```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)
```