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 GEMM, GroupNorm, Swish, Multiply, and Swish operations.
    """
    def __init__(self, in_features, out_features, num_groups, multiply_weight_shape):
        super(Model, self).__init__()
        self.gemm = nn.Linear(in_features, out_features)
        self.group_norm = nn.GroupNorm(num_groups, out_features)
        self.multiply_weight = nn.Parameter(torch.randn(multiply_weight_shape)) 

    def forward(self, x):
        # (batch_size, in_features) -> (batch_size, out_features)
        x = self.gemm(x)
        # (batch_size, out_features) -> (batch_size, out_features)
        x = self.group_norm(x)
        # (batch_size, out_features) -> (batch_size, out_features)
        x = x * torch.sigmoid(x)
        # (batch_size, out_features) -> (batch_size, out_features)
        x = x * self.multiply_weight
        # (batch_size, out_features) -> (batch_size, out_features)
        x = x * torch.sigmoid(x)
        return x

batch_size = 1024
in_features = 8192
out_features = 8192
num_groups = 256
multiply_weight_shape = (out_features,)

def get_inputs():
    return [torch.rand(batch_size, in_features)]

def get_init_inputs():
    return [in_features, out_features, num_groups, multiply_weight_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
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor linear_norm_swish_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    torch::Tensor gamma,
    torch::Tensor beta,
    torch::Tensor multiply_weight,
    int64_t groups,
    double eps);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cublas_v2.h>

__device__ __forceinline__ float warp_sum(float value) {
    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1) {
        value += __shfl_down_sync(0xffffffff, value, offset);
    }
    return __shfl_sync(0xffffffff, value, 0);
}

__device__ __forceinline__ float finish_value(
    float value, float mean, float inv_std,
    float gamma, float beta, float multiplier
) {
    float normalized = ((value - mean) * inv_std) * gamma + beta;
    float activated = normalized / (1.0f + __expf(-normalized));
    float weighted = activated * multiplier;
    return weighted / (1.0f + __expf(-weighted));
}

template<bool GROUP_SIZE_32>
__global__ void fused_norm_kernel(
    const float* __restrict__ input,
    const float* __restrict__ bias,
    const float* __restrict__ gamma,
    const float* __restrict__ beta,
    const float* __restrict__ multiplier,
    float* __restrict__ output,
    int channels,
    int groups,
    int group_size,
    int total_groups,
    float eps
) {
    int lane = threadIdx.x & 31;
    int group = blockIdx.x * (blockDim.x / 32) + threadIdx.x / 32;
    if (group >= total_groups) return;

    int channel_start = (group % groups) * group_size;
    int base = (group / groups) * channels + channel_start;

    if (GROUP_SIZE_32) {
        int channel = channel_start + lane;
        float value = input[base + lane] + bias[channel];
        float mean = warp_sum(value) * (1.0f / 32.0f);
        float centered = value - mean;
        float variance = warp_sum(centered * centered) * (1.0f / 32.0f);
        float inv_std = rsqrtf(variance + eps);

        output[base + lane] = finish_value(
            value, mean, inv_std,
            gamma[channel], beta[channel], multiplier[channel]);
    } else {
        float sum = 0.0f;
        for (int i = lane; i < group_size; i += 32) {
            sum += input[base + i] + bias[channel_start + i];
        }
        float mean = warp_sum(sum) / float(group_size);

        float squared_sum = 0.0f;
        for (int i = lane; i < group_size; i += 32) {
            float value = input[base + i] + bias[channel_start + i];
            float centered = value - mean;
            squared_sum += centered * centered;
        }
        float inv_std = rsqrtf(
            warp_sum(squared_sum) / float(group_size) + eps);

        for (int i = lane; i < group_size; i += 32) {
            int channel = channel_start + i;
            float value = input[base + i] + bias[channel];
            output[base + i] = finish_value(
                value, mean, inv_std,
                gamma[channel], beta[channel], multiplier[channel]);
        }
    }
}

torch::Tensor linear_norm_swish_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    torch::Tensor bias,
    torch::Tensor gamma,
    torch::Tensor beta,
    torch::Tensor multiply_weight,
    int64_t groups,
    double eps
) {
    TORCH_CHECK(input.is_cuda(), "Expected CUDA input");
    const c10::cuda::CUDAGuard guard(input.device());

    TORCH_CHECK(input.dim() == 2 && weight.dim() == 2);
    TORCH_CHECK(input.scalar_type() == at::kFloat);
    TORCH_CHECK(input.is_contiguous());

    const int batch = static_cast<int>(input.size(0));
    const int channels = static_cast<int>(weight.size(0));
    const int features = static_cast<int>(input.size(1));

    TORCH_CHECK(weight.size(1) == features);
    TORCH_CHECK(groups > 0 && channels % groups == 0);

    for (const auto& tensor : {weight, bias, gamma, beta, multiply_weight}) {
        TORCH_CHECK(tensor.device() == input.device());
        TORCH_CHECK(tensor.scalar_type() == at::kFloat);
        TORCH_CHECK(tensor.is_contiguous());
    }
    TORCH_CHECK(bias.numel() == channels);
    TORCH_CHECK(gamma.numel() == channels);
    TORCH_CHECK(beta.numel() == channels);
    TORCH_CHECK(multiply_weight.numel() == channels);

    auto intermediate = torch::empty({batch, channels}, input.options());
    auto output = torch::empty_like(intermediate);
    if (batch == 0) return output;

    auto stream = at::cuda::getCurrentCUDAStream();
    auto handle = at::cuda::getCurrentCUDABlasHandle();

    const float alpha = 1.0f;
    const float gemm_beta = 0.0f;

    // Row-major X @ W.T is column-major W @ X.T.
    // Explicit TF32 compute avoids falling back to the FP32 SIMT GEMM.
    cublasStatus_t status = cublasGemmEx(
        handle,
        CUBLAS_OP_T,
        CUBLAS_OP_N,
        channels,
        batch,
        features,
        &alpha,
        weight.data_ptr<float>(),
        CUDA_R_32F,
        features,
        input.data_ptr<float>(),
        CUDA_R_32F,
        features,
        &gemm_beta,
        intermediate.data_ptr<float>(),
        CUDA_R_32F,
        channels,
        CUBLAS_COMPUTE_32F_FAST_TF32,
        CUBLAS_GEMM_DEFAULT_TENSOR_OP
    );
    TORCH_CHECK(
        status == CUBLAS_STATUS_SUCCESS,
        "cublasGemmEx failed with status ", static_cast<int>(status));

    const int group_size = channels / static_cast<int>(groups);
    const int total_groups = batch * static_cast<int>(groups);
    constexpr int threads = 256;
    const int blocks = (total_groups + 7) / 8;

    if (group_size == 32) {
        fused_norm_kernel<true><<<blocks, threads, 0, stream>>>(
            intermediate.data_ptr<float>(),
            bias.data_ptr<float>(),
            gamma.data_ptr<float>(),
            beta.data_ptr<float>(),
            multiply_weight.data_ptr<float>(),
            output.data_ptr<float>(),
            channels, static_cast<int>(groups), group_size,
            total_groups, static_cast<float>(eps));
    } else {
        fused_norm_kernel<false><<<blocks, threads, 0, stream>>>(
            intermediate.data_ptr<float>(),
            bias.data_ptr<float>(),
            gamma.data_ptr<float>(),
            beta.data_ptr<float>(),
            multiply_weight.data_ptr<float>(),
            output.data_ptr<float>(),
            channels, static_cast<int>(groups), group_size,
            total_groups, static_cast<float>(eps));
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_fused_ops = load_inline(
    name="tf32_linear_fused_groupnorm_swish_v2",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["linear_norm_swish_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    extra_ldflags=["-lcublas"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self, in_features, out_features, num_groups, multiply_weight_shape
    ):
        super().__init__()
        self.gemm = nn.Linear(in_features, out_features)
        self.group_norm = nn.GroupNorm(num_groups, out_features)
        self.multiply_weight = nn.Parameter(torch.randn(multiply_weight_shape))

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and x.shape[1] > 0
            and self.gemm.weight.dtype == torch.float32
            and self.gemm.bias.dtype == torch.float32
            and self.group_norm.weight.dtype == torch.float32
            and self.group_norm.bias.dtype == torch.float32
            and self.multiply_weight.dtype == torch.float32
            and self.multiply_weight.shape == (self.gemm.out_features,)
        ):
            return _fused_ops.linear_norm_swish_cuda(
                x.contiguous(),
                self.gemm.weight.contiguous(),
                self.gemm.bias.contiguous(),
                self.group_norm.weight.contiguous(),
                self.group_norm.bias.contiguous(),
                self.multiply_weight.contiguous(),
                self.group_norm.num_groups,
                self.group_norm.eps,
            )

        x = self.gemm(x)
        x = self.group_norm(x)
        x = x * torch.sigmoid(x)
        x = x * self.multiply_weight
        return x * torch.sigmoid(x)
```
Result of evaluating it:
The solution compiled and ran but its output did not match the reference. Details:
```
{"avg_difference": ["0.000047", "0.000047", "0.000047", "0.000047", "0.000047"], "correctness_issue": "Output mismatch", "correctness_trials": "(0 / 5)", "max_difference": ["0.003496", "0.003567", "0.003987", "0.003476", "0.003744"]}
```

The fastest correct solution so far (0.209x speedup) is:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

__device__ __forceinline__ float warp_sum(float value) {
    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1) {
        value += __shfl_down_sync(0xffffffff, value, offset);
    }
    return __shfl_sync(0xffffffff, value, 0);
}

template <bool GROUP_SIZE_32>
__global__ void fused_group_norm_kernel(
    const float* __restrict__ input,
    const float* __restrict__ gamma,
    const float* __restrict__ beta,
    const float* __restrict__ multiply_weight,
    float* __restrict__ output,
    int channels,
    int groups,
    int group_size,
    int total_groups,
    float eps
) {
    const int lane = threadIdx.x & 31;
    const int group = blockIdx.x * (blockDim.x / 32) + threadIdx.x / 32;

    if (group >= total_groups) {
        return;
    }

    const int channel_start = (group % groups) * group_size;
    const int base = (group / groups) * channels + channel_start;

    if (GROUP_SIZE_32) {
        const float value = input[base + lane];
        const float mean = warp_sum(value) * (1.0f / 32.0f);
        const float centered = value - mean;
        const float variance =
            warp_sum(centered * centered) * (1.0f / 32.0f);
        const float inverse_std = rsqrtf(variance + eps);

        const int channel = channel_start + lane;
        const float normalized =
            (centered * inverse_std) * gamma[channel] + beta[channel];
        const float first_swish =
            normalized * (1.0f / (1.0f + expf(-normalized)));
        const float weighted = first_swish * multiply_weight[channel];

        output[base + lane] =
            weighted * (1.0f / (1.0f + expf(-weighted)));
    } else {
        float sum = 0.0f;
        for (int i = lane; i < group_size; i += 32) {
            sum += input[base + i];
        }
        const float mean = warp_sum(sum) / float(group_size);

        float squared_sum = 0.0f;
        for (int i = lane; i < group_size; i += 32) {
            const float centered = input[base + i] - mean;
            squared_sum += centered * centered;
        }
        const float variance = warp_sum(squared_sum) / float(group_size);
        const float inverse_std = rsqrtf(variance + eps);

        for (int i = lane; i < group_size; i += 32) {
            const int channel = channel_start + i;
            const float normalized =
                ((input[base + i] - mean) * inverse_std) * gamma[channel]
                + beta[channel];
            const float first_swish =
                normalized * (1.0f / (1.0f + expf(-normalized)));
            const float weighted = first_swish * multiply_weight[channel];

            output[base + i] =
                weighted * (1.0f / (1.0f + expf(-weighted)));
        }
    }
}

torch::Tensor fused_group_norm_cuda(
    torch::Tensor input,
    torch::Tensor gamma,
    torch::Tensor beta,
    torch::Tensor multiply_weight,
    int64_t groups,
    double eps
) {
    const c10::cuda::CUDAGuard device_guard(input.device());

    TORCH_CHECK(input.is_cuda() && input.scalar_type() == at::kFloat);
    TORCH_CHECK(input.dim() == 2 && input.is_contiguous());
    TORCH_CHECK(groups > 0 && input.size(1) % groups == 0);

    const int channels = static_cast<int>(input.size(1));
    for (const auto& parameter : {gamma, beta, multiply_weight}) {
        TORCH_CHECK(parameter.device() == input.device());
        TORCH_CHECK(parameter.scalar_type() == at::kFloat);
        TORCH_CHECK(parameter.is_contiguous());
        TORCH_CHECK(parameter.numel() == channels);
    }

    auto output = torch::empty_like(input);
    if (input.numel() == 0) {
        return output;
    }

    const int group_size = channels / static_cast<int>(groups);
    const int total_groups = static_cast<int>(input.size(0) * groups);
    constexpr int threads = 256;
    const int blocks = (total_groups + 7) / 8;
    const auto stream = at::cuda::getCurrentCUDAStream();

    if (group_size == 32) {
        fused_group_norm_kernel<true><<<blocks, threads, 0, stream>>>(
            input.data_ptr<float>(),
            gamma.data_ptr<float>(),
            beta.data_ptr<float>(),
            multiply_weight.data_ptr<float>(),
            output.data_ptr<float>(),
            channels,
            static_cast<int>(groups),
            group_size,
            total_groups,
            static_cast<float>(eps)
        );
    } else {
        fused_group_norm_kernel<false><<<blocks, threads, 0, stream>>>(
            input.data_ptr<float>(),
            gamma.data_ptr<float>(),
            beta.data_ptr<float>(),
            multiply_weight.data_ptr<float>(),
            output.data_ptr<float>(),
            channels,
            static_cast<int>(groups),
            group_size,
            total_groups,
            static_cast<float>(eps)
        );
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor fused_group_norm_cuda(
    torch::Tensor input,
    torch::Tensor gamma,
    torch::Tensor beta,
    torch::Tensor multiply_weight,
    int64_t groups,
    double eps
);
"""

_fused_ops = load_inline(
    name="fused_gn_swish_multiply_swish_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_group_norm_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self, in_features, out_features, num_groups, multiply_weight_shape
    ):
        super().__init__()
        self.gemm = nn.Linear(in_features, out_features)
        self.group_norm = nn.GroupNorm(num_groups, out_features)
        self.multiply_weight = nn.Parameter(torch.randn(multiply_weight_shape))

    def forward(self, x):
        x = self.gemm(x)

        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and self.group_norm.weight.dtype == torch.float32
            and self.group_norm.bias.dtype == torch.float32
            and self.multiply_weight.dtype == torch.float32
            and self.multiply_weight.shape == (x.shape[1],)
        ):
            return _fused_ops.fused_group_norm_cuda(
                x.contiguous(),
                self.group_norm.weight.contiguous(),
                self.group_norm.bias.contiguous(),
                self.multiply_weight.contiguous(),
                self.group_norm.num_groups,
                self.group_norm.eps,
            )

        x = self.group_norm(x)
        x = x * torch.sigmoid(x)
        x = x * self.multiply_weight
        return x * torch.sigmoid(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.
