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 2 of 6 for this task. Your previous solution (turn 1) 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

# Fused CUDA kernel: GroupNorm + Swish + per-channel Multiply + Swish
# The GEMM (nn.Linear) is kept as-is since cuBLAS/cublasLt is already
# near-optimal; everything after the GEMM is fused into a single
# memory-bound kernel (one warp per GroupNorm group).
fused_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

// Specialized kernel for group_size == 32 (one element per lane).
// Each warp handles exactly one (batch, group) pair.
__global__ void fused_gn_swish_mul_swish_g32_kernel(
    const float* __restrict__ x,
    const float* __restrict__ gn_w,
    const float* __restrict__ gn_b,
    const float* __restrict__ mul_w,
    float* __restrict__ out,
    int num_groups,
    float eps,
    long total_groups)
{
    long warp_id = (long)blockIdx.x * (blockDim.x >> 5) + (threadIdx.x >> 5);
    if (warp_id >= total_groups) return;
    int lane = threadIdx.x & 31;

    long idx = warp_id * 32 + lane;
    int channel = (int)(warp_id % num_groups) * 32 + lane;

    float v = x[idx];

    // Two-pass mean/variance for numerical parity with torch GroupNorm.
    float sum = v;
    #pragma unroll
    for (int o = 16; o > 0; o >>= 1)
        sum += __shfl_xor_sync(0xffffffff, sum, o);
    float mean = sum * (1.0f / 32.0f);

    float d = v - mean;
    float ss = d * d;
    #pragma unroll
    for (int o = 16; o > 0; o >>= 1)
        ss += __shfl_xor_sync(0xffffffff, ss, o);
    float rstd = rsqrtf(ss * (1.0f / 32.0f) + eps);

    // GroupNorm affine folded into scale/shift
    float scale = rstd * gn_w[channel];
    float shift = gn_b[channel] - mean * scale;

    float y = fmaf(v, scale, shift);
    y = y / (1.0f + expf(-y));   // Swish
    y = y * mul_w[channel];      // per-channel multiply
    y = y / (1.0f + expf(-y));   // Swish
    out[idx] = y;
}

// Generic fallback: one warp per group, arbitrary group_size.
__global__ void fused_gn_swish_mul_swish_generic_kernel(
    const float* __restrict__ x,
    const float* __restrict__ gn_w,
    const float* __restrict__ gn_b,
    const float* __restrict__ mul_w,
    float* __restrict__ out,
    int num_groups,
    int group_size,
    float eps,
    long total_groups)
{
    long warp_id = (long)blockIdx.x * (blockDim.x >> 5) + (threadIdx.x >> 5);
    if (warp_id >= total_groups) return;
    int lane = threadIdx.x & 31;

    long base = warp_id * (long)group_size;
    int ch0 = (int)(warp_id % num_groups) * group_size;

    float sum = 0.f, sumsq = 0.f;
    for (int i = lane; i < group_size; i += 32) {
        float v = x[base + i];
        sum += v;
        sumsq = fmaf(v, v, sumsq);
    }
    #pragma unroll
    for (int o = 16; o > 0; o >>= 1) {
        sum += __shfl_xor_sync(0xffffffff, sum, o);
        sumsq += __shfl_xor_sync(0xffffffff, sumsq, o);
    }
    float inv_n = 1.0f / (float)group_size;
    float mean = sum * inv_n;
    float var = fmaf(-mean, mean, sumsq * inv_n);
    float rstd = rsqrtf(var + eps);

    for (int i = lane; i < group_size; i += 32) {
        float v = x[base + i];
        int c = ch0 + i;
        float y = fmaf(v - mean, rstd * gn_w[c], gn_b[c]);
        y = y / (1.0f + expf(-y));
        y = y * mul_w[c];
        y = y / (1.0f + expf(-y));
        out[base + i] = y;
    }
}

torch::Tensor fused_gn_swish_mul_swish_cuda(
    torch::Tensor x,
    torch::Tensor gn_w,
    torch::Tensor gn_b,
    torch::Tensor mul_w,
    int64_t num_groups,
    double eps)
{
    TORCH_CHECK(x.is_cuda(), "x must be a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "x must be float32");

    auto xc = x.contiguous();
    auto gnwc = gn_w.contiguous();
    auto gnbc = gn_b.contiguous();
    auto mwc = mul_w.contiguous();

    auto out = at::empty_like(xc);

    int64_t channels = xc.size(-1);
    int64_t batch = xc.numel() / channels;
    int64_t group_size = channels / num_groups;
    int64_t total_groups = batch * num_groups;

    const int threads = 256;
    const int warps_per_block = threads / 32;
    int64_t blocks = (total_groups + warps_per_block - 1) / warps_per_block;

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if (group_size == 32) {
        fused_gn_swish_mul_swish_g32_kernel<<<blocks, threads, 0, stream>>>(
            xc.data_ptr<float>(),
            gnwc.data_ptr<float>(),
            gnbc.data_ptr<float>(),
            mwc.data_ptr<float>(),
            out.data_ptr<float>(),
            (int)num_groups,
            (float)eps,
            total_groups);
    } else {
        fused_gn_swish_mul_swish_generic_kernel<<<blocks, threads, 0, stream>>>(
            xc.data_ptr<float>(),
            gnwc.data_ptr<float>(),
            gnbc.data_ptr<float>(),
            mwc.data_ptr<float>(),
            out.data_ptr<float>(),
            (int)num_groups,
            (int)group_size,
            (float)eps,
            total_groups);
    }

    return out;
}
"""

fused_cpp_source = (
    "torch::Tensor fused_gn_swish_mul_swish_cuda("
    "torch::Tensor x, torch::Tensor gn_w, torch::Tensor gn_b, "
    "torch::Tensor mul_w, int64_t num_groups, double eps);"
)

fused_ops = load_inline(
    name="fused_gn_swish_mul_swish",
    cpp_sources=fused_cpp_source,
    cuda_sources=fused_cuda_source,
    functions=["fused_gn_swish_mul_swish_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model: cuBLAS GEMM + fused
    (GroupNorm + Swish + Multiply + Swish) CUDA kernel.
    """
    def __init__(self, in_features, out_features, num_groups, multiply_weight_shape):
        super(ModelNew, 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))
        self.num_groups = num_groups
        self.fused_ops = fused_ops

    def forward(self, x):
        if x.is_cuda and x.dtype == torch.float32:
            # GEMM via cuBLAS/cublasLt (bias fused in epilogue)
            x = F.linear(x, self.gemm.weight, self.gemm.bias)
            # Fused GroupNorm + Swish + Multiply + Swish
            return self.fused_ops.fused_gn_swish_mul_swish_cuda(
                x,
                self.group_norm.weight,
                self.group_norm.bias,
                self.multiply_weight,
                self.num_groups,
                self.group_norm.eps,
            )
        # Fallback for CPU / non-float32 inputs
        x = self.gemm(x)
        x = self.group_norm(x)
        x = x * torch.sigmoid(x)
        x = x * self.multiply_weight
        x = x * torch.sigmoid(x)
        return x
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 7.96 ms; the PyTorch reference (with TF32 enabled) takes 1.67 ms; speedup 0.210x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| ampere_sgemm_128x32_tn | 7822.8 | 1 |
| fused_gn_swish_mul_swish_g32_kernel(float const*, float const*, float const*, float const* | 89.1 | 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.
