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 standard 3D convolution operation with an asymmetric input and a square kernel.

    Args:
        in_channels (int): Number of channels in the input tensor.
        out_channels (int): Number of channels produced by the convolution.
        kernel_size (int): Size of the square convolution kernel (kernel_size x kernel_size).
        stride (int, optional): Stride of the convolution. Defaults to 1.
        padding (int, optional): Padding applied to the input. Defaults to 0.
        dilation (int, optional): Spacing between kernel elements. 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: int, stride: int = 1, padding: int = 0, dilation: int = 1, groups: int = 1, bias: bool = False):
        super(Model, self).__init__()
        self.conv3d = nn.Conv3d(in_channels, out_channels, (kernel_size, kernel_size, 1), stride=stride, padding=padding, dilation=dilation, groups=groups, bias=bias)
        
    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Performs the 3D convolution.

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

        Returns:
            torch.Tensor: Output tensor of shape (batch_size, out_channels, height_out, width_out, depth_out).
        """
        return self.conv3d(x)

# Test code
batch_size = 16
in_channels = 3
out_channels = 64
kernel_size = 3
width = 256
height = 256
depth = 10

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

def get_init_inputs():
    return [in_channels, out_channels, kernel_size]  # Provide in_channels, out_channels, kernel_size for initialization
    ```
    
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


_cuda_source = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cuda_fp16.h>
#include <stdint.h>

constexpr int TILE = 128;
constexpr int KS = 40;

__device__ __forceinline__
void mma_f16(
    float* d,
    unsigned a0, unsigned a1, unsigned a2, unsigned a3,
    unsigned b0, unsigned b1)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
    asm volatile(
        "mma.sync.aligned.m16n8k16.row.col.f32.f16.f16.f32 "
        "{%0, %1, %2, %3}, "
        "{%4, %5, %6, %7}, "
        "{%8, %9}, "
        "{%0, %1, %2, %3};\n"
        : "+f"(d[0]), "+f"(d[1]), "+f"(d[2]), "+f"(d[3])
        : "r"(a0), "r"(a1), "r"(a2), "r"(a3),
          "r"(b0), "r"(b1));
#endif
}

__device__ __forceinline__
unsigned load_pair(const __half* p)
{
    return *reinterpret_cast<const unsigned*>(p);
}

__device__ __forceinline__
void write_pair(float* dst, int pos, int size, float x, float y)
{
    if ((size & 1) == 0) {
        if (pos < size) {
            *reinterpret_cast<float2*>(dst + pos) = make_float2(x, y);
        }
    } else {
        if (pos < size) dst[pos] = x;
        if (pos + 1 < size) dst[pos + 1] = y;
    }
}

__global__ __launch_bounds__(128)
void asymmetric_conv_mma(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int height,
    int width,
    int depth,
    int output_width,
    int spatial_size)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
    __shared__ __align__(16) __half ah[64][KS];
    __shared__ __align__(16) __half al[64][KS];
    __shared__ __align__(16) __half bh[TILE][KS];
    __shared__ __align__(16) __half bl[TILE][KS];

    const int tid = threadIdx.x;
    const int lane = tid & 31;
    const int warp = tid >> 5;
    const int group = lane >> 2;
    const int pair = (lane & 3) * 2;

    const int batch = blockIdx.y;
    const int start = blockIdx.x * TILE;
    const int position = start + tid;

    const int row_stride = output_width * depth;
    const int ih = position / row_stride;
    const int rem = position - ih * row_stride;
    const int iw = rem / depth;
    const int iz = rem - iw * depth;

    const int64_t channel_stride =
        static_cast<int64_t>(height) * width * depth;
    const int64_t base =
        static_cast<int64_t>(batch) * 3 * channel_stride
        + (static_cast<int64_t>(ih) * width + iw) * depth + iz;

    #pragma unroll
    for (int ic = 0; ic < 3; ++ic) {
        #pragma unroll
        for (int kh = 0; kh < 3; ++kh) {
            #pragma unroll
            for (int kw = 0; kw < 3; ++kw) {
                const int k = ic * 9 + kh * 3 + kw;
                float v = 0.0f;
                if (position < spatial_size) {
                    v = input[
                        base + ic * channel_stride
                        + static_cast<int64_t>(kh) * width * depth
                        + kw * depth];
                }
                const __half hi = __float2half_rn(v);
                bh[tid][k] = hi;
                bl[tid][k] = __float2half_rn(v - __half2float(hi));
            }
        }
    }

    #pragma unroll
    for (int k = 27; k < 32; ++k) {
        bh[tid][k] = __float2half_rn(0.0f);
        bl[tid][k] = __float2half_rn(0.0f);
    }

    #pragma unroll
    for (int i = tid; i < 64 * 32; i += 128) {
        const int oc = i >> 5;
        const int k = i & 31;
        const float v = k < 27 ? weight[oc * 27 + k] : 0.0f;
        const __half hi = __float2half_rn(v);
        ah[oc][k] = hi;
        al[oc][k] = __float2half_rn(v - __half2float(hi));
    }

    __syncthreads();

    float acc[16][4];

    #pragma unroll
    for (int j = 0; j < 16; ++j) {
        #pragma unroll
        for (int q = 0; q < 4; ++q) {
            acc[j][q] = 0.0f;
        }
    }

    const int row = warp * 16 + group;

    #pragma unroll
    for (int k = 0; k < 32; k += 16) {
        const unsigned a0 = load_pair(&ah[row][k + pair]);
        const unsigned a1 = load_pair(&ah[row + 8][k + pair]);
        const unsigned a2 = load_pair(&ah[row][k + pair + 8]);
        const unsigned a3 = load_pair(&ah[row + 8][k + pair + 8]);

        const unsigned l0 = load_pair(&al[row][k + pair]);
        const unsigned l1 = load_pair(&al[row + 8][k + pair]);
        const unsigned l2 = load_pair(&al[row][k + pair + 8]);
        const unsigned l3 = load_pair(&al[row + 8][k + pair + 8]);

        #pragma unroll
        for (int j = 0; j < 16; ++j) {
            const int col = j * 8 + group;
            const unsigned b0 = load_pair(&bh[col][k + pair]);
            const unsigned b1 = load_pair(&bh[col][k + pair + 8]);
            const unsigned r0 = load_pair(&bl[col][k + pair]);
            const unsigned r1 = load_pair(&bl[col][k + pair + 8]);

            mma_f16(acc[j], a0, a1, a2, a3, b0, b1);
            mma_f16(acc[j], l0, l1, l2, l3, b0, b1);
            mma_f16(acc[j], a0, a1, a2, a3, r0, r1);
        }
    }

    float* dst0 = output
        + (static_cast<int64_t>(batch) * 64 + row) * spatial_size;
    float* dst1 = dst0 + static_cast<int64_t>(8) * spatial_size;

    const float bias0 = bias ? bias[row] : 0.0f;
    const float bias1 = bias ? bias[row + 8] : 0.0f;

    #pragma unroll
    for (int j = 0; j < 16; ++j) {
        const int pos = start + j * 8 + pair;
        write_pair(
            dst0, pos, spatial_size,
            acc[j][0] + bias0, acc[j][1] + bias0);
        write_pair(
            dst1, pos, spatial_size,
            acc[j][2] + bias1, acc[j][3] + bias1);
    }
#endif
}

torch::Tensor asymmetric_conv_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias)
{
    const c10::cuda::CUDAGuard guard(input.device());

    const int batch = input.size(0);
    const int height = input.size(2);
    const int width = input.size(3);
    const int depth = input.size(4);
    const int output_height = height - 2;
    const int output_width = width - 2;
    const int spatial_size = output_height * output_width * depth;

    auto output = torch::empty(
        {batch, 64, output_height, output_width, depth},
        input.options());

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

    const dim3 grid((spatial_size + TILE - 1) / TILE, batch);
    const cudaStream_t stream =
        c10::cuda::getCurrentCUDAStream(input.get_device()).stream();

    asymmetric_conv_mma<<<grid, 128, 0, stream>>>(
        input.data_ptr<float>(),
        weight.data_ptr<float>(),
        has_bias ? bias.data_ptr<float>() : nullptr,
        output.data_ptr<float>(),
        height, width, depth, output_width, spatial_size);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_cpp_source = r"""
#include <torch/extension.h>
torch::Tensor asymmetric_conv_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias);
"""

_extension = load_inline(
    name="asymmetric_conv3d_mma_components_v4",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["asymmetric_conv_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: int,
        stride: int = 1,
        padding: int = 0,
        dilation: int = 1,
        groups: int = 1,
        bias: bool = False,
    ):
        super().__init__()
        self.conv3d = nn.Conv3d(
            in_channels,
            out_channels,
            (kernel_size, kernel_size, 1),
            stride=stride,
            padding=padding,
            dilation=dilation,
            groups=groups,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv3d
        weight = conv.weight
        bias = conv.bias

        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 5
            and x.is_contiguous()
            and x.shape[1] == 3
            and x.shape[2] >= 3
            and x.shape[3] >= 3
            and x.shape[4] > 0
            and x.shape[0] <= 65535
            and x.shape[2] * x.shape[3] * x.shape[4] < 2147483392
            and weight.device == x.device
            and weight.dtype == torch.float32
            and weight.is_contiguous()
            and conv.in_channels == 3
            and conv.out_channels == 64
            and conv.kernel_size == (3, 3, 1)
            and conv.stride == (1, 1, 1)
            and conv.padding == (0, 0, 0)
            and conv.dilation == (1, 1, 1)
            and conv.groups == 1
            and not torch.is_autocast_enabled()
            and torch.cuda.get_device_capability(x.device)[0] >= 8
            and (
                bias is None
                or (
                    bias.device == x.device
                    and bias.dtype == torch.float32
                    and bias.is_contiguous()
                )
            )
        ):
            return _extension.asymmetric_conv_cuda(
                x, weight, weight if bias is None else bias, bias is not None
            )

        return conv(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 4.17 ms; the PyTorch reference (with TF32 enabled) takes 8.89 ms; speedup 2.132x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| asymmetric_conv_mma(float const*, float const*, float const*, float*, int, int, int, int,  | 4143.5 | 1 |

The fastest correct solution so far (3.186x speedup) is:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


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

constexpr int TILE = 256;

__global__ __launch_bounds__(256)
void conv3d_3x3x1_vectorized(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int height,
    int width,
    int depth,
    int output_width,
    int spatial_size)
{
    __shared__ __align__(16) float xs[27][TILE];
    __shared__ float ws[64][27];

    const int tid = threadIdx.x;
    const int lane = tid & 31;
    const int channel_group = tid >> 5;
    const int start = blockIdx.x * TILE;
    const int position = start + tid;
    const int batch = blockIdx.y;

    const int64_t channel_stride =
        static_cast<int64_t>(height) * width * depth;
    const int output_row_stride = output_width * depth;
    const int ih = position / output_row_stride;
    const int remainder = position - ih * output_row_stride;
    const int iw = remainder / depth;
    const int iz = remainder - iw * depth;
    const int64_t base =
        static_cast<int64_t>(batch) * 3 * channel_stride
        + (static_cast<int64_t>(ih) * width + iw) * depth + iz;

    #pragma unroll
    for (int ic = 0; ic < 3; ++ic) {
        #pragma unroll
        for (int kh = 0; kh < 3; ++kh) {
            #pragma unroll
            for (int kw = 0; kw < 3; ++kw) {
                const int k = ic * 9 + kh * 3 + kw;
                xs[k][tid] = position < spatial_size
                    ? input[base + ic * channel_stride
                            + static_cast<int64_t>(kh) * width * depth
                            + kw * depth]
                    : 0.0f;
            }
        }
    }

    for (int i = tid; i < 64 * 27; i += 256) {
        ws[i / 27][i % 27] = weight[i];
    }
    __syncthreads();

    float4 accum[8][2];

    #pragma unroll
    for (int c = 0; c < 8; ++c) {
        accum[c][0] = make_float4(0.f, 0.f, 0.f, 0.f);
        accum[c][1] = make_float4(0.f, 0.f, 0.f, 0.f);
    }

    #pragma unroll 1
    for (int k = 0; k < 27; ++k) {
        const float4 x0 =
            reinterpret_cast<const float4*>(xs[k])[lane];
        const float4 x1 =
            reinterpret_cast<const float4*>(xs[k])[lane + 32];

        #pragma unroll
        for (int c = 0; c < 8; ++c) {
            const float w = ws[channel_group + c * 8][k];
            accum[c][0].x = fmaf(x0.x, w, accum[c][0].x);
            accum[c][0].y = fmaf(x0.y, w, accum[c][0].y);
            accum[c][0].z = fmaf(x0.z, w, accum[c][0].z);
            accum[c][0].w = fmaf(x0.w, w, accum[c][0].w);
            accum[c][1].x = fmaf(x1.x, w, accum[c][1].x);
            accum[c][1].y = fmaf(x1.y, w, accum[c][1].y);
            accum[c][1].z = fmaf(x1.z, w, accum[c][1].z);
            accum[c][1].w = fmaf(x1.w, w, accum[c][1].w);
        }
    }

    #pragma unroll
    for (int c = 0; c < 8; ++c) {
        const int oc = channel_group + c * 8;
        const float b = bias ? bias[oc] : 0.f;
        float* dst = output
            + (static_cast<int64_t>(batch) * 64 + oc) * spatial_size;

        #pragma unroll
        for (int p = 0; p < 2; ++p) {
            const int pos = start + lane * 4 + p * 128;
            float4 value = accum[c][p];
            value.x += b;
            value.y += b;
            value.z += b;
            value.w += b;

            if ((spatial_size & 3) == 0) {
                if (pos < spatial_size) {
                    *reinterpret_cast<float4*>(dst + pos) = value;
                }
            } else {
                if (pos < spatial_size) dst[pos] = value.x;
                if (pos + 1 < spatial_size) dst[pos + 1] = value.y;
                if (pos + 2 < spatial_size) dst[pos + 2] = value.z;
                if (pos + 3 < spatial_size) dst[pos + 3] = value.w;
            }
        }
    }
}

torch::Tensor conv3d_specialized(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias)
{
    const c10::cuda::CUDAGuard guard(input.device());

    const int batch = input.size(0);
    const int height = input.size(2);
    const int width = input.size(3);
    const int depth = input.size(4);
    const int output_height = height - 2;
    const int output_width = width - 2;
    const int spatial_size = output_height * output_width * depth;

    auto output = torch::empty(
        {batch, 64, output_height, output_width, depth},
        input.options());

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

    const dim3 grid((spatial_size + TILE - 1) / TILE, batch);
    const cudaStream_t stream =
        c10::cuda::getCurrentCUDAStream(input.get_device()).stream();

    conv3d_3x3x1_vectorized<<<grid, 256, 0, stream>>>(
        input.data_ptr<float>(),
        weight.data_ptr<float>(),
        has_bias ? bias.data_ptr<float>() : nullptr,
        output.data_ptr<float>(),
        height, width, depth, output_width, spatial_size);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_cpp_source = r"""
#include <torch/extension.h>
torch::Tensor conv3d_specialized(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias);
"""

_conv3d_extension = load_inline(
    name="asymmetric_conv3d_vectorized_fp32_v2",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["conv3d_specialized"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size: int,
        stride: int = 1,
        padding: int = 0,
        dilation: int = 1,
        groups: int = 1,
        bias: bool = False,
    ):
        super().__init__()
        self.conv3d = nn.Conv3d(
            in_channels,
            out_channels,
            (kernel_size, kernel_size, 1),
            stride=stride,
            padding=padding,
            dilation=dilation,
            groups=groups,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv3d
        weight = conv.weight
        bias = conv.bias

        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 5
            and x.is_contiguous()
            and x.shape[1] == 3
            and x.shape[2] >= 3
            and x.shape[3] >= 3
            and x.shape[4] > 0
            and x.shape[0] <= 65535
            and x.shape[2] * x.shape[3] * x.shape[4] < 2147483392
            and weight.device == x.device
            and weight.dtype == torch.float32
            and weight.is_contiguous()
            and conv.in_channels == 3
            and conv.out_channels == 64
            and conv.kernel_size == (3, 3, 1)
            and conv.stride == (1, 1, 1)
            and conv.padding == (0, 0, 0)
            and conv.dilation == (1, 1, 1)
            and conv.groups == 1
            and not torch.is_autocast_enabled()
            and (
                bias is None
                or (
                    bias.device == x.device
                    and bias.dtype == torch.float32
                    and bias.is_contiguous()
                )
            )
        ):
            return _conv3d_extension.conv3d_specialized(
                x, weight, weight if bias is None else bias, bias is not None
            )

        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.
