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):
    """
    Model that performs a transposed 3D convolution, applies ReLU, and then applies group normalization.
    """
    def __init__(self, in_channels, out_channels, kernel_size, groups, bias=False):
        super(Model, self).__init__()
        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, bias=bias)
        self.relu = nn.ReLU()
        self.group_norm = nn.GroupNorm(num_groups=groups, num_channels=out_channels)

    def forward(self, x):
        """
        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_channels, D, H, W).

        Returns:
            torch.Tensor: Output tensor of shape (batch_size, out_channels, D, H, W).
        """
        x = self.conv_transpose(x)
        x = self.relu(x)
        x = self.group_norm(x)
        return x

batch_size = 16
in_channels = 64
out_channels = 128
D, H, W = 32, 32, 32
kernel_size = 3
groups = 8
bias = False

def get_inputs():
    return [torch.rand(batch_size, in_channels, D, H, W)]

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, groups, bias]
    ```
    
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
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline


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

torch::Tensor relu_group_norm_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    int64_t groups,
    double eps);
"""

_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>
#include <algorithm>

constexpr int THREADS = 256;
constexpr int VECTORS_PER_CHUNK = 1024;

__device__ __forceinline__ float warp_sum(float value) {
    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1)
        value += __shfl_down_sync(0xffffffff, value, offset);
    return value;
}

__device__ __forceinline__ void block_sum(
    float& sum, float& square_sum,
    float* shared_sum, float* shared_square_sum) {
    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;

    sum = warp_sum(sum);
    square_sum = warp_sum(square_sum);

    if (lane == 0) {
        shared_sum[warp] = sum;
        shared_square_sum[warp] = square_sum;
    }
    __syncthreads();

    if (warp == 0) {
        sum = lane < THREADS / 32 ? shared_sum[lane] : 0.0f;
        square_sum =
            lane < THREADS / 32 ? shared_square_sum[lane] : 0.0f;
        sum = warp_sum(sum);
        square_sum = warp_sum(square_sum);
    }
}

__global__ void relu_partial_stats(
    const float4* __restrict__ x,
    float2* __restrict__ partial,
    int64_t vectors_per_group,
    int chunks) {
    __shared__ float shared_sum[THREADS / 32];
    __shared__ float shared_square_sum[THREADS / 32];

    const int group = blockIdx.x;
    const int chunk = blockIdx.y;
    const int64_t start =
        static_cast<int64_t>(chunk) * VECTORS_PER_CHUNK;
    const int64_t base =
        static_cast<int64_t>(group) * vectors_per_group;

    float sum = 0.0f;
    float square_sum = 0.0f;

    #pragma unroll
    for (int i = 0; i < VECTORS_PER_CHUNK / THREADS; ++i) {
        const int64_t index = start + threadIdx.x + i * THREADS;
        if (index < vectors_per_group) {
            float4 v = x[base + index];
            v.x = v.x < 0.0f ? 0.0f : v.x;
            v.y = v.y < 0.0f ? 0.0f : v.y;
            v.z = v.z < 0.0f ? 0.0f : v.z;
            v.w = v.w < 0.0f ? 0.0f : v.w;

            sum += (v.x + v.y) + (v.z + v.w);
            square_sum +=
                (v.x * v.x + v.y * v.y) +
                (v.z * v.z + v.w * v.w);
        }
    }

    block_sum(sum, square_sum, shared_sum, shared_square_sum);
    if (threadIdx.x == 0)
        partial[static_cast<int64_t>(group) * chunks + chunk] =
            make_float2(sum, square_sum);
}

__global__ void finish_stats(
    const float2* __restrict__ partial,
    float2* __restrict__ stats,
    int chunks,
    int64_t elements_per_group,
    float eps) {
    __shared__ float shared_sum[THREADS / 32];
    __shared__ float shared_square_sum[THREADS / 32];

    const int group = blockIdx.x;
    float sum = 0.0f;
    float square_sum = 0.0f;

    for (int i = threadIdx.x; i < chunks; i += THREADS) {
        const float2 p =
            partial[static_cast<int64_t>(group) * chunks + i];
        sum += p.x;
        square_sum += p.y;
    }

    block_sum(sum, square_sum, shared_sum, shared_square_sum);
    if (threadIdx.x == 0) {
        const float reciprocal_count =
            1.0f / static_cast<float>(elements_per_group);
        const float mean = sum * reciprocal_count;
        const float variance =
            fmaxf(square_sum * reciprocal_count - mean * mean, 0.0f);
        stats[group] = make_float2(mean, rsqrtf(variance + eps));
    }
}

__global__ void relu_normalize(
    const float4* __restrict__ x,
    float4* __restrict__ out,
    const float2* __restrict__ stats,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    int64_t vector_count,
    int64_t vectors_per_group,
    int64_t vectors_per_channel,
    int channels) {
    const int64_t stride =
        static_cast<int64_t>(blockDim.x) * gridDim.x;

    for (int64_t index =
             static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
         index < vector_count;
         index += stride) {
        const int64_t group = index / vectors_per_group;
        const int channel = (index / vectors_per_channel) % channels;

        const float2 st = stats[group];
        const float scale = st.y * weight[channel];
        const float shift = bias[channel];

        float4 v = x[index];
        v.x = v.x < 0.0f ? 0.0f : v.x;
        v.y = v.y < 0.0f ? 0.0f : v.y;
        v.z = v.z < 0.0f ? 0.0f : v.z;
        v.w = v.w < 0.0f ? 0.0f : v.w;

        v.x = (v.x - st.x) * scale + shift;
        v.y = (v.y - st.x) * scale + shift;
        v.z = (v.z - st.x) * scale + shift;
        v.w = (v.w - st.x) * scale + shift;
        out[index] = v;
    }
}

torch::Tensor relu_group_norm_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    int64_t groups,
    double eps) {
    const c10::cuda::CUDAGuard device_guard(x.device());

    const int64_t channels = x.size(1);
    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const int64_t elements_per_group = channels / groups * spatial;
    const int64_t vectors_per_group = elements_per_group / 4;
    const int64_t total_groups = x.size(0) * groups;
    const int chunks =
        (vectors_per_group + VECTORS_PER_CHUNK - 1) / VECTORS_PER_CHUNK;

    auto output = torch::empty(x.sizes(), x.options());
    auto partial = torch::empty({total_groups, chunks, 2}, x.options());
    auto stats = torch::empty({total_groups, 2}, x.options());

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

    relu_partial_stats<<<dim3(total_groups, chunks), THREADS, 0, stream>>>(
        reinterpret_cast<const float4*>(x.data_ptr<float>()),
        reinterpret_cast<float2*>(partial.data_ptr<float>()),
        vectors_per_group,
        chunks);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    finish_stats<<<total_groups, THREADS, 0, stream>>>(
        reinterpret_cast<const float2*>(partial.data_ptr<float>()),
        reinterpret_cast<float2*>(stats.data_ptr<float>()),
        chunks,
        elements_per_group,
        static_cast<float>(eps));
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    const int64_t vector_count = x.numel() / 4;
    const int blocks = static_cast<int>(
        std::min<int64_t>((vector_count + THREADS - 1) / THREADS, 8192));

    relu_normalize<<<blocks, THREADS, 0, stream>>>(
        reinterpret_cast<const float4*>(x.data_ptr<float>()),
        reinterpret_cast<float4*>(output.data_ptr<float>()),
        reinterpret_cast<const float2*>(stats.data_ptr<float>()),
        weight.data_ptr<float>(),
        bias.data_ptr<float>(),
        vector_count,
        vectors_per_group,
        spatial / 4,
        static_cast<int>(channels));
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return output;
}
"""

_fused_ops = load_inline(
    name="fused_relu_groupnorm_3d_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["relu_group_norm_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self, in_channels, out_channels, kernel_size, groups, bias=False
    ):
        super().__init__()
        self.conv_transpose = nn.ConvTranspose3d(
            in_channels, out_channels, kernel_size, bias=bias
        )
        self.relu = nn.ReLU()
        self.group_norm = nn.GroupNorm(groups, out_channels)

    def forward(self, x):
        x = self.conv_transpose(x)
        norm = self.group_norm
        spatial = x.shape[2] * x.shape[3] * x.shape[4]
        group_elements = (x.shape[1] // norm.num_groups) * spatial

        use_custom = (
            x.is_cuda
            and x.dtype == torch.float32
            and x.is_contiguous()
            and x.numel() > 0
            and spatial % 4 == 0
            and (group_elements + 4095) // 4096 <= 65535
            and norm.weight.dtype == torch.float32
            and norm.bias.dtype == torch.float32
            and norm.weight.is_contiguous()
            and norm.bias.is_contiguous()
            and not (
                torch.is_grad_enabled()
                and (
                    x.requires_grad
                    or norm.weight.requires_grad
                    or norm.bias.requires_grad
                )
            )
        )

        if use_custom:
            return _fused_ops.relu_group_norm_cuda(
                x, norm.weight, norm.bias, norm.num_groups, norm.eps
            )

        return F.group_norm(
            F.relu(x), norm.num_groups, norm.weight, norm.bias, norm.eps
        )
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 4.44 ms; the PyTorch reference (with TF32 enabled) takes 4.45 ms; speedup 1.002x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| sm80_xmma_dgrad_implicit_gemm_tf32f32_tf32f32_f32_nhwckrsc_nhwc_tilesize128x128x16_stage4_ | 2025.1 | 1 |
| void at::native::(anonymous namespace)::RowwiseMomentsCUDAKernel<float, float>(long, float | 779.8 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 474.9 | 1 |
| void at::native::vectorized_elementwise_kernel<4, at::native::(anonymous namespace)::launc | 467.8 | 1 |
| void cudnn::engines_precompiled::nhwcToNchwKernel<float, float, float, true, false, (cudnn | 460.3 | 1 |
| void cudnn::engines_precompiled::nchwToNhwcKernel<float, float, float, false, true, (cudnn | 207.3 | 2 |
| void at::native::(anonymous namespace)::ComputeFusedParamsCUDAKernel<float, float>(long, l | 3.4 | 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.
