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):
    """
    Simple model that performs Max Pooling 3D.
    """
    def __init__(self, kernel_size: int, stride: int = None, padding: int = 0, dilation: int = 1, return_indices: bool = False, ceil_mode: bool = False):
        """
        Initializes the Max Pooling 3D layer.

        Args:
            kernel_size (int): Size of the kernel for the max pooling operation.
            stride (int, optional): Stride of the pooling operation. Defaults to None, which means stride is equal to kernel_size.
            padding (int, optional): Padding applied to the input tensor. Defaults to 0.
            dilation (int, optional): Spacing between kernel elements. Defaults to 1.
            return_indices (bool, optional): Whether to return indices of the maximum values. Defaults to False.
            ceil_mode (bool, optional): When True, the output size is ceil(input_size / stride) instead of floor. Defaults to False.
        """
        super(Model, self).__init__()
        self.maxpool = nn.MaxPool3d(kernel_size=kernel_size, stride=stride, padding=padding, dilation=dilation, return_indices=return_indices, ceil_mode=ceil_mode)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Applies Max Pooling 3D to the input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, channels, dim1, dim2, dim3).

        Returns:
            torch.Tensor: Output tensor with Max Pooling 3D applied.
        """
        return self.maxpool(x)

batch_size = 16
channels = 32
dim1 = 128
dim2 = 128
dim3 = 128
kernel_size = 3
stride = 2
padding = 1
dilation = 3

def get_inputs():
    x = torch.rand(batch_size, channels, dim1, dim2, dim3)
    return [x]

def get_init_inputs():
    return [kernel_size, stride, padding, dilation]
    ```
    
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! 

