ENTERPRISE AI ANALYSIS
Space Filling Curves is All You Need: Communication-Avoiding Matrix Multiplication Made Simple
This research introduces SFC-CA GEMM, a novel, communication-avoiding algorithm for General Matrix Multiplication. It leverages Space Filling Curves to achieve platform-oblivious and shape-oblivious matrix multiplication with high data locality and provably minimal data movement. Outperforming state-of-the-art vendor libraries by up to 5.5x, SFC-CA GEMM demonstrates significant speedups in LLM inference (up to 1.85x) and distributed-memory Matrix Multiplication (up to 2.2x), making it a compact, efficient, and tunable solution for HPC and Deep Learning workloads.
Executive Impact & Key Metrics
Our analysis identifies the following key areas of impact and performance gains achieved by implementing SFC-CA GEMM.
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Max Speedup (vs. oneDNN)
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Weighted Harmonic Mean Speedup
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Lines of Code (Core Algo)
Deep Analysis & Enterprise Applications
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SFC-CA GEMM Algorithm
Performance Benchmarking
LLM Inference Acceleration
Distributed MM Efficiency
The SFC-CA GEMM algorithm leverages Generalized Hilbert Curves to partition the matrix multiplication computation space, ensuring inherent data locality. It integrates Communication-Avoiding 2.5D algorithms seamlessly, providing a compact and efficient solution for various CPU platforms.
Extensive benchmarking on contemporary CPU platforms (x86 and Arm) shows SFC-CA GEMM consistently outperforms vendor-optimized libraries across diverse GEMM shapes and aspect ratios. The algorithm exhibits State-Of-The-Art performance with significant speedups and close tracking of roofline models.
Integration of SFC-CA GEMM as a compute backend in a SOTA CPU LLM inference framework (PyTorch-TPP) dramatically accelerates the compute-heavy prefill stage. This demonstrates its practical impact on real-world AI applications.
Leveraging SFC-CA GEMM as a backend for distributed-memory Matrix Multiplication within the COSMA framework resulted in substantial speedups, proving its scalability and efficiency in high-performance computing environments.
Enterprise Process Flow
Block M, K, N dimensions
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Create SFC map for Mb x Nb grid
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Partition K dimension (K_layers)
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Iterate K-blocks (k_block_factor)
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Map SFC index to C block (im, in)
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Perform BRGEMM contraction (A, B, C)
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Reduce C matrices (if K_layers > 1)
49.1 TFLOPS
TFLOPS (WHM, EMR)
LLM Prefill Speedup (Llama-3 8B, BF16)
Our SFC-CA GEMM solution, when integrated into PyTorch-TPP, achieved up to 1.85x speedup over SOTA inference pipelines using vendor-optimized libraries during the prefill stage of LLM inference (Llama-3 8B model with BF16 precision) on Intel Xeon Granite Rapids (GNR). This significantly reduces latency for large batch sizes and input lengths, demonstrating superior performance robustness compared to PARLOOPER-based GEMMs which showed performance degradation.
| Feature | SFC-CA GEMM Backend | COSMA with oneDNN Backend |
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| Performance on EMR (32k×32k×32k) |
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| Compute Throughput (Initial Scale) |
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| Strong Scaling Efficiency |
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Advanced ROI Calculator
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Potential Annual Savings
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Hours Reclaimed Annually
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Implementation Roadmap
A structured approach to integrate SFC-CA GEMM into your enterprise, ensuring maximum impact and minimal disruption.
Phase 1: Initial Assessment & Strategy
Identify current bottlenecks in GEMM workloads and define key performance targets. Develop a tailored strategy for integrating SFC-CA GEMM.
Phase 2: PoC & Customization
Implement a Proof-of-Concept leveraging SFC-CA GEMM for critical kernels. Customize parameters and integrate with existing HPC/DL frameworks.
Phase 3: Full-Scale Deployment & Optimization
Roll out SFC-CA GEMM across all relevant applications. Conduct continuous monitoring and optimization to maximize long-term ROI.
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