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, subtracts a bias term, and applies tanh activation.
    """
    def __init__(self, in_channels, out_channels, kernel_size, bias_shape, stride=2, padding=1, output_padding=1):
        super(Model, self).__init__()
        self.conv_transpose = nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)
        self.bias = nn.Parameter(torch.randn(bias_shape)) 

    def forward(self, x):
        x = self.conv_transpose(x)
        x = x - self.bias
        x = torch.tanh(x)
        return x

batch_size = 32
in_channels  = 64  
out_channels = 64  
height = width = 256 
kernel_size = 4
bias_shape = (out_channels, 1, 1)

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

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, bias_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

cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>
#include <mma.h>

using namespace nvcuda;

#define TILE_M 128
#define TILE_N 64
#define TILE_K 32
#define NTHREADS 256
#define K_CHUNKS 8

// Rearrange ConvTranspose2d weight (CI,CO,4,4) into per-phase GEMM-friendly
// layout Wp[phase][k=(ci,a,b)][co] with kh=2a+1-po, kw=2b+1-pq.
__global__ void rearrange_weight_kernel(const float* __restrict__ w,
                                        float* __restrict__ wp) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx >= 4 * 256 * 64) return;
    int co = idx & 63;
    int k  = (idx >> 6) & 255;
    int p  = idx >> 14;
    int po = p >> 1, pq = p & 1;
    int ci = k >> 2;
    int a  = (k >> 1) & 1;
    int b  = k & 1;
    int kh = 2 * a + 1 - po;
    int kw = 2 * b + 1 - pq;
    wp[idx] = w[ci * (64 * 16) + co * 16 + kh * 4 + kw];
}

// Implicit-GEMM transposed convolution (k=4, s=2, p=1, op=1) using TF32
// tensor cores, with fused (-bias, +conv_bias, tanh) epilogue.
__global__ void deconv_gemm_kernel(const float* __restrict__ x,
                                   const float* __restrict__ wp,
                                   const float* __restrict__ conv_bias,
                                   const float* __restrict__ sub_bias,
                                   float* __restrict__ y,
                                   int N, int H, int W, int Ho, int Wo,
                                   int has_cb) {
#if defined(__CUDA_ARCH__) && (__CUDA_ARCH__ >= 800)
    const int phase = blockIdx.z;
    const int po = phase >> 1, pq = phase & 1;
    const int Hp = (Ho - po + 1) >> 1;
    const int Wp2 = (Wo - pq + 1) >> 1;
    const int M = N * Hp * Wp2;
    const int row0 = blockIdx.x * TILE_M;
    if (row0 >= M) return;

    extern __shared__ float smem[];
    float* As = smem;                                   // [2][TILE_K][TILE_M]
    float* Bs = As + 2 * TILE_K * TILE_M;               // [2][TILE_K][TILE_N]
    float* wbuf = As;                                   // reused in epilogue (32KB)
    int* soff  = (int*)(Bs + 2 * TILE_K * TILE_N);      // [TILE_M*4]
    int* sbase = soff + TILE_M * 4;                     // [TILE_M]
    int* sorow = sbase + TILE_M;                        // [TILE_M]

    const int tid = threadIdx.x;
    const int xsc = H * W;
    const int xsn = 64 * xsc;
    const int ytc = Ho * Wo;
    const int ytn = 64 * ytc;

    // Per-row geometry precompute
    if (tid < TILE_M) {
        int row = row0 + tid;
        if (row < M) {
            int hw = Hp * Wp2;
            int n = row / hw;
            int rem = row - n * hw;
            int oh2 = rem / Wp2;
            int ow2 = rem - oh2 * Wp2;
            sbase[tid] = n * xsn;
            #pragma unroll
            for (int ab = 0; ab < 4; ++ab) {
                int a = ab >> 1, b = ab & 1;
                int ih = oh2 + po - a;
                int iw = ow2 + pq - b;
                bool v = (ih >= 0 && ih < H && iw >= 0 && iw < W);
                soff[tid * 4 + ab] = v ? (ih * W + iw) : -1;
            }
            int oh = 2 * oh2 + po;
            int ow = 2 * ow2 + pq;
            sorow[tid] = n * ytn + oh * Wo + ow;
        } else {
            sbase[tid] = 0;
            #pragma unroll
            for (int ab = 0; ab < 4; ++ab) soff[tid * 4 + ab] = -1;
            sorow[tid] = -1;
        }
    }
    __syncthreads();

    const int wid  = tid >> 5;
    const int lane = tid & 31;
    const int wm = (wid & 3) * 32;
    const int wn = (wid >> 2) * 32;

    wmma::fragment<wmma::accumulator, 16, 8, 8, float> acc[2][4];
    #pragma unroll
    for (int i = 0; i < 2; ++i)
        #pragma unroll
        for (int j = 0; j < 4; ++j)
            wmma::fill_fragment(acc[i][j], 0.0f);

    const float* wphase = wp + phase * (256 * 64);

    // ---- prologue: load chunk 0 into buffer 0 ----
    {
        float* Asb = As;
        #pragma unroll
        for (int it = 0; it < (TILE_M * TILE_K) / NTHREADS; ++it) {
            int idx = tid + it * NTHREADS;
            int m = idx & (TILE_M - 1);
            int kk = idx >> 7;
            int ci = kk >> 2;
            int ab = kk & 3;
            int off = soff[m * 4 + ab];
            float v = 0.f;
            if (off >= 0) v = __ldg(x + sbase[m] + ci * xsc + off);
            Asb[kk * TILE_M + m] = wmma::__float_to_tf32(v);
        }
        float* Bsb = Bs;
        #pragma unroll
        for (int it = 0; it < (TILE_K * TILE_N) / NTHREADS; ++it) {
            int idx = tid + it * NTHREADS;
            Bsb[idx] = wmma::__float_to_tf32(__ldg(wphase + idx));
        }
    }
    __syncthreads();

    // ---- main K loop with double buffering ----
    #pragma unroll
    for (int kc = 0; kc < K_CHUNKS; ++kc) {
        int buf = kc & 1;
        if (kc + 1 < K_CHUNKS) {
            int nb = buf ^ 1;
            float* Asb = As + nb * (TILE_K * TILE_M);
            #pragma unroll
            for (int it = 0; it < (TILE_M * TILE_K) / NTHREADS; ++it) {
                int idx = tid + it * NTHREADS;
                int m = idx & (TILE_M - 1);
                int kk = idx >> 7;
                int ci = kk >> 2;
                int ab = kk & 3;
                int off = soff[m * 4 + ab];
                float v = 0.f;
                if (off >= 0) v = __ldg(x + sbase[m] + ci * xsc + off);
                Asb[kk * TILE_M + m] = wmma::__float_to_tf32(v);
            }
            float* Bsb = Bs + nb * (TILE_K * TILE_N);
            const float* wpp = wphase + (kc + 1) * (TILE_K * TILE_N);
            #pragma unroll
            for (int it = 0; it < (TILE_K * TILE_N) / NTHREADS; ++it) {
                int idx = tid + it * NTHREADS;
                Bsb[idx] = wmma::__float_to_tf32(__ldg(wpp + idx));
            }
        }
        {
            const float* Asb = As + buf * (TILE_K * TILE_M);
            const float* Bsb = Bs + buf * (TILE_K * TILE_N);
            #pragma unroll
            for (int ks = 0; ks < TILE_K / 8; ++ks) {
                wmma::fragment<wmma::matrix_a, 16, 8, 8, wmma::precision::tf32, wmma::col_major> af[2];
                wmma::fragment<wmma::matrix_b, 16, 8, 8, wmma::precision::tf32, wmma::row_major> bf[4];
                #pragma unroll
                for (int i = 0; i < 2; ++i)
                    wmma::load_matrix_sync(af[i], Asb + (ks * 8) * TILE_M + wm + i * 16, TILE_M);
                #pragma unroll
                for (int j = 0; j < 4; ++j)
                    wmma::load_matrix_sync(bf[j], Bsb + (ks * 8) * TILE_N + wn + j * 8, TILE_N);
                #pragma unroll
                for (int i = 0; i < 2; ++i)
                    #pragma unroll
                    for (int j = 0; j < 4; ++j)
                        wmma::mma_sync(acc[i][j], af[i], bf[j], acc[i][j]);
            }
        }
        __syncthreads();
    }

    // ---- epilogue: stage through smem, fused bias/sub/tanh ----
    float* my = wbuf + wid * 1024;   // [32(co)][32(m)] col-major staging
    #pragma unroll
    for (int i = 0; i < 2; ++i)
        #pragma unroll
        for (int j = 0; j < 4; ++j)
            wmma::store_matrix_sync(my + (j * 8) * 32 + i * 16, acc[i][j], 32, wmma::mem_col_major);
    __syncwarp();

    int m = wm + lane;
    int orow = sorow[m];
    if (orow >= 0) {
        #pragma unroll 4
        for (int c = 0; c < 32; ++c) {
            int co = wn + c;
            float v = my[c * 32 + lane];
            if (has_cb) v += __ldg(conv_bias + co);
            v -= __ldg(sub_bias + co);
            y[orow + co * ytc] = tanhf(v);
        }
    }
#endif
}

// Fused elementwise: y = tanh(x + conv_bias - sub_bias) per channel (fallback path)
__global__ void fused_bias_tanh_kernel(const float* __restrict__ x,
                                       const float* __restrict__ conv_bias,
                                       const float* __restrict__ sub_bias,
                                       float* __restrict__ y,
                                       long HW, long total, int has_cb) {
    long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (idx >= total) return;
    int co = (int)((idx / HW) % 64);
    float v = x[idx];
    if (has_cb) v += __ldg(conv_bias + co);
    v -= __ldg(sub_bias + co);
    y[idx] = tanhf(v);
}

static bool g_smem_configured = false;

torch::Tensor deconv_forward(torch::Tensor x, torch::Tensor weight,
                             c10::optional<torch::Tensor> conv_bias,
                             torch::Tensor sub_bias,
                             int64_t stride, int64_t padding,
                             int64_t output_padding) {
    TORCH_CHECK(x.is_cuda() && x.dtype() == torch::kFloat32, "x must be CUDA fp32");
    auto xc = x.contiguous();
    auto wc = weight.contiguous();
    auto bc = sub_bias.contiguous();

    const int N = xc.size(0);
    const int CI = xc.size(1);
    const int H = xc.size(2);
    const int W = xc.size(3);
    const int CO = wc.size(1);
    const int KH = wc.size(2);
    const int KW = wc.size(3);

    const int Ho = (H - 1) * (int)stride - 2 * (int)padding + KH + (int)output_padding;
    const int Wo = (W - 1) * (int)stride - 2 * (int)padding + KW + (int)output_padding;

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

    torch::Tensor cb;
    const float* cb_ptr = nullptr;
    int has_cb = 0;
    if (conv_bias.has_value() && conv_bias->defined()) {
        cb = conv_bias->contiguous();
        cb_ptr = cb.data_ptr<float>();
        has_cb = 1;
    }

    // check fast-path feasibility
    int dev = 0; cudaGetDevice(&dev);
    static int arch_major = -1;
    if (arch_major < 0) {
        cudaDeviceGetAttribute(&arch_major, cudaDevAttrComputeCapabilityMajor, dev);
    }
    bool fast = (arch_major >= 8) && CI == 64 && CO == 64 && KH == 4 && KW == 4 &&
                stride == 2 && padding == 1 && output_padding == 1;

    auto y = torch::empty({N, CO, (long)Ho, (long)Wo}, xc.options());

    if (!fast) {
        auto tmp = at::conv_transpose2d(xc, wc, conv_bias.has_value() ? cb : torch::Tensor(),
                                        {stride, stride}, {padding, padding}, {output_padding, output_padding}, 1);
        long total = tmp.numel();
        long HW = (long)Ho * Wo;
        int threads = 256;
        long blocks = (total + threads - 1) / threads;
        fused_bias_tanh_kernel<<<(unsigned)blocks, threads, 0, stream>>>(
            tmp.data_ptr<float>(), cb_ptr, bc.data_ptr<float>(),
            y.data_ptr<float>(), HW, total, has_cb);
        return y;
    }

    // rearranged weights (4 phases x 256 x 64)
    auto wp = torch::empty({4 * 256 * 64}, xc.options());
    rearrange_weight_kernel<<<256, 256, 0, stream>>>(wc.data_ptr<float>(), wp.data_ptr<float>());

    // tiles per phase (max over phases)
    int maxM = 0;
    for (int p = 0; p < 4; ++p) {
        int po = p >> 1, pq = p & 1;
        int Hp = (Ho - po + 1) >> 1;
        int Wp2 = (Wo - pq + 1) >> 1;
        int M = N * Hp * Wp2;
        if (M > maxM) maxM = M;
    }
    int tiles = (maxM + TILE_M - 1) / TILE_M;

    size_t smem = (size_t)(2 * TILE_K * TILE_M + 2 * TILE_K * TILE_N) * sizeof(float)
                + (size_t)(TILE_M * 6) * sizeof(int);
    if (!g_smem_configured) {
        cudaFuncSetAttribute(deconv_gemm_kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, (int)smem);
        g_smem_configured = true;
    }
    dim3 grid(tiles, 1, 4);
    deconv_gemm_kernel<<<grid, NTHREADS, smem, stream>>>(
        xc.data_ptr<float>(), wp.data_ptr<float>(), cb_ptr, bc.data_ptr<float>(),
        y.data_ptr<float>(), N, H, W, Ho, Wo, has_cb);
    return y;
}
"""

cpp_source = """
torch::Tensor deconv_forward(torch::Tensor x, torch::Tensor weight,
                             c10::optional<torch::Tensor> conv_bias,
                             torch::Tensor sub_bias,
                             int64_t stride, int64_t padding,
                             int64_t output_padding);
"""

deconv_mod = load_inline(
    name="deconv_fused",
    cpp_sources=cpp_source,
    cuda_sources=cuda_source,
    functions=["deconv_forward"],
    verbose=False,
    extra_cuda_cflags=["-O3", "--use_fast_math"],
)


class ModelNew(nn.Module):
    """
    Optimized model: transposed convolution via a TF32 tensor-core implicit-GEMM
    CUDA kernel with fused (- bias + conv_bias, tanh) epilogue.
    """
    def __init__(self, in_channels, out_channels, kernel_size, bias_shape, stride=2, padding=1, output_padding=1):
        super(ModelNew, self).__init__()
        self.conv_transpose = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,
                                                 stride=stride, padding=padding,
                                                 output_padding=output_padding)
        self.bias = nn.Parameter(torch.randn(bias_shape))
        self.stride = stride
        self.padding = padding
        self.output_padding = output_padding

    def forward(self, x):
        return deconv_mod.deconv_forward(
            x,
            self.conv_transpose.weight,
            self.conv_transpose.bias,
            self.bias.view(-1),
            self.stride,
            self.padding,
            self.output_padding,
        )
```
Result of evaluating it:
The solution failed to compile. Error output:
```
RuntimeError: Error building extension 'deconv_fused': [1/3] c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=deconv_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include/torch/csrc/api/include -isystem /opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/include -isystem /usr/include/python3.12 -fPIC -std=c++20 -c /srv/jobs/1791682053326673908-526805-0/build/deconv_fused/main.cpp -o main.o 
[2/3] /opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/bin/nvcc -MD -MF cuda.cuda.o.d -DTORCH_EXTENSION_NAME=deconv_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include/torch/csrc/api/include -isystem /opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/include -isystem /usr/include/python3.12 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_80,code=sm_80 --compiler-options '-fPIC' -O3 --use_fast_math -std=c++20 -c /srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu -o cuda.cuda.o 
FAILED: [code=1] cuda.cuda.o 
/opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/bin/nvcc -MD -MF cuda.cuda.o.d -DTORCH_EXTENSION_NAME=deconv_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include -isystem /opt/kbv/v/lib/python3.12/site-packages/torch/include/torch/csrc/api/include -isystem /opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/include -isystem /usr/include/python3.12 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_80,code=sm_80 --compiler-options '-fPIC' -O3 --use_fast_math -std=c++20 -c /srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu -o cuda.cuda.o 
/srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu(103): error: incomplete type "nvcuda::wmma::fragment<nvcuda::wmma::accumulator, 16, 8, 8, float, void> [2][4]" is not allowed
      wmma::fragment<wmma::accumulator, 16, 8, 8, float> acc[2][4];
                                                         ^

/srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu(108): error: no instance of function template "nvcuda::wmma::fill_fragment" matches the argument list
            argument types are: (<error-type>, float)
              wmma::fill_fragment(acc[i][j], 0.0f);
              ^
/opt/kbv/v/lib/python3.12/site-packages/nvidia/cu13/include/crt/mma.h(260): note #3327-D: candidate function template "nvcuda::wmma::fill_fragment" failed deduction
      static __attribute__((device)) __inline__ void fill_fragment(__frag_base<FragEleType, size, packed_size>& f,
                                                     ^

/srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu(168): error: incomplete type "nvcuda::wmma::fragment<nvcuda::wmma::matrix_a, 16, 8, 8, nvcuda::wmma::precision::tf32, nvcuda::wmma::col_major> [2]" is not allowed
                  wmma::fragment<wmma::matrix_a, 16, 8, 8, wmma::precision::tf32, wmma::col_major> af[2];
                                                                                                   ^

/srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu(169): error: incomplete type "nvcuda::wmma::fragment<nvcuda::wmma::matrix_b, 16, 8, 8, nvcuda::wmma::precision::tf32, nvcuda::wmma::row_major> [4]" is not allowed
                  wmma::fragment<wmma::matrix_b, 16, 8, 8, wmma::precision::tf32, wmma::row_major> bf[4];
                                                                                                   ^

4 errors detected in the compilation of "/srv/jobs/1791682053326673908-526805-0/build/deconv_fused/cuda.cu".
ninja: build stopped: subcommand failed.

```

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.


Precision rule: the timed forward must compute in FP32 (TF32 tensor-core math is allowed, as in the PyTorch reference). Do not cast inputs, weights or intermediate results to float16 or bfloat16 and do not call half-precision kernels in forward().
