You write custom CUDA kernels to replace the pytorch operators in the given architecture to get speedups. 

    You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.


        Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is: 

        ``` 

        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()

    def forward(self, a, b):
        return a + b


def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]


def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

        ``` 

        The example new arch with custom CUDA kernels looks like this:
        ```
        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline

# Define the custom CUDA kernel for element-wise addition
elementwise_add_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>

__global__ void elementwise_add_kernel(const float* a, const float* b, float* out, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        out[idx] = a[idx] + b[idx];
    }
}

torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b) {
    auto size = a.numel();
    auto out = torch::zeros_like(a);

    const int block_size = 256;
    const int num_blocks = (size + block_size - 1) / block_size;

    elementwise_add_kernel<<<num_blocks, block_size>>>(a.data_ptr<float>(), b.data_ptr<float>(), out.data_ptr<float>(), size);

    return out;
}
"""

elementwise_add_cpp_source = (
    "torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b);"
)

# Compile the inline CUDA code for element-wise addition
elementwise_add = load_inline(
    name="elementwise_add",
    cpp_sources=elementwise_add_cpp_source,
    cuda_sources=elementwise_add_source,
    functions=["elementwise_add_cuda"],
    verbose=True,
    extra_cflags=[""],
    extra_ldflags=[""],
)


class ModelNew(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.elementwise_add = elementwise_add

    def forward(self, a, b):
        return self.elementwise_add.elementwise_add_cuda(a, b)

        ``` 

        
    You are given the following architecture: 

    ```
    # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn

class Model(nn.Module):
    """
    Performs a depthwise 2D convolution with asymmetric input and asymmetric kernel.

    Args:
        in_channels (int): Number of channels in the input tensor.
        out_channels (int): Number of channels produced by the convolution.
        kernel_size_h (int): Height of the convolution kernel.
        kernel_size_w (int): Width of the convolution kernel.
        stride_h (int, optional): Stride of the convolution in height dimension. Defaults to 1.
        stride_w (int, optional): Stride of the convolution in width dimension. Defaults to 1.
        padding_h (int, optional): Padding applied to the input in height dimension. Defaults to 0.
        padding_w (int, optional): Padding applied to the input in width dimension. Defaults to 0.
        dilation_h (int, optional): Spacing between kernel elements in height dimension. Defaults to 1.
        dilation_w (int, optional): Spacing between kernel elements in width dimension. Defaults to 1.
        groups (int, optional): Number of blocked connections from input channels to output channels. Defaults to 1.
        bias (bool, optional): If `True`, adds a learnable bias to the output. Defaults to `False`.
    """
    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int, stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0, dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):
        super(Model, self).__init__()
        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w), stride=(stride_h, stride_w), padding=(padding_h, padding_w), dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)
        
    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Performs the depthwise 2D convolution.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_channels, height, width).

        Returns:
            torch.Tensor: Output tensor of shape (batch_size, out_channels, height_out, width_out).
        """
        return self.conv2d(x)

# Test code
batch_size = 32
in_channels = 128
out_channels = 128
kernel_size_h = 3
kernel_size_w = 7
width = 256
height = 128
stride_h = 1
stride_w = 1
padding_h = 0
padding_w = 0
dilation_h = 1
dilation_w = 1
groups = in_channels

def get_inputs():
    x = torch.rand(batch_size, in_channels, height, width)
    return [x]

def get_init_inputs():
    return [in_channels, out_channels, kernel_size_h, kernel_size_w, stride_h, stride_w, padding_h, padding_w, dilation_h, dilation_w, groups]
    ```
    
Optimize the architecture named Model with custom CUDA operators! Name your optimized output architecture ModelNew. Output the new code in codeblocks. Please generate real code, NOT pseudocode, make sure the code compiles and is fully functional. Just output the new model code, no other text, and NO testing code! 



This is turn 5 of 6 for this task. Your previous solution (turn 4) was:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor depthwise_3x7_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

__device__ __forceinline__ void accumulate_eight(
    float (&sum)[8],
    const float (&values)[14],
    const float* __restrict__ weights)
{
    #pragma unroll
    for (int k = 0; k < 7; ++k) {
        const float w = weights[k];
        #pragma unroll
        for (int j = 0; j < 8; ++j)
            sum[j] = fmaf(values[j + k], w, sum[j]);
    }
}

template<int ROWS>
__global__ __launch_bounds__(128)
void depthwise_3x7_eight_kernel(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels,
    int height)
{
    constexpr int WIDTH = 256;

    const int lane = threadIdx.x & 31;
    const int row_group = threadIdx.x >> 5;
    const int y0 = blockIdx.x * (4 * ROWS) + row_group * ROWS;
    const int out_height = height - 2;

    if (y0 >= out_height)
        return;

    const int plane = blockIdx.y;
    const int channel = plane % channels;
    const int column = lane * 8;

    const float* __restrict__ source =
        input + static_cast<int64_t>(plane) * height * WIDTH
              + static_cast<int64_t>(y0) * WIDTH + column;

    float weights[21];
    #pragma unroll
    for (int k = 0; k < 21; ++k)
        weights[k] = __ldg(weight + channel * 21 + k);

    float sums[ROWS][8];
    #pragma unroll
    for (int r = 0; r < ROWS; ++r) {
        #pragma unroll
        for (int j = 0; j < 8; ++j)
            sums[r][j] = 0.f;
    }

    #pragma unroll
    for (int r = 0; r < ROWS + 2; ++r) {
        float4 a = make_float4(0.f, 0.f, 0.f, 0.f);
        float4 b = make_float4(0.f, 0.f, 0.f, 0.f);
        float4 c = make_float4(0.f, 0.f, 0.f, 0.f);
        float2 d = make_float2(0.f, 0.f);

        if (y0 + r < height) {
            const float* row = source + r * WIDTH;
            a = __ldg(reinterpret_cast<const float4*>(row));
            b = __ldg(reinterpret_cast<const float4*>(row + 4));
            if (lane < 31) {
                c = __ldg(reinterpret_cast<const float4*>(row + 8));
                d = __ldg(reinterpret_cast<const float2*>(row + 12));
            }
        }

        const float values[14] = {
            a.x, a.y, a.z, a.w,
            b.x, b.y, b.z, b.w,
            c.x, c.y, c.z, c.w,
            d.x, d.y
        };

        if (r < ROWS)
            accumulate_eight(sums[r], values, weights);
        if (r >= 1 && r < ROWS + 1)
            accumulate_eight(sums[r - 1], values, weights + 7);
        if (r >= 2)
            accumulate_eight(sums[r - 2], values, weights + 14);
    }

    const float bv = bias ? __ldg(bias + channel) : 0.f;
    float* __restrict__ destination =
        output + static_cast<int64_t>(plane) * out_height * WIDTH
               + static_cast<int64_t>(y0) * WIDTH + column;

    #pragma unroll
    for (int r = 0; r < ROWS; ++r) {
        if (y0 + r < out_height) {
            float4* dst = reinterpret_cast<float4*>(
                destination + r * WIDTH);
            dst[0] = make_float4(
                sums[r][0] + bv,
                sums[r][1] + bv,
                sums[r][2] + bv,
                sums[r][3] + bv);
            dst[1] = make_float4(
                sums[r][4] + bv,
                sums[r][5] + bv,
                sums[r][6] + bv,
                sums[r][7] + bv);
        }
    }
}

torch::Tensor depthwise_3x7_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias)
{
    TORCH_CHECK(input.is_cuda() && weight.is_cuda(),
                "Input and weight must be CUDA tensors");
    TORCH_CHECK(input.device() == weight.device(), "Device mismatch");
    TORCH_CHECK(input.scalar_type() == at::kFloat &&
                weight.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(input.is_contiguous() && weight.is_contiguous(),
                "Expected contiguous tensors");
    TORCH_CHECK(input.dim() == 4 &&
                input.size(2) >= 3 && input.size(3) == 256,
                "Expected NCHW input with width 256 and height >= 3");
    TORCH_CHECK(weight.dim() == 4 &&
                weight.size(0) == input.size(1) &&
                weight.size(1) == 1 &&
                weight.size(2) == 3 &&
                weight.size(3) == 7,
                "Expected depthwise 3x7 weights");

    const c10::cuda::CUDAGuard guard(input.device());
    const int64_t batch = input.size(0);
    const int64_t channels = input.size(1);
    const int64_t height = input.size(2);

    TORCH_CHECK(batch * channels <= 65535, "Too many input planes");

    const float* bias_ptr = nullptr;
    if (bias.numel() != 0) {
        TORCH_CHECK(bias.is_cuda() &&
                    bias.device() == input.device() &&
                    bias.scalar_type() == at::kFloat &&
                    bias.is_contiguous() &&
                    bias.numel() == channels,
                    "Invalid bias");
        bias_ptr = bias.data_ptr<float>();
    }

    // Padded rows permit aligned vector stores throughout the output.
    auto storage = torch::empty(
        {batch, channels, height - 2, 256}, input.options());

    if (storage.numel() != 0) {
        constexpr int ROWS = 4;
        const dim3 grid(
            static_cast<unsigned>(
                (height - 2 + 4 * ROWS - 1) / (4 * ROWS)),
            static_cast<unsigned>(batch * channels));

        depthwise_3x7_eight_kernel<ROWS>
            <<<grid, 128, 0, at::cuda::getCurrentCUDAStream()>>>(
                input.data_ptr<float>(),
                weight.data_ptr<float>(),
                bias_ptr,
                storage.data_ptr<float>(),
                static_cast<int>(channels),
                static_cast<int>(height));

        C10_CUDA_KERNEL_LAUNCH_CHECK();
    }

    return storage.narrow(3, 0, 250);
}
"""

_depthwise_extension = load_inline(
    name="depthwise_3x7_eight_aligned_v4",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depthwise_3x7_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size_h: int,
        kernel_size_w: int,
        stride_h: int = 1,
        stride_w: int = 1,
        padding_h: int = 0,
        padding_w: int = 0,
        dilation_h: int = 1,
        dilation_w: int = 1,
        groups: int = 1,
        bias: bool = False,
    ):
        super().__init__()
        self.conv2d = nn.Conv2d(
            in_channels,
            in_channels,
            (kernel_size_h, kernel_size_w),
            stride=(stride_h, stride_w),
            padding=(padding_h, padding_w),
            dilation=(dilation_h, dilation_w),
            groups=in_channels,
            bias=bias,
        )
        self.register_buffer("_empty_bias", torch.empty(0), persistent=False)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.dim() == 4
            and x.is_contiguous()
            and x.shape[1] == conv.in_channels
            and x.shape[2] >= 3
            and x.shape[3] == 256
            and x.shape[0] * x.shape[1] <= 65535
            and conv.weight.device == x.device
            and conv.weight.dtype == torch.float32
            and conv.weight.is_contiguous()
            and conv.kernel_size == (3, 7)
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.dilation == (1, 1)
            and not torch.is_autocast_enabled()
        ):
            return _depthwise_extension.depthwise_3x7_cuda(
                x,
                conv.weight,
                conv.bias if conv.bias is not None else self._empty_bias,
            )
        return conv(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 0.831 ms; the PyTorch reference (with TF32 enabled) takes 3.7 ms; speedup 4.452x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void depthwise_3x7_eight_kernel<4>(float const*, float const*, float const*, float*, int,  | 805.6 | 1 |

The fastest correct solution so far (4.648x speedup) is:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor depthwise_3x7_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

__device__ __forceinline__ void accumulate_pair(
    float2& sum,
    const float2 a,
    const float2 b,
    const float2 c,
    const float2 d,
    const float* __restrict__ w)
{
    sum.x = fmaf(a.x, w[0], sum.x);
    sum.y = fmaf(a.y, w[0], sum.y);
    sum.x = fmaf(a.y, w[1], sum.x);
    sum.y = fmaf(b.x, w[1], sum.y);
    sum.x = fmaf(b.x, w[2], sum.x);
    sum.y = fmaf(b.y, w[2], sum.y);
    sum.x = fmaf(b.y, w[3], sum.x);
    sum.y = fmaf(c.x, w[3], sum.y);
    sum.x = fmaf(c.x, w[4], sum.x);
    sum.y = fmaf(c.y, w[4], sum.y);
    sum.x = fmaf(c.y, w[5], sum.x);
    sum.y = fmaf(d.x, w[5], sum.y);
    sum.x = fmaf(d.x, w[6], sum.x);
    sum.y = fmaf(d.y, w[6], sum.y);
}

template<int ROWS>
__global__ __launch_bounds__(128)
void depthwise_3x7_vector_kernel(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels,
    int height)
{
    constexpr int WIDTH = 256;
    constexpr int OUT_WIDTH = 250;
    constexpr int INPUT_ROWS = ROWS + 2;

    __shared__ float4 tile[INPUT_ROWS * (WIDTH / 4)];
    __shared__ float shared_weight[21];

    const int tid = threadIdx.x;
    const int plane = blockIdx.y;
    const int channel = plane % channels;
    const int y0 = blockIdx.x * ROWS;
    const int out_height = height - 2;

    const float4* __restrict__ input4 =
        reinterpret_cast<const float4*>(
            input + static_cast<int64_t>(plane) * height * WIDTH);

    #pragma unroll
    for (int i = 0; i < INPUT_ROWS / 2; ++i) {
        const int row = 2 * i + tid / 64;
        const int col = tid % 64;
        const int iy = y0 + row;
        float4 value = make_float4(0.f, 0.f, 0.f, 0.f);
        if (iy < height)
            value = input4[static_cast<int64_t>(iy) * 64 + col];
        tile[row * 64 + col] = value;
    }

    if (tid < 21)
        shared_weight[tid] = weight[channel * 21 + tid];

    __syncthreads();

    if (tid >= OUT_WIDTH / 2)
        return;

    float w[21];
    #pragma unroll
    for (int k = 0; k < 21; ++k)
        w[k] = shared_weight[k];

    float2 sums[ROWS];
    #pragma unroll
    for (int r = 0; r < ROWS; ++r)
        sums[r] = make_float2(0.f, 0.f);

    const float2* shared2 = reinterpret_cast<const float2*>(tile);

    #pragma unroll
    for (int r = 0; r < INPUT_ROWS; ++r) {
        const float2* row = shared2 + r * (WIDTH / 2) + tid;
        const float2 a = row[0];
        const float2 b = row[1];
        const float2 c = row[2];
        const float2 d = row[3];

        if (r < ROWS)
            accumulate_pair(sums[r], a, b, c, d, w);

        if (r >= 1 && r < ROWS + 1)
            accumulate_pair(sums[r - 1], a, b, c, d, w + 7);

        if (r >= 2)
            accumulate_pair(sums[r - 2], a, b, c, d, w + 14);
    }

    const float bias_value = bias ? bias[channel] : 0.f;
    float2* __restrict__ output2 =
        reinterpret_cast<float2*>(
            output + static_cast<int64_t>(plane) * out_height * OUT_WIDTH);

    #pragma unroll
    for (int r = 0; r < ROWS; ++r) {
        if (y0 + r < out_height) {
            float2 value = sums[r];
            value.x += bias_value;
            value.y += bias_value;
            output2[static_cast<int64_t>(y0 + r) * (OUT_WIDTH / 2) + tid]
                = value;
        }
    }
}

torch::Tensor depthwise_3x7_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias)
{
    TORCH_CHECK(x.is_cuda() && weight.is_cuda(),
                "Input and weight must be CUDA tensors");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                weight.scalar_type() == at::kFloat,
                "Input and weight must be float32");
    TORCH_CHECK(x.is_contiguous() && weight.is_contiguous(),
                "Input and weight must be contiguous");
    TORCH_CHECK(x.dim() == 4 && x.size(3) == 256 && x.size(2) >= 3,
                "Expected NCHW input with width 256 and height >= 3");
    TORCH_CHECK(weight.dim() == 4 &&
                weight.size(0) == x.size(1) &&
                weight.size(1) == 1 &&
                weight.size(2) == 3 &&
                weight.size(3) == 7,
                "Expected depthwise 3x7 weights");
    TORCH_CHECK(x.device() == weight.device(), "Device mismatch");

    const c10::cuda::CUDAGuard guard(x.device());

    const int64_t batch = x.size(0);
    const int64_t channels = x.size(1);
    const int64_t height = x.size(2);

    TORCH_CHECK(batch * channels <= 65535,
                "Too many input planes");

    const float* bias_ptr = nullptr;
    if (bias.numel() != 0) {
        TORCH_CHECK(bias.is_cuda() &&
                    bias.device() == x.device() &&
                    bias.scalar_type() == at::kFloat &&
                    bias.is_contiguous() &&
                    bias.numel() == channels,
                    "Invalid bias");
        bias_ptr = bias.data_ptr<float>();
    }

    auto output = torch::empty(
        {batch, channels, height - 2, 250}, x.options());

    if (output.numel() == 0)
        return output;

    constexpr int ROWS = 16;
    const dim3 grid(
        static_cast<unsigned>((height - 2 + ROWS - 1) / ROWS),
        static_cast<unsigned>(batch * channels));

    depthwise_3x7_vector_kernel<ROWS>
        <<<grid, 128, 0, at::cuda::getCurrentCUDAStream()>>>(
            x.data_ptr<float>(),
            weight.data_ptr<float>(),
            bias_ptr,
            output.data_ptr<float>(),
            static_cast<int>(channels),
            static_cast<int>(height));

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_depthwise_extension = load_inline(
    name="depthwise_3x7_vector_rows16",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depthwise_3x7_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size_h: int,
        kernel_size_w: int,
        stride_h: int = 1,
        stride_w: int = 1,
        padding_h: int = 0,
        padding_w: int = 0,
        dilation_h: int = 1,
        dilation_w: int = 1,
        groups: int = 1,
        bias: bool = False,
    ):
        super().__init__()
        self.conv2d = nn.Conv2d(
            in_channels,
            in_channels,
            (kernel_size_h, kernel_size_w),
            stride=(stride_h, stride_w),
            padding=(padding_h, padding_w),
            dilation=(dilation_h, dilation_w),
            groups=in_channels,
            bias=bias,
        )
        self.register_buffer("_empty_bias", torch.empty(0), persistent=False)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.dim() == 4
            and x.is_contiguous()
            and x.shape[1] == conv.in_channels
            and x.shape[2] >= 3
            and x.shape[3] == 256
            and x.shape[0] * x.shape[1] <= 65535
            and conv.weight.dtype == torch.float32
            and conv.weight.is_contiguous()
            and conv.kernel_size == (3, 7)
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.dilation == (1, 1)
            and not torch.is_autocast_enabled()
        ):
            return _depthwise_extension.depthwise_3x7_cuda(
                x,
                conv.weight,
                conv.bias if conv.bias is not None else self._empty_bias,
            )
        return conv(x)
```

Write an improved complete ModelNew: fix any error, and if the solution is already correct, make it faster. Output the new code in one ```python codeblock. Just the model code, no other text, and NO testing code.
