reasoning
Now let me write the optimized causal conv1d kernel. The key operations are:
1. Left pad with zeros (kernel_size - 1) * dilation elements
2. Apply convolution with dilation
The convolution formula for causal conv1d:
- For each output position t, we compute:
output[b, oc, t] = sum over (ic, k) of weight[oc, ic, k] * input[b, ic, t + (kernel_size - 1 - k) * dilation]
Actually, let me think more carefully. The PyTorch implementation:
1. Left-pads the input with causal_padding = (kernel_size - 1) * dilation zeros
2. Then applies a standard Conv1d with dilation
For a dilated convolution with padding P, the formula is:
- output[b, oc, t] = sum over (ic, k) of weight[oc, ic, k] * padded_input[b, ic, t + k * dilation]
- where padded_input has length seq_len + P
With left padding P = (kernel_size - 1) * dilation:
- At output position t, we access input positions: t + k*dilation - P
- When k=0: position t (in the padded input, this is the t-th element after the padding, which is the t-th element in the original input)
- When k=kernel_size-1: position t + (kernel_size-1)*dilation - P = t + P - P = t
So for causal convolution:
- output[b, oc, t] depends on input[b, ic, t - k*dilation] for k = 0 to kernel_size-1
- Wait, that's not right for the kernel order...
Let me reconsider. In PyTorch Conv1d:
- weight shape: [out_channels, in_channels, kernel_size]
- For dilated conv with dilation d:
output[n, oc, t] = sum_{ic=0}^{in_ch-1} sum_{k=0}^{ks-1} weight[oc, ic, k] * input[n, ic, t*d_s + k*d]
where d_s is the stride (default 1).
So for causal conv with left padding P:
- padded_input[n, ic, i] = 0 for i < P
- padded_input[n, ic, i] = original_input[n, ic, i - P] for i >= P
- output[n, oc, t] = sum_{ic, k} weight[oc, ic, k] * padded_input[n, ic, t + k*d]
For position t in the output:
- We need padded_input at positions t, t+d, t+2d, ..., t+(ks-1)*d
- For k=0: we need padded_input at t, which is original_input at t - P if t >= P, else 0
- For t < P (in the early part of the output), some padded_input values will be zero
- For the causal requirement: output at position t should only depend on original_input up to position t
With P = (ks-1)*d:
- padded_input at position t + k*d corresponds to original_input at t + k*d - P = t + k*d - (ks-1)*d
- For k=ks-1: original_input at t + (ks-1)*d - (ks-1)*d = t
- For k=0: original_input at t - (ks-1)*d
So output at position t depends on original_input from position t - (ks-1)*d to t, which is exactly causal!
Now for the kernel implementation, I want to:
1. Use shared memory to cache input tiles
2. Use coalesced memory access
3. Optimize for the case where kernel_size and dilation might be small
Let me design the kernel:
- Each thread block handles a subset of output positions
- Each thread can handle multiple output channels and/or multiple input channels
- Use shared memory to cache a tile of the input
Actually, for Conv1d, a common efficient approach is:
- Have each thread handle one output position (batch, out_channel, sequence_position)
- Load input values needed for that output position
- Accumulate the dot product
For better memory access, we can:
- Have threads in a warp cooperate on loading input values
- Use shared memory to cache a window of input values
Let me write a simple but correct implementation first:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
__global__ void causal_conv1d_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int batch_size,
int in_channels,
int out_channels,
int kernel_size,
int dilation,
int seq_len,
int causal_padding
) {
int t = blockIdx.x * blockDim.x + threadIdx.x; // output position
int oc = blockIdx.y; // output channel
int b = blockIdx.z; // batch
if (t >= seq_len || oc >= out_channels || b >= batch_size) return;
float sum = 0.0f;
for (int ic = 0; ic < in_channels; ic++) {
for (int k = 0; k < kernel_size; k++) {
int input_pos = t + k * dilation - causal_padding;
float input_val = 0.0f;
if (input_pos >= 0) {
input_val = input[b * in_channels * seq_len + ic * seq_len + input_pos];
}
int weight_idx = oc * in_channels * kernel_size + ic * kernel_size + k;
sum += input_val * weight[weight_idx];
}
}
if (bias != nullptr) {
sum += bias[oc];
}
output[b * out_channels * seq_len + oc * seq_len + t] = sum;
}
torch::Tensor causal_conv1d_cuda(
torch::Tensor input,
torch::Tensor weight,
c10::optional<torch::Tensor> bias,
int kernel_size,
int dilation
) {
int batch_size = input.size(0);
int in_channels = input.size(1);
int seq_len = input.size(2);
int out_channels = weight.size(0);
int causal_padding = (kernel_size - 1) * dilation;
auto output = torch::empty({batch_size, out_channels, seq_len}, input.options());
const int BLOCK_SIZE = 256;
dim3 blocks((seq_len + BLOCK_SIZE - 1) / BLOCK_SIZE, out_channels, batch_size);
causal_conv1d_kernel<<<blocks, BLOCK_SIZE>>>(
input.data_ptr<float>(),
weight.data_ptr<float>(),
bias.has_value() ? bias.value().data_ptr<float>() : nullptr,
output.data_ptr<float>(),
batch_size,
in_channels,
out_channels,
kernel_size,
dilation,
seq_len,
causal_padding
);
return output;
}
"""
cpp_source = "torch::Tensor causal_conv1d_cuda(torch::Tensor input, torch::Tensor weight, c10::optional<torch::Tensor> bias, int kernel_size, int dilation);"
causal_conv1d_op = load_inline(
name='causal_conv1d',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['causal_conv1d_cuda'],
extra_cuda_cflags=['-O3'],
verbose=True
)
class ModelNew(nn.Module):
def __init__(self, in_channels: int, out_channels: int, kernel_size: int, dilation: int = 1, bias: bool = False):
super(ModelNew, self).__init__()
self.kernel_size = kernel_size
self.dilation = dilation
# Create weight parameter same as Conv1d
self.weight = nn.Parameter(torch.empty(out_channels, in_channels, kernel_size))
nn.init.kaiming_uniform_(self.weight, a=5**0.5)
if bias:
self.bias = nn.Parameter(torch.empty(out_channels))
nn.init.zeros_(self.bias)
else:
self.register_parameter('bias', None)
def forward(self, x: torch.Tensor) -> torch.Tensor:
return causal_conv1d_op.causal_conv1d_cuda(x, self.weight, self.bias, self.kernel_size, self.dilation)
```
Actually, I realize the weight layout might be different. Let me check the Conv1d weight layout:
- nn.Conv1d weight shape: [out_channels, in_channels, kernel_size]
- The indexing should be correct.
But wait, I need to make sure I'm not creating the weights twice. The reference Model creates a Conv1d which has its own weights. I need to match the parameter initialization.
Let me refine the code:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
__global__ void causal_conv1d_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int batch_size,
int in_channels,
int out_channels,
int kernel_size,
int dilation,
int seq_len
) {
int t = blockIdx.x * blockDim.x + threadIdx.x; // output position
int oc = blockIdx.y; // output channel
int b = blockIdx.z; // batch
if (t >= seq_len || oc >= out_channels || b >= batch_size) return;
float sum = 0.0f;
int causal_padding = (kernel_size - 1) * dilation;
for (int ic = 0; ic < in_channels; ic++) {
for (int k = 0; k < kernel_size; k++) {
int input_pos = t + k * dilation - causal_padding;
float input_val = 0.0f;
if (input_pos >= 0) {
input_val = input[b * in_channels * seq_len + ic * seq_len + input_pos];
}
int weight_idx = oc * in_channels * kernel_size + ic * kernel_size + k;
sum += input_val * weight[weight_idx];
}
}
if (bias != nullptr) {
sum += bias[oc];
}
output[b * out_channels * seq_len + oc * seq_len + t] = sum;
}
torch::Tensor causal_conv1d_cuda(
torch::Tensor input,
torch::Tensor weight,
c10::optional<torch::Tensor> bias,
int kernel_size,
int dilation
) {
int batch_size = input.size(0);
int in_channels = input.size(1);
int seq_len = input.size(2);
int out_channels = weight.size(0);
auto output = torch::empty({batch_size, out_channels, seq_len}, input.options());
const int BLOCK_SIZE = 256;
dim3 blocks((seq_len + BLOCK_SIZE - 1) / BLOCK_SIZE, out_channels, batch_size);
causal_conv1d_kernel<<<blocks, BLOCK_SIZE>>>(
input.data_ptr<float>(),
weight.data_ptr<float>(),
bias.has_value() ? bias.value().data_ptr<float>() : nullptr,
output.data_ptr<float>(),
batch_size,
in_channels,
out_channels,
kernel_size,
dilation,
seq_len
);
return output;
}
"""
cpp_source = "torch::Tensor causal_conv1d_cuda(torch::Tensor input, torch::Tensor weight, c10::optional<torch::Tensor> bias, int kernel_size, int dilation);"
causal_conv1d_op = load_inline(
name='causal_conv1d',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['causal_conv1d_cuda'],
extra_cuda_cflags=['-O3'],
verbose=True
)
class ModelNew(nn.Module):
def __init__(self, in_channels: int, out_channels: int, kernel_size: int, dilation: int = 1, bias: bool = False):
super(ModelNew, self).__init__()
self.kernel_size = kernel_size
self.dilation = dilation
# Create weight parameter same as Conv1d
self.weight = nn.Parameter(torch.empty(out_channels, in_channels, kernel_size))
nn.init.kaiming_uniform_(self.weight, a=5**0.5)
if bias:
self.bias = nn.Parameter(torch.empty(out_channels))
fan_in = in_channels * kernel_size
bound = 1 / sqrt(fan_in) if fan_in > 0 else 0
nn.init.uniform_(self.bias, -bound, bound)
else:
self.register_parameter('bias', None)
def forward(self, x: torch.Tensor) -> torch.Tensor:
return causal_conv1d_op.causal_conv1d_cuda(x, self.weight, self.bias, self.kernel_size, self.dilation)
```
Let me try this first and see if it compiles and is correct.
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport math\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void causal_conv1d_kernel(\n const float* __restrict__ input,\n const float* __restrict__ weight,\n const float* __restrict__ bias,\n float* __restrict__ output,\n int batch_size,\n int in_channels,\n int out_channels,\n int kernel_size,\n int dilation,\n int seq_len\n) {\n int t = blockIdx.x * blockDim.x + threadIdx.x; // output position\n int oc = blockIdx.y; // output channel\n int b = blockIdx.z; // batch\n \n if (t >= seq_len || oc >= out_channels || b >= batch_size) return;\n \n float sum = 0.0f;\n int causal_padding = (kernel_size - 1) * dilation;\n \n for (int ic = 0; ic < in_channels; ic++) {\n for (int k = 0; k < kernel_size; k++) {\n int input_pos = t + k * dilation - causal_padding;\n float input_val = 0.0f;\n if (input_pos >= 0) {\n input_val = input[b * in_channels * seq_len + ic * seq_len + input_pos];\n }\n int weight_idx = oc * in_channels * kernel_size + ic * kernel_size + k;\n sum += input_val * weight[weight_idx];\n }\n }\n \n if (bias != nullptr) {\n sum += bias[oc];\n }\n \n output[b * out_channels * seq_len + oc * seq_len + t] = sum;\n}\n\ntorch::Tensor causal_conv1d_cuda(\n torch::Tensor input,\n torch::Tensor weight,\n c10::optional<torch::Tensor> bias,\n int kernel_size,\n int dilation\n) {\n int batch_size = input.size(0);\n int in_channels = input.size(1);\n int seq_len = input.size(2);\n int out_channels = weight.size(0);\n \n auto output = torch::empty({batch_size, out_channels, seq_len}, input.options());\n \n const int BLOCK_SIZE = 256;\n dim3 blocks((seq_len + BLOCK_SIZE - 1) / BLOCK_SIZE, out_channels, batch_size);\n \n causal_conv1d_kernel<<<blocks, BLOCK_SIZE>>>(\n input.data_ptr<float>(),\n weight.data_ptr<float>(),\n bias.has_value() ? bias.value().data_ptr<float>() : nullptr,\n output.data_ptr<float>(),\n batch_size,\n in_channels,\n out_channels,\n kernel_size,\n dilation,\n seq_len\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"torch::Tensor causal_conv1d_cuda(torch::Tensor input, torch::Tensor weight, c10::optional<torch::Tensor> bias, int kernel_size, int dilation);\"\n\ncausal_conv1d_op = load_inline(\n name='causal_conv1d_v1',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['causal_conv1d_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, in_channels: int, out_channels: int, kernel_size: int, dilation: int = 1, bias: bool = False):\n super(ModelNew, self).__init__()\n self.kernel_size = kernel_size\n self.dilation = dilation\n \n # Create weight parameter same as Conv1d\n self.weight = nn.Parameter(torch.empty(out_channels, in_channels, kernel_size))\n nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))\n \n if bias:\n self.bias = nn.Parameter(torch.empty(out_channels))\n fan_in = in_channels * kernel_size\n bound = 1 / math.sqrt(fan_in) if fan_in > 0 else 0\n nn.init.uniform_(self.bias, -bound, bound)\n else:\n self.register_parameter('bias', None)\n \n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return causal_conv1d_op.causal_conv1d_cuda(x, self.weight, self.bias, self.kernel_size, self.dilation)"
}