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 3 of 6 for this task. Your previous solution (turn 2) 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 fastest engine for the fixed shapes/layouts.
torch.backends.cudnn.benchmark = True
torch.backends.cudnn.allow_tf32 = True

# Key idea (v2): keep the convolution fully in channels_last_3d (NDHWC) so
# cuDNN runs its fast NHWC tensor-core kernel with NO layout-transform kernels.
# A tiny custom kernel converts the input NCDHW->NDHWC (replaces cuDNN's slow
# precompiled nchwToNhwc), and a fused epilogue kernel applies
# bias + LeakyReLU(0.2) + per-channel add + clamp(-1,1) + exact GELU while
# transposing NDHWC->NCDHW through shared memory (replaces cuDNN's slow
# nhwcToNchw + 4 separate elementwise kernels) in one memory-bound pass.
_fused_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 per-channel sum
    v = fminf(fmaxf(v, CLAMP_LO), CLAMP_HI);       // clamp(-1, 1)
    return 0.5f * v * (1.0f + erff(v * RSQRT2));   // exact GELU
}

// ---------------- NCDHW -> NDHWC transform (one block per (n,d,h) tile) ------
__global__ void ncdhw_to_ndhwc_kernel(const float* __restrict__ in,
                                      float* __restrict__ out,
                                      int C, int D, int H, int W) {
    extern __shared__ float smem[];  // (C+1)*W floats, [w*(C+1) + c]
    int DH = D * H;
    long ndh = blockIdx.x;
    long n = ndh / DH;
    int rem = (int)(ndh - n * DH);
    int d = rem / H;
    int h = rem - d * H;
    long HW = (long)H * W;
    long cstride = (long)D * HW;
    const float* in_base = in + (n * C * D + d) * HW + h * W;
    float* out_base = out + ((n * D + d) * H + h) * ((long)W * C);
    int CW = C * W;
    int Cp = C + 1;
    for (int idx = threadIdx.x; idx < CW; idx += blockDim.x) {
        int c = idx / W;
        int w = idx - c * W;
        smem[w * Cp + c] = in_base[c * cstride + w];   // coalesced loads along w
    }
    __syncthreads();
    for (int idx = threadIdx.x; idx < CW; idx += blockDim.x) {
        int w = idx / C;
        int c = idx - w * C;
        out_base[idx] = smem[w * Cp + c];              // fully coalesced stores
    }
}

// ---- fused epilogue: NDHWC in -> NCDHW out (one block per (n,d,h) tile) -----
__global__ void epilogue_ndhwc_to_ncdhw_kernel(const float* __restrict__ in,
                                               const float* __restrict__ bias,
                                               const float* __restrict__ sumt,
                                               float* __restrict__ out,
                                               int C, int D, int H, int W) {
    extern __shared__ float smem[];  // C*(W+1) floats, [c*(W+1) + w]
    int DH = D * H;
    long ndh = blockIdx.x;
    long n = ndh / DH;
    int rem = (int)(ndh - n * DH);
    int d = rem / H;
    int h = rem - d * H;
    long HW = (long)H * W;
    long cstride = (long)D * HW;
    const float* in_base = in + ((n * D + d) * H + h) * ((long)W * C);
    float* out_base = out + (n * C * D + d) * HW + h * W;
    int CW = C * W;
    int Wp = W + 1;
    for (int idx = threadIdx.x; idx < CW; idx += blockDim.x) {
        int w = idx / C;
        int c = idx - w * C;
        float v = epilogue(in_base[idx], bias[c], sumt[c]);  // coalesced loads
        smem[c * Wp + w] = v;
    }
    __syncthreads();
    for (int idx = threadIdx.x; idx < CW; idx += blockDim.x) {
        int c = idx / W;
        int w = idx - c * W;
        out_base[c * cstride + w] = smem[c * Wp + w];        // coalesced stores
    }
}

// Fallback: scalar elementwise epilogue directly on NDHWC data (any shape).
__global__ void epilogue_ndhwc_scalar_kernel(const float* __restrict__ in,
                                             const float* __restrict__ bias,
                                             const float* __restrict__ sumt,
                                             float* __restrict__ out,
                                             long n, int C) {
    long i = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (i < n) {
        int c = (int)(i % C);
        out[i] = epilogue(in[i], bias[c], sumt[c]);
    }
}

torch::Tensor ncdhw_to_ndhwc_cuda(torch::Tensor x) {
    TORCH_CHECK(x.is_cuda(), "x must be CUDA");
    TORCH_CHECK(x.dim() == 5, "x must be 5D");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "x must be float32");
    auto xc = x.contiguous();
    long N = xc.size(0), C = xc.size(1), D = xc.size(2), H = xc.size(3), W = xc.size(4);
    auto out = at::empty_like(xc, at::MemoryFormat::ChannelsLast3d);
    long blocks = N * D * H;
    if (blocks == 0) return out;
    int smem = (int)((C + 1) * W * 4);
    TORCH_CHECK(smem <= 48 * 1024, "C*W too large for transform kernel");
    ncdhw_to_ndhwc_kernel<<<(int)blocks, 256, smem>>>(
        xc.data_ptr<float>(), out.data_ptr<float>(),
        (int)C, (int)D, (int)H, (int)W);
    return out;
}

torch::Tensor fused_epilogue_cuda(torch::Tensor y, torch::Tensor bias, torch::Tensor sum_t) {
    TORCH_CHECK(y.is_cuda(), "y must be CUDA");
    TORCH_CHECK(y.dim() == 5, "y must be 5D");
    TORCH_CHECK(y.scalar_type() == at::kFloat, "y must be float32");
    auto yc = y.is_contiguous(at::MemoryFormat::ChannelsLast3d)
                  ? y
                  : y.contiguous(at::MemoryFormat::ChannelsLast3d);
    long N = yc.size(0), C = yc.size(1), D = yc.size(2), H = yc.size(3), W = yc.size(4);
    auto bc = bias.contiguous();
    auto sc = sum_t.contiguous();

    long smem_floats = C * (W + 1);
    if (smem_floats * 4 <= 48 * 1024) {
        auto out = at::empty({N, C, D, H, W}, yc.options());  // NCDHW contiguous
        long blocks = N * D * H;
        if (blocks == 0) return out;
        epilogue_ndhwc_to_ncdhw_kernel<<<(int)blocks, 256, (int)(smem_floats * 4)>>>(
            yc.data_ptr<float>(), bc.data_ptr<float>(), sc.data_ptr<float>(),
            out.data_ptr<float>(), (int)C, (int)D, (int)H, (int)W);
        return out;
    }
    // Generic fallback: elementwise on NDHWC, then convert layout with ATen.
    auto out = at::empty_like(yc);
    long n = out.numel();
    if (n == 0) return out.contiguous();
    long blocks = (n + 255) / 256;
    epilogue_ndhwc_scalar_kernel<<<(int)blocks, 256>>>(
        yc.data_ptr<float>(), bc.data_ptr<float>(), sc.data_ptr<float>(),
        out.data_ptr<float>(), n, (int)C);
    return out.contiguous();
}
"""

_fused_cpp_source = (
    "torch::Tensor ncdhw_to_ndhwc_cuda(torch::Tensor x);\n"
    "torch::Tensor fused_epilogue_cuda(torch::Tensor y, torch::Tensor bias, torch::Tensor sum_t);"
)

_fused_ext = load_inline(
    name="fused_conv3d_nhwc_epilogue_v2",
    cpp_sources=_fused_cpp_source,
    cuda_sources=_fused_cuda_source,
    functions=["ncdhw_to_ndhwc_cuda", "fused_epilogue_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model:
      * input converted NCDHW->NDHWC by a fast custom kernel,
      * cuDNN conv3d runs natively in channels_last_3d (no transform kernels),
      * one fused custom kernel applies bias + LeakyReLU + tensor-sum + clamp +
        GELU and writes the final NCDHW-contiguous result via an in-kernel
        shared-memory transpose.
    """
    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.ext = _fused_ext
        # Keep the weight in channels_last_3d so cuDNN avoids weight transforms.
        with torch.no_grad():
            self.conv.weight.data = self.conv.weight.data.to(
                memory_format=torch.channels_last_3d
            )

    def forward(self, x):
        # Safety fallback for unexpected parameter shapes: plain eager path.
        if self.sum_tensor.numel() != self.conv.out_channels or x.dim() != 5:
            y = self.conv(x)
            y = F.leaky_relu(y, negative_slope=0.2)
            y = y + self.sum_tensor
            y = torch.clamp(y, min=-1.0, max=1.0)
            return F.gelu(y)

        w = self.conv.weight
        if not w.is_contiguous(memory_format=torch.channels_last_3d):
            w = w.contiguous(memory_format=torch.channels_last_3d)

        # Fast custom NCDHW -> NDHWC conversion (fits in shared memory here).
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and (x.size(1) + 1) * x.size(4) * 4 <= 48 * 1024
        ):
            x_cl = self.ext.ncdhw_to_ndhwc_cuda(x)
        else:
            x_cl = x.to(memory_format=torch.channels_last_3d)

        # Bias is applied inside the fused epilogue kernel.
        y = F.conv3d(
            x_cl,
            w,
            None,
            self.conv.stride,
            self.conv.padding,
            self.conv.dilation,
            self.conv.groups,
        )
        return self.ext.fused_epilogue_cuda(y, self.conv.bias, self.sum_tensor)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 8.4 ms; the PyTorch reference (with TF32 enabled) takes 21.6 ms; speedup 2.571x.
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 | 3994.1 | 1 |
| epilogue_ndhwc_to_ncdhw_kernel(float const*, float const*, float const*, float*, int, int, | 3394.1 | 1 |
| ncdhw_to_ndhwc_kernel(float const*, float*, int, int, int, int) | 595.7 | 1 |
| void cudnn::engines_precompiled::convertTensor_kernel<float, float, float, (cudnnKernelDat | 435.3 | 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.
