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 3D convolution, applies LeakyReLU, sums with a tensor, clamps, and applies GELU activation.
    """
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super(Model, self).__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.sum_tensor = nn.Parameter(torch.randn(sum_tensor_shape))

    def forward(self, x):
        x = self.conv(x)
        x = torch.nn.functional.leaky_relu(x, negative_slope=0.2)
        x = x + self.sum_tensor
        x = torch.clamp(x, min=-1.0, max=1.0)
        x = torch.nn.functional.gelu(x)
        return x

batch_size = 128
in_channels = 8
out_channels = 64
depth, height, width = 16, 64, 64
kernel_size = 3
sum_tensor_shape = (out_channels, 1, 1, 1)

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

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, sum_tensor_shape]
    ```
    
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
# 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

# Let cuDNN autotune the best 3D-conv algorithm for the fixed input shape.
torch.backends.cudnn.benchmark = True

# Fused epilogue kernel: (conv bias) + LeakyReLU(0.2) + add per-channel
# sum_tensor + clamp(-1, 1) + exact GELU, all in a single memory pass.
fused_epilogue_cuda_source = r"""
#include <torch/extension.h>
#include <cuda_runtime.h>

#define NEG_SLOPE 0.2f
#define CLAMP_LO  -1.0f
#define CLAMP_HI   1.0f
#define RSQRT2    0.70710678118654752440f  // 1 / sqrt(2)

__device__ __forceinline__ float epilogue(float v, float b, float s) {
    v += b;                                        // conv bias
    v = v > 0.0f ? v : NEG_SLOPE * v;              // leaky_relu(0.2)
    v += s;                                        // broadcast sum tensor
    v = fminf(fmaxf(v, CLAMP_LO), CLAMP_HI);       // clamp(-1, 1)
    return 0.5f * v * (1.0f + erff(v * RSQRT2));   // exact GELU
}

__global__ void fused_epilogue_vec4_kernel(
    const float4* __restrict__ x,
    const float* __restrict__ bias,
    const float* __restrict__ sum_t,
    float4* __restrict__ out,
    long n_vec,
    int channels,
    long spatial_vec) {
    long i = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (i < n_vec) {
        int c = (int)((i / spatial_vec) % channels);
        float b = bias[c];
        float s = sum_t[c];
        float4 v = x[i];
        v.x = epilogue(v.x, b, s);
        v.y = epilogue(v.y, b, s);
        v.z = epilogue(v.z, b, s);
        v.w = epilogue(v.w, b, s);
        out[i] = v;
    }
}

__global__ void fused_epilogue_scalar_kernel(
    const float* __restrict__ x,
    const float* __restrict__ bias,
    const float* __restrict__ sum_t,
    float* __restrict__ out,
    long n,
    int channels,
    long spatial) {
    long i = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (i < n) {
        int c = (int)((i / spatial) % channels);
        out[i] = epilogue(x[i], bias[c], sum_t[c]);
    }
}

torch::Tensor fused_epilogue_cuda(torch::Tensor x, torch::Tensor bias, torch::Tensor sum_t) {
    TORCH_CHECK(x.is_cuda(), "x must be a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "x must be float32");

    auto xc = x.contiguous();
    auto bc = bias.contiguous();
    auto sc = sum_t.contiguous();
    auto out = torch::empty_like(xc);

    long n = xc.numel();
    if (n == 0) return out;

    int C = (int)xc.size(1);
    long spatial = 1;
    for (int i = 2; i < (int)xc.dim(); ++i) spatial *= xc.size(i);

    const int threads = 256;
    const float* xp = xc.data_ptr<float>();
    const float* bp = bc.data_ptr<float>();
    const float* sp = sc.data_ptr<float>();
    float* op = out.data_ptr<float>();

    if ((n & 3L) == 0 && (spatial & 3L) == 0) {
        // Vectorized path: 4 floats per thread (16 bytes per load/store).
        long n_vec = n >> 2;
        long spatial_vec = spatial >> 2;
        long blocks = (n_vec + threads - 1) / threads;
        fused_epilogue_vec4_kernel<<<blocks, threads>>>(
            reinterpret_cast<const float4*>(xp), bp, sp,
            reinterpret_cast<float4*>(op), n_vec, C, spatial_vec);
    } else {
        long blocks = (n + threads - 1) / threads;
        fused_epilogue_scalar_kernel<<<blocks, threads>>>(xp, bp, sp, op, n, C, spatial);
    }
    return out;
}
"""

fused_epilogue_cpp_source = (
    "torch::Tensor fused_epilogue_cuda(torch::Tensor x, torch::Tensor bias, torch::Tensor sum_t);"
)

fused_epilogue = load_inline(
    name="fused_conv3d_epilogue",
    cpp_sources=fused_epilogue_cpp_source,
    cuda_sources=fused_epilogue_cuda_source,
    functions=["fused_epilogue_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model: cuDNN 3D convolution (bias handled in the epilogue) plus a
    single fused CUDA kernel for bias + LeakyReLU + tensor-sum + clamp + GELU.
    This replaces 4 separate elementwise CUDA kernels (and their global-memory
    round trips) with one vectorized pass.
    """
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super(ModelNew, self).__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.sum_tensor = nn.Parameter(torch.randn(sum_tensor_shape))
        self.epilogue = fused_epilogue

    def forward(self, x):
        # Bias is applied inside the fused epilogue kernel.
        x = F.conv3d(
            x,
            self.conv.weight,
            None,
            self.conv.stride,
            self.conv.padding,
            self.conv.dilation,
            self.conv.groups,
        )
        return self.epilogue.fused_epilogue_cuda(x, self.conv.bias, self.sum_tensor)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 9.6 ms; the PyTorch reference (with TF32 enabled) takes 21.6 ms; speedup 2.250x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| sm80_xmma_fprop_implicit_gemm_indexed_wo_smem_tf32f32_tf32f32_f32_nhwckrsc_nhwc_tilesize12 | 3995.0 | 1 |
| fused_epilogue_vec4_kernel(float4 const*, float const*, float const*, float4*, long, int,  | 2517.5 | 1 |
| void cudnn::engines_precompiled::nhwcToNchwKernel<float, float, float, true, false, (cudnn | 2513.6 | 1 |
| void cudnn::engines_precompiled::nchwToNhwcKernel<float, float, float, false, true, (cudnn | 573.9 | 2 |

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.
