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 2 of 6 for this task. Your previous solution (turn 1) was:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_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>

__global__ void depthwise_3x7_kernel(
    const float* __restrict__ x,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels, int height, int width,
    int out_height, int out_width)
{
    constexpr int TILE_W = 128;
    constexpr int TILE_H = 8;
    constexpr int SHARED_W = TILE_W + 6;
    constexpr int SHARED_H = TILE_H + 2;

    __shared__ float tile[SHARED_H * SHARED_W];
    __shared__ float weights[21];

    const int tid = threadIdx.x;
    const int plane = blockIdx.z;
    const int channel = plane % channels;
    const int x0 = blockIdx.x * TILE_W;
    const int y0 = blockIdx.y * TILE_H;

    const float* input_plane =
        x + static_cast<int64_t>(plane) * height * width;

    for (int i = tid; i < SHARED_H * SHARED_W; i += TILE_W) {
        const int iy = y0 + i / SHARED_W;
        const int ix = x0 + i % SHARED_W;
        tile[i] = (iy < height && ix < width)
            ? input_plane[static_cast<int64_t>(iy) * width + ix]
            : 0.0f;
    }

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

    __syncthreads();

    float sums[TILE_H];

    #pragma unroll
    for (int r = 0; r < TILE_H; ++r)
        sums[r] = 0.0f;

    // Each shared-memory input value contributes to up to three output rows.
    #pragma unroll
    for (int iy = 0; iy < SHARED_H; ++iy) {
        #pragma unroll
        for (int kx = 0; kx < 7; ++kx) {
            const float value = tile[iy * SHARED_W + tid + kx];

            if (iy < TILE_H)
                sums[iy] = fmaf(value, weights[kx], sums[iy]);

            if (iy >= 1 && iy < TILE_H + 1)
                sums[iy - 1] =
                    fmaf(value, weights[7 + kx], sums[iy - 1]);

            if (iy >= 2)
                sums[iy - 2] =
                    fmaf(value, weights[14 + kx], sums[iy - 2]);
        }
    }

    const int ox = x0 + tid;
    const float b = bias ? bias[channel] : 0.0f;

    if (ox < out_width) {
        float* output_plane =
            output + static_cast<int64_t>(plane) * out_height * out_width;

        #pragma unroll
        for (int r = 0; r < TILE_H; ++r) {
            if (y0 + r < out_height)
                output_plane[static_cast<int64_t>(y0 + r) * out_width + ox]
                    = sums[r] + b;
        }
    }
}

__global__ void depthwise_generic_kernel(
    const float* __restrict__ x,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int64_t total,
    int channels, int height, int width,
    int out_height, int out_width,
    int kh, int kw, int sh, int sw,
    int ph, int pw, int dh, int dw)
{
    const int64_t spatial = static_cast<int64_t>(out_height) * out_width;

    for (int64_t index =
             static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
         index < total;
         index += static_cast<int64_t>(blockDim.x) * gridDim.x)
    {
        const int ox = index % out_width;
        const int oy = (index / out_width) % out_height;
        const int64_t plane = index / spatial;
        const int channel = plane % channels;

        const float* input_plane =
            x + plane * static_cast<int64_t>(height) * width;
        const float* kernel =
            weight + static_cast<int64_t>(channel) * kh * kw;

        float sum = 0.0f;

        for (int ky = 0; ky < kh; ++ky) {
            const int iy = oy * sh - ph + ky * dh;
            if (iy < 0 || iy >= height)
                continue;

            for (int kx = 0; kx < kw; ++kx) {
                const int ix = ox * sw - pw + kx * dw;
                if (ix >= 0 && ix < width)
                    sum = fmaf(
                        input_plane[static_cast<int64_t>(iy) * width + ix],
                        kernel[ky * kw + kx],
                        sum);
            }
        }

        output[index] = sum + (bias ? bias[channel] : 0.0f);
    }
}

torch::Tensor depthwise_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    int64_t sh, int64_t sw,
    int64_t ph, int64_t pw,
    int64_t dh, int64_t dw)
{
    TORCH_CHECK(x.is_cuda() && weight.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                weight.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.dim() == 4 && weight.dim() == 4,
                "Expected four-dimensional tensors");
    TORCH_CHECK(x.is_contiguous() && weight.is_contiguous(),
                "Expected contiguous tensors");
    TORCH_CHECK(x.device() == weight.device(), "Device mismatch");
    TORCH_CHECK(weight.size(0) == x.size(1) && weight.size(1) == 1,
                "Invalid depthwise convolution weight");
    TORCH_CHECK(sh > 0 && sw > 0 && dh > 0 && dw > 0 &&
                ph >= 0 && pw >= 0, "Invalid convolution parameters");

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

    const int64_t n = x.size(0);
    const int64_t c = x.size(1);
    const int64_t h = x.size(2);
    const int64_t w = x.size(3);
    const int64_t kh = weight.size(2);
    const int64_t kw = weight.size(3);

    TORCH_CHECK(h + 2 * ph >= dh * (kh - 1) + 1 &&
                w + 2 * pw >= dw * (kw - 1) + 1,
                "Kernel exceeds padded input dimensions");

    const int64_t oh = (h + 2 * ph - dh * (kh - 1) - 1) / sh + 1;
    const int64_t ow = (w + 2 * pw - dw * (kw - 1) - 1) / sw + 1;

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

    auto output = torch::empty({n, c, oh, ow}, x.options());
    if (output.numel() == 0)
        return output;

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if (kh == 3 && kw == 7 &&
        sh == 1 && sw == 1 &&
        ph == 0 && pw == 0 &&
        dh == 1 && dw == 1 &&
        n * c <= 65535 && (oh + 7) / 8 <= 65535)
    {
        dim3 grid(
            static_cast<unsigned>((ow + 127) / 128),
            static_cast<unsigned>((oh + 7) / 8),
            static_cast<unsigned>(n * c));

        depthwise_3x7_kernel<<<grid, 128, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(),
            bias_ptr, output.data_ptr<float>(),
            c, h, w, oh, ow);
    } else {
        const int64_t needed = (output.numel() + 255) / 256;
        const int blocks = static_cast<int>(needed < 65535 ? needed : 65535);

        depthwise_generic_kernel<<<blocks, 256, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(),
            bias_ptr, output.data_ptr<float>(), output.numel(),
            c, h, w, oh, ow, kh, kw, sh, sw, ph, pw, dh, dw);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

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

torch::Tensor depthwise_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    int64_t sh, int64_t sw,
    int64_t ph, int64_t pw,
    int64_t dh, int64_t dw);
"""

_depthwise_extension = load_inline(
    name="depthwise_asymmetric_tiled_cuda",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depthwise_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 (
            not x.is_cuda
            or x.dtype != torch.float32
            or conv.weight.dtype != torch.float32
            or x.dim() != 4
            or torch.is_autocast_enabled()
        ):
            return conv(x)

        return _depthwise_extension.depthwise_cuda(
            x.contiguous(),
            conv.weight.contiguous(),
            conv.bias if conv.bias is not None else self._empty_bias,
            conv.stride[0],
            conv.stride[1],
            conv.padding[0],
            conv.padding[1],
            conv.dilation[0],
            conv.dilation[1],
        )
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 0.994 ms; the PyTorch reference (with TF32 enabled) takes 3.7 ms; speedup 3.722x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| depthwise_3x7_kernel(float const*, float const*, float const*, float*, int, int, int, int, | 972.3 | 1 |

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.
