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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 ofYover the normalization axis\sigma^2: variance ofYover 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
cd composable_kernel/build
make -j install
Build and Execute
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.template <typename ALayout, typename BLayout, typename DsLayout, typename ELayout, typename ADataType, typename BDataType, typename DsDataType, typename EDataType, typename AElementwiseOperation, typename BElementwiseOperation, typename CDEElementwiseOperation> struct DeviceGemmLayerNorm : public BaseOperator - 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.