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
from torch.utils.cpp_extension import load_inline

# Autotune cuDNN (exhaustive search) for the fixed conv shapes used here.
torch.backends.cudnn.benchmark = True
torch.backends.cudnn.benchmark_limit = 0
torch.backends.cudnn.allow_tf32 = True
torch.backends.cuda.matmul.allow_tf32 = True

# Key idea: cuDNN's fastest algo for this conv is a native NHWC (channels-last
# 3D) tensor-core kernel. In the previous version the NCDHW tensors forced
# cuDNN to pay for NCHW->NHWC and NHWC->NCHW transposes, and our post-process
# kernel then ran on the transposed layout (~5.7ms of pure layout traffic).
# Here we keep weights/activations channels-last end to end, and run the fused
# LeakyReLU -> +sum_tensor -> clamp -> GELU epilogue directly on the NHWC data
# (float4 spans 4 consecutive channels), so no transpose kernels remain except
# a single one-time conversion of the input.
fused_postprocess_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

__device__ __forceinline__ float fused_op(float v, float s) {
    v = (v > 0.0f) ? v : v * 0.2f;                                   // LeakyReLU(0.2)
    v += s;                                                          // per-channel add
    v = fminf(fmaxf(v, -1.0f), 1.0f);                                // clamp(-1, 1)
    return 0.5f * v * (1.0f + erff(v * 0.70710678118654752440f));    // exact GELU
}

// ---- channels-last (NDHWC) path: float4 spans 4 consecutive channels ----
__global__ void fused_cl_vec4_kernel(const float4* __restrict__ x,
                                     const float4* __restrict__ s4,
                                     float4* __restrict__ out,
                                     long total_vec,
                                     int c_vec,
                                     long c_mask) {
    const long stride = (long)gridDim.x * blockDim.x;
    for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < total_vec; i += stride) {
        const int cv = (c_mask >= 0) ? (int)(i & c_mask) : (int)(i % c_vec);
        const float4 sv = s4[cv];
        const float4 v = x[i];
        float4 r;
        r.x = fused_op(v.x, sv.x);
        r.y = fused_op(v.y, sv.y);
        r.z = fused_op(v.z, sv.z);
        r.w = fused_op(v.w, sv.w);
        out[i] = r;
    }
}

__global__ void fused_cl_scalar_kernel(const float* __restrict__ x,
                                       const float* __restrict__ s,
                                       float* __restrict__ out,
                                       long total,
                                       int channels) {
    const long stride = (long)gridDim.x * blockDim.x;
    for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < total; i += stride) {
        out[i] = fused_op(x[i], s[i % channels]);
    }
}

// ---- NCDHW fallback path: float4 spans 4 consecutive spatial locations ----
__global__ void fused_vec4_kernel(const float4* __restrict__ x,
                                  const float* __restrict__ sum_tensor,
                                  float4* __restrict__ out,
                                  int spatial_vec,
                                  int channels) {
    const int nc = blockIdx.y;
    const float sv = sum_tensor[nc % channels];
    const long base = (long)nc * spatial_vec;
    const float4* xs = x + base;
    float4* os = out + base;
    const int stride = gridDim.x * blockDim.x;
    for (int i = blockIdx.x * blockDim.x + threadIdx.x; i < spatial_vec; i += stride) {
        const float4 v = xs[i];
        float4 r;
        r.x = fused_op(v.x, sv);
        r.y = fused_op(v.y, sv);
        r.z = fused_op(v.z, sv);
        r.w = fused_op(v.w, sv);
        os[i] = r;
    }
}

__global__ void fused_scalar_kernel(const float* __restrict__ x,
                                    const float* __restrict__ sum_tensor,
                                    float* __restrict__ out,
                                    long spatial_size,
                                    int channels) {
    const int nc = blockIdx.y;
    const float sv = sum_tensor[nc % channels];
    const long base = (long)nc * spatial_size;
    const float* xs = x + base;
    float* os = out + base;
    const long stride = (long)gridDim.x * blockDim.x;
    for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < spatial_size; i += stride) {
        os[i] = fused_op(xs[i], sv);
    }
}

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

    auto sc = sum_tensor.contiguous();
    const int channels = (int)x.size(1);
    const int block = 256;
    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if (x.is_contiguous(at::MemoryFormat::ChannelsLast3d)) {
        const long total = x.numel();
        if ((channels & 3) == 0) {
            const long total_vec = total >> 2;
            const int c_vec = channels >> 2;
            const long c_mask = ((c_vec & (c_vec - 1)) == 0) ? (long)(c_vec - 1) : -1L;
            long want = (total_vec + block - 1) / block;
            int gx = (int)(want > 65535 ? 65535 : want);
            fused_cl_vec4_kernel<<<gx, block, 0, stream>>>(
                reinterpret_cast<const float4*>(x.data_ptr<float>()),
                reinterpret_cast<const float4*>(sc.data_ptr<float>()),
                reinterpret_cast<float4*>(x.data_ptr<float>()),
                total_vec, c_vec, c_mask);
        } else {
            long want = (total + block - 1) / block;
            int gx = (int)(want > 65535 ? 65535 : want);
            fused_cl_scalar_kernel<<<gx, block, 0, stream>>>(
                x.data_ptr<float>(), sc.data_ptr<float>(), x.data_ptr<float>(),
                total, channels);
        }
        return x;
    }

    auto xc = x.contiguous();
    long spatial = 1;
    for (int i = 2; i < xc.dim(); ++i) spatial *= xc.size(i);
    const long nc_total = xc.numel() / spatial;

    if (spatial % 4 == 0) {
        const int spatial_vec = (int)(spatial >> 2);
        long want = (spatial_vec + block - 1) / block;
        int gx = (int)(want > 65535 ? 65535 : want);
        dim3 grid(gx, (unsigned)nc_total);
        fused_vec4_kernel<<<grid, block, 0, stream>>>(
            reinterpret_cast<const float4*>(xc.data_ptr<float>()),
            sc.data_ptr<float>(),
            reinterpret_cast<float4*>(xc.data_ptr<float>()),
            spatial_vec, channels);
    } else {
        long want = (spatial + block - 1) / block;
        int gx = (int)(want > 65535 ? 65535 : want);
        dim3 grid(gx, (unsigned)nc_total);
        fused_scalar_kernel<<<grid, block, 0, stream>>>(
            xc.data_ptr<float>(), sc.data_ptr<float>(), xc.data_ptr<float>(),
            spatial, channels);
    }
    return xc;
}
"""

fused_postprocess_cpp_source = (
    "torch::Tensor fused_postprocess_cuda(torch::Tensor x, torch::Tensor sum_tensor);"
)

fused_postprocess = load_inline(
    name="fused_postprocess_cl",
    cpp_sources=fused_postprocess_cpp_source,
    cuda_sources=fused_postprocess_source,
    functions=["fused_postprocess_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model: runs the 3D convolution natively in channels-last (NHWC)
    layout so cuDNN uses its tensor-core NHWC kernels without any layout
    transpose kernels, then applies LeakyReLU + per-channel sum + clamp + GELU
    in a single fused, vectorized CUDA kernel over the NHWC data.
    """
    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))
        # Keep conv weights in channels-last layout (one-time cost) so cuDNN
        # never inserts NCHW<->NHWC transpose kernels.
        with torch.no_grad():
            self.conv.weight.data = self.conv.weight.data.contiguous(
                memory_format=torch.channels_last_3d)

    def forward(self, x):
        x = x.contiguous(memory_format=torch.channels_last_3d)
        x = self.conv(x)
        x = fused_postprocess.fused_postprocess_cuda(
            x, self.sum_tensor.view(-1))
        return x
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 10.1 ms; the PyTorch reference (with TF32 enabled) takes 21.6 ms; speedup 2.139x.
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 | 4002.4 | 1 |
| fused_cl_vec4_kernel(float4 const*, float4 const*, float4*, long, int, long) | 2602.7 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 2587.7 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 441.6 | 1 |
| void cudnn::engines_precompiled::convertTensor_kernel<float, float, float, (cudnnKernelDat | 433.7 | 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.


Precision rule: the timed forward must compute in FP32 (TF32 tensor-core math is allowed, as in the PyTorch reference). Do not cast inputs, weights or intermediate results to float16 or bfloat16 and do not call half-precision kernels in forward().
