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 5 of 6 for this task. Your previous solution (turn 4) 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

# v4: The layout conversions are re-formulated as plain per-sample 2D matrix
# transposes (valid because both NCDHW and NDHWC are contiguous per sample):
#   * input  NCDHW [8, M] -> NDHWC [M, 8]   (M = D*H*W)
#   * output NDHWC [M, 64] -> NCDHW [64, M] with the fused epilogue
#     (bias + LeakyReLU(0.2) + per-channel sum + clamp(-1,1) + exact GELU)
#     applied on the fly while loading.
# Both kernels use float4 global loads AND stores, padded shared-memory tiles
# arranged so all shared accesses are (nearly) bank-conflict free, run at full
# occupancy, and move exactly the minimum required bytes (memory bound).
# cuDNN still runs the conv natively in channels_last_3d.
_fused_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

#define NEG_SLOPE 0.2f
#define RSQRT2    0.70710678118654752440f  // 1 / sqrt(2)

__device__ __forceinline__ float epilogue_fn(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, -1.0f), 1.0f);              // clamp(-1, 1)
    return 0.5f * v * (1.0f + erff(v * RSQRT2));   // exact GELU
}

// -------------- NCDHW -> NDHWC: per-sample [8, M] -> [M, 8] -----------------
// Tile: 256 m x 8 c per block, 256 threads, float4 on both global sides.
// Requires C == 8 and M % 4 == 0. grid = (ceil(M/256), N).
__global__ void __launch_bounds__(256)
ncdhw_to_ndhwc_c8_kernel(const float4* __restrict__ in,
                         float4* __restrict__ out,
                         long M) {
    __shared__ float smem[8][260];  // 260 % 4 == 0 -> aligned float4 writes
    long n = blockIdx.y;
    long m0 = (long)blockIdx.x * 256;
    long M4 = M >> 2;
    const float4* inb = in + n * (8 * M4);
    float4* outb = out + n * (2 * M);
    int t = threadIdx.x;

    #pragma unroll
    for (int it = 0; it < 2; ++it) {
        int f4 = t + (it << 8);   // 0..511
        int c = f4 >> 6;          // 0..7 (64 float4 per channel row)
        int m4 = f4 & 63;         // 0..63
        long m = m0 + (m4 << 2);
        if (m < M) {
            float4 v = inb[c * M4 + (m >> 2)];          // 512B coalesced
            *reinterpret_cast<float4*>(&smem[c][m4 << 2]) = v;
        }
    }
    __syncthreads();
    #pragma unroll
    for (int it = 0; it < 2; ++it) {
        int f4 = t + (it << 8);   // 0..511
        int ml = f4 >> 1;         // 0..255
        int half = f4 & 1;
        long m = m0 + ml;
        if (m < M) {
            int c0 = half << 2;                         // 0 or 4
            float4 v;
            v.x = smem[c0 + 0][ml];                     // conflict-free reads
            v.y = smem[c0 + 1][ml];
            v.z = smem[c0 + 2][ml];
            v.w = smem[c0 + 3][ml];
            outb[(m << 1) + half] = v;                  // 512B coalesced
        }
    }
}

// ------- fused epilogue + transpose: NDHWC [M, C] -> NCDHW [C, M] -----------
// Tile: 32 m x 64 c per block, 256 threads, float4 global loads/stores.
// Requires C % 4 == 0, C <= 64, M % 4 == 0. grid = (ceil(M/32), N).
__global__ void __launch_bounds__(256)
epilogue_ndhwc_to_ncdhw_kernel(const float4* __restrict__ in,
                               float4* __restrict__ out,
                               const float* __restrict__ bias,
                               const float* __restrict__ sumt,
                               long M, int C) {
    __shared__ float smem[64][33];  // +1 pad: conflict-free scalar reads
    long n = blockIdx.y;
    long m0 = (long)blockIdx.x * 32;
    long M4 = M >> 2;
    int C4 = C >> 2;
    const float4* inb = in + n * (M4 * C);
    float4* outb = out + n * (M4 * C);
    int t = threadIdx.x;

    #pragma unroll
    for (int it = 0; it < 2; ++it) {
        int f4 = t + (it << 8);   // 0..511
        int ml = f4 >> 4;         // 0..31
        int c4 = f4 & 15;         // 0..15
        long m = m0 + ml;
        if (c4 < C4 && m < M) {
            float4 v = inb[m * C4 + c4];                // 256B+ coalesced
            int c0 = c4 << 2;
            v.x = epilogue_fn(v.x, __ldg(bias + c0 + 0), __ldg(sumt + c0 + 0));
            v.y = epilogue_fn(v.y, __ldg(bias + c0 + 1), __ldg(sumt + c0 + 1));
            v.z = epilogue_fn(v.z, __ldg(bias + c0 + 2), __ldg(sumt + c0 + 2));
            v.w = epilogue_fn(v.w, __ldg(bias + c0 + 3), __ldg(sumt + c0 + 3));
            smem[c0 + 0][ml] = v.x;
            smem[c0 + 1][ml] = v.y;
            smem[c0 + 2][ml] = v.z;
            smem[c0 + 3][ml] = v.w;
        }
    }
    __syncthreads();
    #pragma unroll
    for (int it = 0; it < 2; ++it) {
        int f4 = t + (it << 8);       // 0..511
        int c = f4 >> 3;              // 0..63
        int ml = (f4 & 7) << 2;       // 0,4,...,28
        long m = m0 + ml;
        if (c < C && m < M) {
            float4 v;
            v.x = smem[c][ml + 0];    // conflict-free scalar reads
            v.y = smem[c][ml + 1];
            v.z = smem[c][ml + 2];
            v.w = smem[c][ml + 3];
            outb[(long)c * M4 + (m >> 2)] = v;          // coalesced float4
        }
    }
}

// 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_fn(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);
    long M = xc.size(2) * xc.size(3) * xc.size(4);
    TORCH_CHECK(C == 8 && (M & 3) == 0 && N <= 65535, "unsupported shape");
    auto out = at::empty_like(xc, at::MemoryFormat::ChannelsLast3d);
    if (N * M == 0) return out;
    dim3 grid((unsigned)((M + 255) / 256), (unsigned)N);
    auto stream = at::cuda::getCurrentCUDAStream();
    ncdhw_to_ndhwc_c8_kernel<<<grid, 256, 0, stream>>>(
        reinterpret_cast<const float4*>(xc.data_ptr<float>()),
        reinterpret_cast<float4*>(out.data_ptr<float>()), M);
    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);
    long M = yc.size(2) * yc.size(3) * yc.size(4);
    auto bc = bias.contiguous();
    auto sc = sum_t.contiguous();
    auto stream = at::cuda::getCurrentCUDAStream();

    if (N > 0 && M > 0 && (C & 3) == 0 && C <= 64 && (M & 3) == 0 && N <= 65535) {
        auto out = at::empty({yc.size(0), yc.size(1), yc.size(2), yc.size(3), yc.size(4)},
                             yc.options());  // NCDHW contiguous
        dim3 grid((unsigned)((M + 31) / 32), (unsigned)N);
        epilogue_ndhwc_to_ncdhw_kernel<<<grid, 256, 0, stream>>>(
            reinterpret_cast<const float4*>(yc.data_ptr<float>()),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            bc.data_ptr<float>(), sc.data_ptr<float>(), M, (int)C);
        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, 0, stream>>>(
        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_v4",
    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 fully-vectorized custom
        transpose kernel,
      * cuDNN conv3d runs natively in channels_last_3d (tensor cores),
      * one fused custom kernel applies bias + LeakyReLU + tensor-sum + clamp +
        GELU and writes the final NCDHW-contiguous result via a shared-memory
        tile transpose with float4 accesses on both sides.
    """
    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/input configurations.
        if (
            self.sum_tensor.numel() != self.conv.out_channels
            or x.dim() != 5
            or not x.is_cuda
            or x.dtype != torch.float32
        ):
            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):
            with torch.no_grad():
                self.conv.weight.data = w.contiguous(
                    memory_format=torch.channels_last_3d
                )
            w = self.conv.weight

        # Fast custom NCDHW -> NDHWC conversion (vectorized for C == 8).
        M_in = x.size(2) * x.size(3) * x.size(4)
        if x.size(1) == 8 and (M_in % 4) == 0 and x.size(0) <= 65535:
            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 7.48 ms; the PyTorch reference (with TF32 enabled) takes 21.6 ms; speedup 2.888x.
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 | 3994.6 | 1 |
| epilogue_ndhwc_to_ncdhw_kernel(float4 const*, float4*, float const*, float const*, long, i | 2642.4 | 1 |
| void cudnn::engines_precompiled::convertTensor_kernel<float, float, float, (cudnnKernelDat | 437.9 | 2 |
| ncdhw_to_ndhwc_c8_kernel(float4 const*, float4*, long) | 393.2 | 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.
