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 4 of 6 for this task. Your previous solution (turn 3) 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 fused_activation_cuda(
    torch::Tensor x,
    torch::Tensor bias,
    torch::Tensor addition);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <algorithm>
#include <cstdint>

// On the clamped interval [-1, 1], this polynomial evaluates exact
// GELU to float32 accuracy, without the general-purpose erf routine.
__device__ __forceinline__ float activate(float x, float bias, float addition) {
    x = __fadd_rn(x, bias);
    x = x > 0.0f ? x : __fmul_rn(0.2f, x);
    x = __fadd_rn(x, addition);
    x = x < -1.0f ? -1.0f : x;
    x = x >  1.0f ?  1.0f : x;

    const float z = x * x;
    float p = -1.0f / 9676800.0f;
    p = fmaf(p, z,  1.0f / 599040.0f);
    p = fmaf(p, z, -1.0f / 42240.0f);
    p = fmaf(p, z,  1.0f / 3456.0f);
    p = fmaf(p, z, -1.0f / 336.0f);
    p = fmaf(p, z,  1.0f / 40.0f);
    p = fmaf(p, z, -1.0f / 6.0f);
    p = fmaf(p, z,  1.0f);

    return fmaf(0.3989422804014327f * z, p, 0.5f * x);
}

__device__ __forceinline__ float4 activate4(
    float4 x, const float4 b, const float4 a
) {
    x.x = activate(x.x, b.x, a.x);
    x.y = activate(x.y, b.y, a.y);
    x.z = activate(x.z, b.z, a.z);
    x.w = activate(x.w, b.w, a.w);
    return x;
}

// Every iteration visits the same four channels. Load their parameters
// once and keep them in registers throughout the grid-stride loop.
__global__ void fused_channels64_kernel(
    float4* __restrict__ output,
    const float4* __restrict__ bias,
    const float4* __restrict__ addition,
    int64_t vectors
) {
    const int c = threadIdx.x & 15;
    const float4 b = bias[c];
    const float4 a = addition[c];
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;

    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vectors; i += stride) {
        output[i] = activate4(output[i], b, a);
    }
}

template<bool CHANNELS_LAST>
__global__ void fused_vector_kernel(
    float4* __restrict__ output,
    const float* __restrict__ bias,
    const float* __restrict__ addition,
    int64_t vectors,
    int64_t spatial,
    int channels
) {
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vectors; i += stride) {
        float4 b;
        float4 a;
        if (CHANNELS_LAST) {
            const int c = i % (channels / 4);
            b = reinterpret_cast<const float4*>(bias)[c];
            a = reinterpret_cast<const float4*>(addition)[c];
        } else {
            const int c = ((i * 4) / spatial) % channels;
            b = make_float4(bias[c], bias[c], bias[c], bias[c]);
            a = make_float4(addition[c], addition[c],
                            addition[c], addition[c]);
        }
        output[i] = activate4(output[i], b, a);
    }
}

template<bool CHANNELS_LAST>
__global__ void fused_scalar_kernel(
    float* __restrict__ output,
    const float* __restrict__ bias,
    const float* __restrict__ addition,
    int64_t count,
    int64_t spatial,
    int channels
) {
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count; i += stride) {
        const int c = CHANNELS_LAST
            ? i % channels
            : (i / spatial) % channels;
        output[i] = activate(output[i], bias[c], addition[c]);
    }
}

torch::Tensor fused_activation_cuda(
    torch::Tensor x,
    torch::Tensor bias,
    torch::Tensor addition
) {
    TORCH_CHECK(x.is_cuda() && bias.is_cuda() && addition.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.device() == bias.device() &&
                x.device() == addition.device(), "Device mismatch");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                bias.scalar_type() == at::kFloat &&
                addition.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.dim() == 5, "Expected a five-dimensional tensor");
    TORCH_CHECK(bias.is_contiguous() && addition.is_contiguous(),
                "Expected contiguous parameters");
    TORCH_CHECK(bias.numel() == x.size(1) &&
                addition.numel() == x.size(1),
                "Expected one parameter value per channel");

    const bool channels_last =
        x.is_contiguous(at::MemoryFormat::ChannelsLast3d);
    TORCH_CHECK(channels_last || x.is_contiguous(),
                "Unsupported tensor layout");

    const c10::cuda::CUDAGuard guard(x.device());
    const cudaStream_t stream =
        c10::cuda::getCurrentCUDAStream(x.get_device()).stream();

    const int64_t count = x.numel();
    if (count == 0) return x;

    const int channels = static_cast<int>(x.size(1));
    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const bool aligned =
        reinterpret_cast<uintptr_t>(x.data_ptr<float>()) % 16 == 0 &&
        reinterpret_cast<uintptr_t>(bias.data_ptr<float>()) % 16 == 0 &&
        reinterpret_cast<uintptr_t>(addition.data_ptr<float>()) % 16 == 0;
    const bool vectorized =
        aligned && (channels_last ? channels % 4 == 0 : spatial % 4 == 0);

    constexpr int threads = 256;
    const int64_t work = vectorized ? count / 4 : count;
    const int blocks = static_cast<int>(
        std::min<int64_t>((work + threads - 1) / threads, 4096));

    if (vectorized && channels_last && channels == 64) {
        fused_channels64_kernel<<<blocks, threads, 0, stream>>>(
            reinterpret_cast<float4*>(x.data_ptr<float>()),
            reinterpret_cast<const float4*>(bias.data_ptr<float>()),
            reinterpret_cast<const float4*>(addition.data_ptr<float>()),
            work);
    } else if (vectorized) {
        auto output = reinterpret_cast<float4*>(x.data_ptr<float>());
        if (channels_last) {
            fused_vector_kernel<true><<<blocks, threads, 0, stream>>>(
                output, bias.data_ptr<float>(), addition.data_ptr<float>(),
                work, spatial, channels);
        } else {
            fused_vector_kernel<false><<<blocks, threads, 0, stream>>>(
                output, bias.data_ptr<float>(), addition.data_ptr<float>(),
                work, spatial, channels);
        }
    } else if (channels_last) {
        fused_scalar_kernel<true><<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), bias.data_ptr<float>(),
            addition.data_ptr<float>(), count, spatial, channels);
    } else {
        fused_scalar_kernel<false><<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), bias.data_ptr<float>(),
            addition.data_ptr<float>(), count, spatial, channels);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return x;
}
"""

_fused_ops = load_inline(
    name="conv3d_fused_gelu_channels64_v3",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_activation_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.sum_tensor = nn.Parameter(torch.randn(sum_tensor_shape))
        self.conv.to(memory_format=torch.channels_last_3d)

    def forward(self, x):
        use_custom = (
            x.is_cuda
            and x.dtype == torch.float32
            and self.conv.weight.dtype == torch.float32
            and self.conv.bias is not None
            and self.conv.bias.dtype == torch.float32
            and self.sum_tensor.dtype == torch.float32
            and tuple(self.sum_tensor.shape)
            == (self.conv.out_channels, 1, 1, 1)
            and not torch.is_autocast_enabled()
        )

        if use_custom:
            x = x.contiguous(memory_format=torch.channels_last_3d)
            weight = self.conv.weight.contiguous(
                memory_format=torch.channels_last_3d
            )
            x = F.conv3d(
                x,
                weight,
                None,
                self.conv.stride,
                self.conv.padding,
                self.conv.dilation,
                self.conv.groups,
            )
            return _fused_ops.fused_activation_cuda(
                x,
                self.conv.bias.contiguous(),
                self.sum_tensor.contiguous(),
            )

        x = self.conv(x)
        x = F.leaky_relu(x, negative_slope=0.2)
        x = torch.clamp(x + self.sum_tensor, min=-1.0, max=1.0)
        return F.gelu(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 7.51 ms; the PyTorch reference (with TF32 enabled) takes 21.6 ms; speedup 2.876x.
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 | 3993.8 | 1 |
| fused_channels64_kernel(float4*, float4 const*, float4 const*, long) | 2631.4 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 442.7 | 1 |
| void cudnn::engines_precompiled::convertTensor_kernel<float, float, float, (cudnnKernelDat | 435.6 | 2 |

The fastest correct solution so far (2.888x speedup) is:
```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 fused_bias_activation_cuda(
    torch::Tensor x, torch::Tensor bias, torch::Tensor addition);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <algorithm>
#include <cstdint>

__device__ __forceinline__ float activate(
    float x, float bias, float addition
) {
    x = x + bias;
    x = x > 0.0f ? x : 0.2f * x;
    x = x + addition;
    x = x < -1.0f ? -1.0f : x;
    x = x > 1.0f ? 1.0f : x;
    return (0.5f * x) *
           (1.0f + erff(x * 0.7071067811865475244f));
}

template<bool CHANNELS_LAST>
__global__ void fused_vector_kernel(
    float4* __restrict__ output,
    const float* __restrict__ bias,
    const float* __restrict__ addition,
    int64_t vectors,
    int64_t spatial,
    int channels
) {
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vectors; i += stride) {
        float4 v = output[i];
        if (CHANNELS_LAST) {
            const int c4 = i % (channels / 4);
            const float4 b = reinterpret_cast<const float4*>(bias)[c4];
            const float4 a = reinterpret_cast<const float4*>(addition)[c4];
            v.x = activate(v.x, b.x, a.x);
            v.y = activate(v.y, b.y, a.y);
            v.z = activate(v.z, b.z, a.z);
            v.w = activate(v.w, b.w, a.w);
        } else {
            const int c = ((i * 4) / spatial) % channels;
            const float b = bias[c];
            const float a = addition[c];
            v.x = activate(v.x, b, a);
            v.y = activate(v.y, b, a);
            v.z = activate(v.z, b, a);
            v.w = activate(v.w, b, a);
        }
        output[i] = v;
    }
}

template<bool CHANNELS_LAST>
__global__ void fused_scalar_kernel(
    float* __restrict__ output,
    const float* __restrict__ bias,
    const float* __restrict__ addition,
    int64_t count,
    int64_t spatial,
    int channels
) {
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count; i += stride) {
        const int c = CHANNELS_LAST ? i % channels
                                    : (i / spatial) % channels;
        output[i] = activate(output[i], bias[c], addition[c]);
    }
}

torch::Tensor fused_bias_activation_cuda(
    torch::Tensor x, torch::Tensor bias, torch::Tensor addition
) {
    TORCH_CHECK(x.is_cuda() && bias.is_cuda() && addition.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.device() == bias.device() &&
                x.device() == addition.device(), "Device mismatch");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                bias.scalar_type() == at::kFloat &&
                addition.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.dim() == 5, "Expected a five-dimensional tensor");
    TORCH_CHECK(bias.is_contiguous() && addition.is_contiguous(),
                "Expected contiguous parameters");
    TORCH_CHECK(bias.numel() == x.size(1) &&
                addition.numel() == x.size(1),
                "Expected one bias and addition value per channel");

    const bool channels_last =
        x.is_contiguous(at::MemoryFormat::ChannelsLast3d);
    TORCH_CHECK(channels_last || x.is_contiguous(),
                "Unsupported output layout");

    const c10::cuda::CUDAGuard guard(x.device());
    const cudaStream_t stream =
        c10::cuda::getCurrentCUDAStream(x.get_device()).stream();

    const int64_t count = x.numel();
    if (count == 0) return x;

    const int channels = static_cast<int>(x.size(1));
    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const bool aligned =
        reinterpret_cast<uintptr_t>(x.data_ptr<float>()) % 16 == 0 &&
        reinterpret_cast<uintptr_t>(bias.data_ptr<float>()) % 16 == 0 &&
        reinterpret_cast<uintptr_t>(addition.data_ptr<float>()) % 16 == 0;
    const bool vectorized =
        aligned && (channels_last ? channels % 4 == 0 : spatial % 4 == 0);

    constexpr int threads = 256;
    const int64_t work = vectorized ? count / 4 : count;
    const int blocks = static_cast<int>(
        std::min<int64_t>((work + threads - 1) / threads, 65535));

    if (vectorized) {
        auto ptr = reinterpret_cast<float4*>(x.data_ptr<float>());
        if (channels_last) {
            fused_vector_kernel<true><<<blocks, threads, 0, stream>>>(
                ptr, bias.data_ptr<float>(), addition.data_ptr<float>(),
                work, spatial, channels);
        } else {
            fused_vector_kernel<false><<<blocks, threads, 0, stream>>>(
                ptr, bias.data_ptr<float>(), addition.data_ptr<float>(),
                work, spatial, channels);
        }
    } else if (channels_last) {
        fused_scalar_kernel<true><<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), bias.data_ptr<float>(),
            addition.data_ptr<float>(), count, spatial, channels);
    } else {
        fused_scalar_kernel<false><<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), bias.data_ptr<float>(),
            addition.data_ptr<float>(), count, spatial, channels);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return x;
}
"""

_fused_ops = load_inline(
    name="conv3d_channels_last_fused_bias_leaky_add_clamp_gelu_v2",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_bias_activation_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super().__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):
        use_custom = (
            x.is_cuda
            and x.dtype == torch.float32
            and self.conv.weight.dtype == torch.float32
            and self.conv.bias is not None
            and self.conv.bias.dtype == torch.float32
            and self.sum_tensor.dtype == torch.float32
            and tuple(self.sum_tensor.shape)
            == (self.conv.out_channels, 1, 1, 1)
            and not torch.is_autocast_enabled()
        )

        if use_custom:
            x = x.contiguous(memory_format=torch.channels_last_3d)
            weight = self.conv.weight.contiguous(
                memory_format=torch.channels_last_3d
            )
            x = F.conv3d(
                x,
                weight,
                None,
                self.conv.stride,
                self.conv.padding,
                self.conv.dilation,
                self.conv.groups,
            )
            return _fused_ops.fused_bias_activation_cuda(
                x,
                self.conv.bias.contiguous(),
                self.sum_tensor.contiguous(),
            )

        x = self.conv(x)
        x = F.leaky_relu(x, negative_slope=0.2)
        x = torch.clamp(x + self.sum_tensor, min=-1.0, max=1.0)
        return F.gelu(x)
```

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.
