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81 lines
3.1 KiB
Markdown
81 lines
3.1 KiB
Markdown
# N-Dimensional Convolution Forward
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## Theory
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This example demonstrates the **N-dimensional convolution forward pass** using Composable Kernel. Convolution is a fundamental operation in deep learning, especially in convolutional neural networks (CNNs) for images, audio, and volumetric data.
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**Mathematical Formulation:**
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Given:
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- Input tensor: $X[N, C_{in}, D_1, D_2, ..., D_n]$
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- Weight tensor: $W[C_{out}, C_{in}, K_1, K_2, ..., K_n]$
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- Output tensor: $Y[N, C_{out}, O_1, O_2, ..., O_n]$
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The convolution computes:
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$$
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Y[n, c_{out}, o_1, ..., o_n] = \sum_{c_{in}} \sum_{k_1} ... \sum_{k_n} X[n, c_{in}, o_1 + k_1, ..., o_n + k_n] \cdot W[c_{out}, c_{in}, k_1, ..., k_n]
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$$
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Stride, padding, and dilation parameters control the mapping between input and output indices.
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**Algorithmic Background:**
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- Composable Kernel implements convolution as an implicit GEMM (matrix multiplication) for efficiency.
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- The input and weight tensors are transformed into matrices, and the convolution is performed as a GEMM.
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## How to Run
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### Prerequisites
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Please follow the instructions in the main [Build Guide](../../README.md#building-ck) section as a prerequisite to building and running this example.
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### Build and run
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```bash
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cd composable_kernel/example/09_convnd_fwd
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mkdir build && cd build
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cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
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make -j
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```
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### Run ```example_convnd_fwd_xdl```
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```bash
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#arg1: verification (0=no, 1=yes)
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#arg2: initialization (0=no init, 1=integer value, 2=decimal value)
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#arg3: run kernel # of times (>1)
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#arg4: N spatial dimensions (default 2)
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#Following arguments (depending on number of spatial dims):
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# N, K, C,
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# <filter spatial dimensions>, (ie Y, X for 2D)
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# <input image spatial dimensions>, (ie Hi, Wi for 2D)
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# <strides>, (ie Sy, Sx for 2D)
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# <dilations>, (ie Dy, Dx for 2D)
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# <left padding>, (ie LeftPy, LeftPx for 2D)
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# <right padding>, (ie RightPy, RightPx for 2D)
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./bin/example_convnd_fwd_xdl 0 1 100
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```
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## Source Code Structure
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### Directory Layout
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```
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example/09_convnd_fwd/
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├── convnd_fwd_xdl.cpp # Main example: sets up, runs, and verifies N-D convolution
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include/ck/tensor_operation/gpu/device/
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│ └── device_convnd_fwd.hpp # Device-level convolution API
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include/ck/tensor_operation/gpu/device/impl/
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│ └── device_convnd_fwd_xdl.hpp # XDL-based convolution implementation
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include/ck/tensor_operation/gpu/grid/
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│ └── gridwise_convnd_fwd_xdl.hpp # Grid-level convolution kernel
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include/ck/tensor_operation/gpu/block/
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└── blockwise_convnd_fwd_xdl.hpp # Block-level convolution
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```
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### Key Classes and Functions
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- **DeviceConvNdFwd** (in `device_convnd_fwd.hpp`):
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Device API for N-dimensional convolution.
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- **gridwise_convnd_fwd_xdl** (in `gridwise_convnd_fwd_xdl.hpp`):
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Implements the tiled/blocking convolution kernel.
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- **blockwise_convnd_fwd_xdl** (in `blockwise_convnd_fwd_xdl.hpp`):
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Handles block-level computation and shared memory tiling.
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This example demonstrates how Composable Kernel implements efficient N-dimensional convolution using implicit GEMM, supporting a wide range of deep learning applications.
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