SABLE: Staging Blocked Evaluation of Sparse Matrix Computations

2024-04-03

AI Summary

Existing sparse matrix optimization methods often coarsely classify structured sparsity (e.g., clustered non-zeros) as either fully dense or fully sparse, leading to redundant zero computations in fixed-block formats (e.g., BCSR) or substantial overhead in variable-block approaches due to unknown loop bounds at compile time. This work proposes a region-aware, multi-stage compilation framework that automatically identifies high-benefit variable-size blocks, statically infers dynamic loop bounds, and generates customized vectorized code—balancing efficiency and adaptability. Key techniques include sparse partition analysis, domain-specific code generation, loop vectorization, and compile-time scheduling specialization. Evaluated on the SuiteSparse dataset, our approach achieves 1.07×, 2.73×, and 1.9× higher single-threaded SpMV performance over Intel MKL, CSR5, and Partial Strided Codelets, respectively; parallel scalability further enhances throughput.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Structured sparsity, like regions of non-zero elements in sparse matrices, can offer optimization opportunities often overlooked by existing solutions that treat matrices as entirely dense or sparse. Block-based approaches, such as BCSR, partially address this issue by choosing between fixed-size blocks which results in wasted computation on zero elements. On the other hand, variable-sized blocks introduce overheads due to variable loop bounds unknown at compile time. We present SABLE, a novel staging framework that achieves the best of both approaches by generating region-specific code tailored for variable-sized blocks. SABLE partitions the matrix to identify profitable blocks and specializes generated code for vectorization. We evaluate SABLE on the SpMV kernel using the SuiteSparse collection. SABLE achieves a geomean of $1.07$, $2.73$ and $1.9$ speedup over the state of the art systems: Intel MKL, CSR5 and Partially-Strided Codelets, respectively, single threaded and even more when parallelized.

Problem

• Optimizing sparse matrix computations with structured sparsity
• Reducing wasted computation on zero elements in blocks
• Overcoming overheads from variable-sized block processing

Innovation

• Staging framework for variable-sized blocks
• Region-specific code generation for optimization
• Matrix partitioning for vectorization specialization