GEMM with Bias, Elementwise, and Permute Fusion

Theory

This example demonstrates GEMM fused with bias addition, elementwise operation, and permutation. This pattern is used in transformer models and other neural architectures where a linear transformation is followed by bias, activation, and layout transformation.

Mathematical Formulation:

• GEMM: $Y = A \times B$
• Bias: $Z = Y + \text{bias}$
• Elementwise: $E = f(Z)$ (e.g., activation)
• Permute: $O = \text{permute}(E, \text{axes})$

Algorithmic Background:

• The GEMM result is kept in registers, bias and elementwise ops are fused in the epilogue, and permutation is applied before writing to global memory.
• Permutation changes the layout/order of tensor axes (e.g., NCHW to NHWC).
• This fusion reduces memory traffic and is common in transformer and CNN pipelines.

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/25_gemm_bias_e_permute
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j

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

Source Code Structure

Directory Layout

example/25_gemm_bias_e_permute/
├── gemm_bias_e_permute_xdl.cpp         # Main example: sets up, runs, and verifies GEMM+Bias+Elementwise+Permute
include/ck/tensor_operation/gpu/device/
│   └── device_gemm_bias_e_permute.hpp       # Device-level API for fused GEMM
include/ck/tensor_operation/gpu/device/impl/
│   └── device_gemm_bias_e_permute_impl.hpp  # Implementation
include/ck/tensor_operation/gpu/grid/
    └── gridwise_gemm_bias_e_permute.hpp     # Grid-level kernel

Key Classes and Functions

• DeviceGemmBiasEPermute (in device_gemm_bias_e_permute.hpp):
  Device API for GEMM fused with bias, elementwise, and permutation.
• gridwise_gemm_bias_e_permute (in gridwise_gemm_bias_e_permute.hpp):
  Implements the tiled/blocking GEMM kernel with fused epilogue and permutation.

This example demonstrates how Composable Kernel supports efficient fusion of linear, bias, activation, and layout operations for deep learning models.