N-Dimensional Convolution Forward with Bias

Theory

This example demonstrates N-dimensional convolution forward with bias addition. This is a common pattern in convolutional neural networks (CNNs), where a bias term is added to each output channel after the convolution operation.

Mathematical Formulation: $$ Y[n, c_{out}, o_1, ..., o_n] = \sum_{c_{in}} \sum_{k_1} ... \sum_{k_n} X[n, c_{in}, o_1 + k_1, ..., o_n + k_n] \cdot W[c_{out}, c_{in}, k_1, ..., k_n] + B[c_{out}] $$

• $X$: [N, C_in, D1, D2, ..., Dn] input tensor
• $W$: [C_out, C_in, K1, K2, ..., Kn] weight tensor
• $B$: [C_out] bias tensor
• $Y$: [N, C_out, O1, O2, ..., On] output tensor

Algorithmic Background:

• Composable Kernel implements convolution as an implicit GEMM, with bias addition fused in the epilogue for efficiency.

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/11_convnd_fwd_bias
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j

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

Source Code Structure

Directory Layout

example/11_convnd_fwd_bias/
├── convnd_fwd_bias_xdl.cpp         # Main example: sets up, runs, and verifies N-D convolution with bias
include/ck/tensor_operation/gpu/device/
│   └── device_convnd_fwd_bias.hpp       # Device-level convolution API with bias
include/ck/tensor_operation/gpu/device/impl/
│   └── device_convnd_fwd_bias_impl.hpp  # Implementation
include/ck/tensor_operation/gpu/grid/
    └── gridwise_convnd_fwd_bias.hpp     # Grid-level kernel

Key Classes and Functions

• DeviceConvNdFwdBias (in device_convnd_fwd_bias.hpp):
  Device API for N-dimensional convolution with bias.
• gridwise_convnd_fwd_bias (in gridwise_convnd_fwd_bias.hpp):
  Implements the tiled/blocking convolution kernel with bias epilogue.

This example demonstrates how Composable Kernel fuses bias addition into the convolution forward pass for efficient CNN layer implementation.