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2D Layer Normalization Forward
Theory
This example demonstrates 2D layer normalization forward pass. Layer normalization is used in transformers and other neural networks to normalize activations across the feature dimension, improving training stability.
Mathematical Formulation:
Given input X[N, C, H, W]:
- Mean:
\mu = \frac{1}{CHW} \sum_{c,h,w} X_{n,c,h,w} - Variance:
\sigma^2 = \frac{1}{CHW} \sum_{c,h,w} (X_{n,c,h,w} - \mu)^2 - Normalized:
\hat{X}_{n,c,h,w} = \frac{X_{n,c,h,w} - \mu}{\sqrt{\sigma^2 + \epsilon}} - Output:
Y_{n,c,h,w} = \gamma \hat{X}_{n,c,h,w} + \beta
\gamma, \beta are learnable scale and shift parameters.
Algorithmic Background:
- Computes mean and variance per sample (across all features).
- Applies normalization and affine transformation.
- Used in transformer blocks and normalization layers.
How to Run
Prerequisites
cd composable_kernel/build
make -j install
Build and Execute
cd composable_kernel/example/27_layernorm2d_fwd
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j
# Example run
./layernorm2d_fwd_xdl --verify=1 --time=1
Source Code Structure
Directory Layout
example/27_layernorm2d_fwd/
├── layernorm2d_fwd_xdl.cpp # Main example: sets up, runs, and verifies 2D layernorm
include/ck/tensor_operation/gpu/device/
│ └── device_layernorm_fwd.hpp # Device-level layernorm API
include/ck/tensor_operation/gpu/device/impl/
│ └── device_layernorm_fwd_impl.hpp # Implementation
include/ck/tensor_operation/gpu/grid/
└── gridwise_layernorm_fwd.hpp # Grid-level kernel
Key Classes and Functions
- DeviceLayernormFwd (in
device_layernorm_fwd.hpp):
Device API for layer normalization.template <typename XDataType, typename GammaBetaDataType, typename YDataType, typename MeanVarDataType, typename XElementwiseOperation, typename YElementwiseOperation> struct DeviceLayernormFwd : public BaseOperator - gridwise_layernorm_fwd (in
gridwise_layernorm_fwd.hpp):
Implements the tiled/blocking layernorm kernel.
This example demonstrates how Composable Kernel implements efficient layer normalization for transformer and deep learning models.