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composable_kernel/example/21_gemm_layernorm/README.md
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2.2 KiB

GEMM with LayerNorm Fusion

Theory

This example demonstrates GEMM fused with layer normalization. This pattern is used in transformer feed-forward networks and other architectures where a linear transformation is followed by normalization for improved training stability.

Mathematical Formulation:

  • GEMM: Y = A \times B
  • LayerNorm: \text{LayerNorm}(Y) = \gamma \cdot \frac{Y - \mu}{\sqrt{\sigma^2 + \epsilon}} + \beta
    • \mu: mean of Y over the normalization axis
    • \sigma^2: variance of Y over the normalization axis
    • \gamma, \beta: learnable scale and shift parameters

Algorithmic Background:

  • The GEMM result is kept in registers, and layer normalization is applied before writing to global memory.
  • LayerNorm is typically applied over the last dimension (features).
  • This fusion reduces memory traffic and is common in transformer MLP blocks.

How to Run

Prerequisites

Please follow the instructions in the main Build Guide section as a prerequisite to building and running this example.

Build and run

cd composable_kernel/example/21_gemm_layernorm
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j

# Example run
./gemm_layernorm_xdl --verify=1 --time=1

Source Code Structure

Directory Layout

example/21_gemm_layernorm/
├── gemm_layernorm_xdl.cpp         # Main example: sets up, runs, and verifies GEMM+LayerNorm
include/ck/tensor_operation/gpu/device/
│   └── device_gemm_layernorm.hpp       # Device-level GEMM+LayerNorm API
include/ck/tensor_operation/gpu/device/impl/
│   └── device_gemm_layernorm_impl.hpp  # Implementation
include/ck/tensor_operation/gpu/grid/
    └── gridwise_gemm_layernorm.hpp     # Grid-level kernel

Key Classes and Functions

  • DeviceGemmLayerNorm (in device_gemm_layernorm.hpp):
    Device API for GEMM fused with layer normalization.
  • gridwise_gemm_layernorm (in gridwise_gemm_layernorm.hpp):
    Implements the tiled/blocking GEMM kernel with layer normalization epilogue.

This example demonstrates how Composable Kernel supports efficient fusion of linear and normalization layers for transformer and deep learning models.