Mathematical visualization framework systematically derives optimal GPU implementations.
This paper introduces a diagrammatic approach to optimize deep learning algorithms for IO-awareness, particularly focusing on FlashAttention. It provides a systematic method to derive optimized implementations and performance models that consider memory hierarchy, helping achieve better hardware efficiency.
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https://arxiv.org/abs/2412.03317
🤔 Original Problem:
→ Current optimization of deep learning algorithms requires slow, manual derivation, potentially missing performance opportunities. Even successful optimizations like FlashAttention needed three iterations over three years, while automated methods consistently lag behind.
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🔧 Solution in this Paper:
→ The paper presents a diagrammatic scheme for representing deep learning algorithms based on Neural Circuit Diagrams.
→ These diagrams use alternating columns of data types and functions to represent algorithmic operations.
→ The approach allows for simple relabelings to derive optimal implementations and performance models.
→ The diagrams generalize down the GPU hierarchy, providing a universal model for comparing hardware and quantization choices.
→ The method reveals applications of hardware-specific features like coalesced memory access and tensor core operations.
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💡 Key Insights:
→ Memory bandwidth accounts for 46% of GPU energy costs, making IO-awareness crucial
→ The paper's approach fits 13 warps per SM compared to FlashAttention's 8
→ Diagrams can effectively model and optimize trade-offs between compute capability and memory bandwidth
→ The method enables systematic exploitation of hardware-specific features
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📊 Results:
→ Achieved 6x performance improvement over native PyTorch
→ Developed Hopper attention algorithm that may achieve 1.32 PFLOPs
→ Increased warps per SM from 8 to 13 compared to FlashAttention
