composable_kernel/example/21_gemm_layernorm

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.