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 transposed convolution, applies Mish activation, adds a value, 
    applies Hardtanh activation, and scales the output.
    """
    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, add_value, scale):
        super(Model, self).__init__()
        self.conv_transpose = nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride, padding, output_padding)
        self.add_value = add_value
        self.scale = scale

    def forward(self, x):
        x = self.conv_transpose(x)
        x = torch.nn.functional.mish(x) # Mish activation
        x = x + self.add_value
        x = torch.nn.functional.hardtanh(x, min_val=-1, max_val=1) # Hardtanh activation
        x = x * self.scale # Scaling
        return x

batch_size = 128
in_channels  = 64  
out_channels = 64  
height = width = 128  
kernel_size  = 3
stride       = 2  
padding      = 1
output_padding = 1
add_value = 0.5
scale = 2

def get_inputs():
    return [torch.rand(batch_size, in_channels, height, width)]

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, stride, padding, output_padding, add_value, scale]
    ```
    
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
# 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

torch.backends.cudnn.benchmark = True
torch.backends.cudnn.benchmark_limit = 0  # exhaustive cudnn algo search
torch.backends.cudnn.allow_tf32 = True
torch.backends.cuda.matmul.allow_tf32 = True

# Fused epilogue operating directly on the channels_last (NHWC) output of the
# transposed convolution. In NHWC a flat index maps to channel via (idx % C),
# so one float4 spans 4 consecutive channels and the bias is an aligned float4
# load. Fuses: bias add -> Mish -> add_value -> Hardtanh -> scale into a single
# streaming pass with cache-streaming loads/stores (data is used exactly once).
fused_epilogue_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <cuda_runtime.h>

__device__ __forceinline__ float epilogue(float v, float b, float add_value, float scale) {
    float x = v + b;
    // mish(x) = x * tanh(softplus(x)) = x * u / (u + 2), u = t*(t+2), t = exp(x)
    float t = expf(fminf(x, 20.0f));
    float u = t * (t + 2.0f);
    float m = x * (u / (u + 2.0f));
    float y = m + add_value;
    y = fminf(fmaxf(y, -1.0f), 1.0f);  // hardtanh in [-1, 1]
    return y * scale;
}

__device__ __forceinline__ float4 epilogue4(float4 val, float4 b, float add_value, float scale) {
    float4 r;
    r.x = epilogue(val.x, b.x, add_value, scale);
    r.y = epilogue(val.y, b.y, add_value, scale);
    r.z = epilogue(val.z, b.z, add_value, scale);
    r.w = epilogue(val.w, b.w, add_value, scale);
    return r;
}

// Vectorized path (numel % 4 == 0 and C % 4 == 0). Each thread handles two
// float4s in an interleaved pattern to keep full coalescing while increasing
// memory-level parallelism. Streaming cache hints avoid L2 thrash.
__global__ __launch_bounds__(256) void fused_epilogue_nhwc_vec4_kernel(
        const float4* __restrict__ in,
        float4* __restrict__ out,
        const float4* __restrict__ bias4,
        long n4, long c4,
        float add_value, float scale) {
    long stride = (long)gridDim.x * blockDim.x * 2;
    for (long base = (long)blockIdx.x * blockDim.x * 2 + threadIdx.x; base < n4; base += stride) {
        long v0 = base;
        long v1 = base + blockDim.x;
        {
            float4 val = __ldcs(in + v0);
            float4 b = __ldg(bias4 + (v0 % c4));
            __stcs(out + v0, epilogue4(val, b, add_value, scale));
        }
        if (v1 < n4) {
            float4 val = __ldcs(in + v1);
            float4 b = __ldg(bias4 + (v1 % c4));
            __stcs(out + v1, epilogue4(val, b, add_value, scale));
        }
    }
}

// Generic fallback path.
__global__ void fused_epilogue_nhwc_kernel(const float* __restrict__ in,
                                           float* __restrict__ out,
                                           const float* __restrict__ bias,
                                           long n, long C,
                                           float add_value, float scale) {
    long stride = (long)gridDim.x * blockDim.x;
    for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < n; i += stride) {
        long c = i % C;
        out[i] = epilogue(in[i], bias[c], add_value, scale);
    }
}

torch::Tensor fused_epilogue_nhwc_cuda(torch::Tensor x, torch::Tensor bias, double add_value, double scale) {
    TORCH_CHECK(x.is_cuda(), "x must be a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == torch::kFloat32, "x must be float32");
    TORCH_CHECK(x.is_contiguous(at::MemoryFormat::ChannelsLast), "x must be channels_last contiguous");
    TORCH_CHECK(bias.is_cuda() && bias.scalar_type() == torch::kFloat32, "bias must be CUDA float32");

    const c10::cuda::OptionalCUDAGuard guard(x.device());
    auto b = bias.contiguous();
    const long C = x.size(1);
    TORCH_CHECK(b.numel() == C, "bias size mismatch");

    auto out = torch::empty_like(x);  // preserves channels_last layout
    const long n = x.numel();
    if (n == 0) return out;

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

    if ((n % 4 == 0) && (C % 4 == 0) &&
        ((reinterpret_cast<uintptr_t>(x.data_ptr<float>()) & 0xF) == 0) &&
        ((reinterpret_cast<uintptr_t>(out.data_ptr<float>()) & 0xF) == 0) &&
        ((reinterpret_cast<uintptr_t>(b.data_ptr<float>()) & 0xF) == 0)) {
        const int block = 256;
        const long n4 = n >> 2;
        long blocks = (n4 + (long)block * 2 - 1) / ((long)block * 2);
        if (blocks > 2147483647L) blocks = 2147483647L;
        fused_epilogue_nhwc_vec4_kernel<<<(unsigned int)blocks, block, 0, stream>>>(
            reinterpret_cast<const float4*>(x.data_ptr<float>()),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            reinterpret_cast<const float4*>(b.data_ptr<float>()),
            n4, C >> 2,
            (float)add_value, (float)scale);
    } else {
        const int block = 256;
        long blocks = (n + block - 1) / block;
        if (blocks > 2147483647L) blocks = 2147483647L;
        fused_epilogue_nhwc_kernel<<<(unsigned int)blocks, block, 0, stream>>>(
            x.data_ptr<float>(), out.data_ptr<float>(), b.data_ptr<float>(),
            n, C, (float)add_value, (float)scale);
    }
    return out;
}
"""

fused_epilogue_cpp_source = (
    "torch::Tensor fused_epilogue_nhwc_cuda(torch::Tensor x, torch::Tensor bias, double add_value, double scale);"
)

fused_epilogue = load_inline(
    name="fused_bias_mish_add_hardtanh_scale_nhwc_v3",
    cpp_sources=fused_epilogue_cpp_source,
    cuda_sources=fused_epilogue_source,
    functions=["fused_epilogue_nhwc_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model:
      * Runs the transposed convolution in channels_last so cudnn's fast NHWC
        dgrad GEMM is used without the expensive NHWC->NCHW output transpose.
      * Caches a channels_last copy of the conv weight so neither ATen nor
        cudnn has to re-transpose the filter on every forward pass.
      * Calls F.conv_transpose2d with bias=None and folds the bias into a
        single fused CUDA epilogue (bias + Mish + add + Hardtanh + scale),
        removing ATen's separate bias-add pass and three memory round-trips.
      * The conv_transpose module (incl. its bias parameter) is kept intact so
        the state_dict remains identical to the reference model.
    """
    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, add_value, scale):
        super(ModelNew, self).__init__()
        self.conv_transpose = nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride, padding, output_padding)
        self.add_value = add_value
        self.scale = scale
        self.fused_epilogue = fused_epilogue
        self._w_cl = None
        self._w_key = None
        self._zero_bias = None

    def _weight_channels_last(self, w):
        key = (w.data_ptr(), w._version, w.device, w.dtype)
        if self._w_cl is None or self._w_key != key:
            self._w_cl = w.detach().contiguous(memory_format=torch.channels_last)
            self._w_key = key
        return self._w_cl

    def forward(self, x):
        if (not x.is_cuda) or x.dtype != torch.float32:
            y = self.conv_transpose(x)
            y = F.mish(y)
            y = y + self.add_value
            y = F.hardtanh(y, min_val=-1, max_val=1)
            return y * self.scale

        ct = self.conv_transpose
        x = x.contiguous(memory_format=torch.channels_last)
        w = self._weight_channels_last(ct.weight)
        y = F.conv_transpose2d(
            x,
            w,
            None,  # bias folded into the fused epilogue
            ct.stride,
            ct.padding,
            ct.output_padding,
            ct.groups,
            ct.dilation,
        )
        if not y.is_contiguous(memory_format=torch.channels_last):
            y = y.contiguous(memory_format=torch.channels_last)
        bias = ct.bias
        if bias is None:
            if self._zero_bias is None or self._zero_bias.device != y.device or self._zero_bias.numel() != y.size(1):
                self._zero_bias = torch.zeros(y.size(1), device=y.device, dtype=torch.float32)
            bias = self._zero_bias
        return self.fused_epilogue.fused_epilogue_nhwc_cuda(y, bias, float(self.add_value), float(self.scale))
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 8.77 ms; the PyTorch reference (with TF32 enabled) takes 23.2 ms; speedup 2.645x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| sm80_xmma_dgrad_implicit_gemm_indexed_tf32f32_tf32f32_f32_nhwckrsc_nhwc_tilesize256x64x32_ | 3642.8 | 1 |
| fused_epilogue_nhwc_vec4_kernel(float4 const*, float4*, float4 const*, long, long, float,  | 3226.7 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 985.4 | 1 |
| void cudnn::engines_precompiled::convertTensor_kernel<float, float, float, (cudnnKernelDat | 870.6 | 2 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_3<xmma__5x_ | 48.9 | 1 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_1<xmma__5x_ | 3.9 | 1 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_2<xmma__5x_ | 3.3 | 1 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_0<xmma__5x_ | 3.1 | 1 |

The fastest correct solution so far (2.691x speedup) is:
```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

torch.backends.cudnn.benchmark = True
torch.backends.cudnn.benchmark_limit = 0  # exhaustive cudnn algo search
torch.backends.cudnn.allow_tf32 = True
torch.backends.cuda.matmul.allow_tf32 = True

# Fused epilogue operating directly on the channels_last (NHWC) output of the
# transposed convolution. Since the epilogue is element-wise, the NHWC layout
# is irrelevant except for mapping a flat index -> channel for the bias add,
# which in NHWC is simply (flat_idx % C). This kernel fuses:
#   bias add -> Mish -> add_value -> Hardtanh -> scale
# eliminating ATen's separate bias pass and cudnn's NHWC->NCHW transpose.
fused_epilogue_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

__device__ __forceinline__ float epilogue(float v, float b, float add_value, float scale) {
    float x = v + b;
    // mish(x) = x * tanh(softplus(x)) = x * u / (u + 2), u = t*(t+2), t = exp(x)
    float t = expf(fminf(x, 20.0f));
    float u = t * (t + 2.0f);
    float m = x * (u / (u + 2.0f));
    float y = m + add_value;
    y = fminf(fmaxf(y, -1.0f), 1.0f);  // hardtanh in [-1, 1]
    return y * scale;
}

// Vectorized path (requires numel % 4 == 0 and C % 4 == 0): each float4 spans
// 4 consecutive channels in NHWC, so the bias is also read as an aligned float4.
__global__ void fused_epilogue_nhwc_vec4_kernel(const float4* __restrict__ in,
                                                float4* __restrict__ out,
                                                const float* __restrict__ bias,
                                                long n4, long c4,
                                                float add_value, float scale) {
    long stride = (long)gridDim.x * blockDim.x;
    for (long v = (long)blockIdx.x * blockDim.x + threadIdx.x; v < n4; v += stride) {
        long cbase = (v % c4) << 2;
        float4 b = *reinterpret_cast<const float4*>(bias + cbase);
        float4 val = in[v];
        float4 r;
        r.x = epilogue(val.x, b.x, add_value, scale);
        r.y = epilogue(val.y, b.y, add_value, scale);
        r.z = epilogue(val.z, b.z, add_value, scale);
        r.w = epilogue(val.w, b.w, add_value, scale);
        out[v] = r;
    }
}

// Generic fallback path.
__global__ void fused_epilogue_nhwc_kernel(const float* __restrict__ in,
                                           float* __restrict__ out,
                                           const float* __restrict__ bias,
                                           long n, long C,
                                           float add_value, float scale) {
    long stride = (long)gridDim.x * blockDim.x;
    for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < n; i += stride) {
        long c = i % C;
        out[i] = epilogue(in[i], bias[c], add_value, scale);
    }
}

torch::Tensor fused_epilogue_nhwc_cuda(torch::Tensor x, torch::Tensor bias, double add_value, double scale) {
    TORCH_CHECK(x.is_cuda(), "x must be a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == torch::kFloat32, "x must be float32");
    TORCH_CHECK(x.is_contiguous(at::MemoryFormat::ChannelsLast), "x must be channels_last contiguous");
    TORCH_CHECK(bias.is_cuda() && bias.scalar_type() == torch::kFloat32, "bias must be CUDA float32");

    auto b = bias.contiguous();
    const long C = x.size(1);
    TORCH_CHECK(b.numel() == C, "bias size mismatch");

    auto out = torch::empty_like(x);  // preserves channels_last layout
    const long n = x.numel();
    if (n == 0) return out;

    auto stream = at::cuda::getCurrentCUDAStream();
    const int block = 256;

    if ((n % 4 == 0) && (C % 4 == 0)) {
        const long n4 = n >> 2;
        long blocks = (n4 + block - 1) / block;
        if (blocks > 2147483647L) blocks = 2147483647L;
        fused_epilogue_nhwc_vec4_kernel<<<(unsigned int)blocks, block, 0, stream>>>(
            reinterpret_cast<const float4*>(x.data_ptr<float>()),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            b.data_ptr<float>(), n4, C >> 2,
            (float)add_value, (float)scale);
    } else {
        long blocks = (n + block - 1) / block;
        if (blocks > 2147483647L) blocks = 2147483647L;
        fused_epilogue_nhwc_kernel<<<(unsigned int)blocks, block, 0, stream>>>(
            x.data_ptr<float>(), out.data_ptr<float>(), b.data_ptr<float>(),
            n, C, (float)add_value, (float)scale);
    }
    return out;
}
"""

fused_epilogue_cpp_source = (
    "torch::Tensor fused_epilogue_nhwc_cuda(torch::Tensor x, torch::Tensor bias, double add_value, double scale);"
)

fused_epilogue = load_inline(
    name="fused_bias_mish_add_hardtanh_scale_nhwc_v2",
    cpp_sources=fused_epilogue_cpp_source,
    cuda_sources=fused_epilogue_source,
    functions=["fused_epilogue_nhwc_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized model:
      * Runs the transposed convolution in channels_last so cudnn's fast NHWC
        dgrad GEMM is used without the expensive NHWC->NCHW output transpose.
      * Calls F.conv_transpose2d with bias=None and folds the bias into a
        single fused CUDA epilogue (bias + Mish + add + Hardtanh + scale),
        removing ATen's separate bias-add pass and three memory round-trips.
      * The conv_transpose module (incl. its bias parameter) is kept intact so
        the state_dict remains identical to the reference model.
    """
    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, add_value, scale):
        super(ModelNew, self).__init__()
        self.conv_transpose = nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride, padding, output_padding)
        self.add_value = add_value
        self.scale = scale
        self.fused_epilogue = fused_epilogue

    def forward(self, x):
        x = x.contiguous(memory_format=torch.channels_last)
        y = F.conv_transpose2d(
            x,
            self.conv_transpose.weight,
            None,  # bias folded into the fused epilogue
            self.conv_transpose.stride,
            self.conv_transpose.padding,
            self.conv_transpose.output_padding,
            self.conv_transpose.groups,
            self.conv_transpose.dilation,
        )
        y = y.contiguous(memory_format=torch.channels_last)
        bias = self.conv_transpose.bias
        if bias is None:
            bias = torch.zeros(y.size(1), device=y.device, dtype=y.dtype)
        y = self.fused_epilogue.fused_epilogue_nhwc_cuda(y, bias, self.add_value, self.scale)
        return y
```

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.
