookup efficiency and load balancing across parallel processors deteriorate
Solution Approach 1:
The patent segments the matrix into tiles that balance the distribution of nonzero elements, enabling efficient column lookups and load balancing while maintaining the simplicity of row-based operations through the hierarchical structure.
Solution Approach 2:
The hierarchical tile structure serves multiple functions simultaneously: it maintains row-based operation simplicity, enables efficient column lookups, provides balanced load distribution, and supports parallel processing, making it a universal solution for various matrix operations.
Data Source
AI summary
One embodiment sets forth a technique for performing matrix operations. The technique includes traversing a tree structure to access one or more non-empty regions within a matrix. The tree structure includes a first plurality of nodes and a second plurality of nodes corresponding to non-empty regions in the matrix. The first plurality of nodes includes a first node representing a first region and one or more second nodes that are children of the first node and represent second region(s) with an equal size formed within the first region. The second plurality of nodes include a third node representing a third region and one or more fourth nodes that are children of the third node and represent fourth region(s) with substantially equal numbers of non-zero matrix values formed within the third region. The technique also includes performing matrix operation(s) based on the non-empty region(s) to generate a matrix operation result.