The math behind tiled v/s naive matrix multiplication in CUDA
4 days ago
- #deep learning
- #matrix multiplication
- #optimization
- Matrix multiplication is optimized using 'tiling' to improve resource utilization in power, memory, and compute.
- Tiling reduces latency by decreasing memory accesses, crucial for models like transformers that rely on dense matrix multiplication.
- The technique involves reusing rows and columns of matrices to minimize fetches, reducing total memory accesses by a factor of the block size.
- Parallelization and better memory management are key benefits of tiling, making matrix multiplication faster.
- Hardware memory constraints limit the block size, but strategies like partial fetching can help mitigate these limits.
- Tiling's effectiveness is quantified by the reduction in memory accesses, which scales with the block size.
- The post concludes with practical considerations for implementing tiling, including memory subsystem hierarchies and block size trade-offs.