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 6 of 6 for this task. Your previous solution (turn 5) 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
from torch.utils.cpp_extension import load_inline

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

// ---------------------------------------------------------------------------
// Fused ConvTranspose2d(k=4,s=2,p=1,op=1) + bias-subtract + tanh.
//
// Parity-phase decomposition: for phase (po,pq) = (oh&1, ow&1) the op is an
// exact GEMM over output pixels M=(n,oh2,ow2), K=(ci,a,b), N=co:
//   out = sum_{ci,a,b} x[n,ci,oh2+po-a,ow2+pq-b] * w[ci,co,2a+1-po,2b+1-pq]
//
// TF32 tensor-core (mma.sync m16n8k8) implicit GEMM, 3-stage cp.async
// pipeline, fused (+conv_bias -bias, tanh) epilogue.
// gridDim.x = phase (4): the 4 phase-CTAs of a tile are scheduled together,
// so their interleaved output writes merge in L2 and input reads are shared.
// ---------------------------------------------------------------------------

#define TILE_M 128
#define TILE_N 64
#define TILE_K 32
#define KTILES 8
#define STAGES 3
#define NTHREADS 256
#define LDA 136
#define LDB 72
#define LDC 136

#define PIPE_SMEM ((STAGES * (TILE_K * LDA + TILE_K * LDB)) * 4)
#define CS_SMEM (TILE_N * LDC * 4)
#define DYN_SMEM (PIPE_SMEM > CS_SMEM ? PIPE_SMEM : CS_SMEM)

__device__ __forceinline__ unsigned smem_u32(const void* p) {
    return (unsigned)__cvta_generic_to_shared(p);
}

__device__ __forceinline__ void cp_async4(void* dst, const void* src, bool p) {
    int sz = p ? 4 : 0;
    asm volatile("cp.async.ca.shared.global [%0], [%1], 4, %2;\n" ::
                 "r"(smem_u32(dst)), "l"(src), "r"(sz));
}

__device__ __forceinline__ void cp_async16(void* dst, const void* src) {
    asm volatile("cp.async.cg.shared.global [%0], [%1], 16;\n" ::
                 "r"(smem_u32(dst)), "l"(src));
}

__device__ __forceinline__ void cp_commit() {
    asm volatile("cp.async.commit_group;\n" ::);
}

template <int N>
__device__ __forceinline__ void cp_wait() {
    asm volatile("cp.async.wait_group %0;\n" :: "n"(N));
}

__device__ __forceinline__ float to_tf32(float x) {
    unsigned u = __float_as_uint(x);
    u = (u + 0x1000u) & ~0x1FFFu;
    return __uint_as_float(u);
}

__device__ __forceinline__ void mma_tf32(float* c, const float* a, const float* b) {
    asm volatile(
        "mma.sync.aligned.m16n8k8.row.col.f32.tf32.tf32.f32 "
        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%0,%1,%2,%3};\n"
        : "+f"(c[0]), "+f"(c[1]), "+f"(c[2]), "+f"(c[3])
        : "r"(__float_as_uint(a[0])), "r"(__float_as_uint(a[1])),
          "r"(__float_as_uint(a[2])), "r"(__float_as_uint(a[3])),
          "r"(__float_as_uint(b[0])), "r"(__float_as_uint(b[1])));
}

// wp[phase][k=(ci,a,b)][co] (tf32-rounded); comb[co] = conv_bias - sub_bias
__global__ void rearrange_weight_kernel(const float* __restrict__ w,
                                        const float* __restrict__ conv_bias,
                                        const float* __restrict__ sub_bias,
                                        float* __restrict__ wp,
                                        float* __restrict__ comb,
                                        int has_cb) {
    if (blockIdx.x == 256) {
        int co = threadIdx.x;
        if (co < 64) {
            float cb = has_cb ? __ldg(conv_bias + co) : 0.0f;
            comb[co] = cb - __ldg(sub_bias + co);
        }
        return;
    }
    int idx = blockIdx.x * blockDim.x + threadIdx.x;   // 4*256*64 elements
    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] = to_tf32(w[(long)ci * 1024 + co * 16 + kh * 4 + kw]);
}

__global__ void __launch_bounds__(NTHREADS) deconv_fused_tc_kernel(
        const float* __restrict__ x,
        const float* __restrict__ wp,
        const float* __restrict__ comb,
        float* __restrict__ y,
        int N, int H, int W, int Ho, int Wo) {

    extern __shared__ char dynsmem[];
    float* As = reinterpret_cast<float*>(dynsmem);                       // [STAGES][TILE_K][LDA]
    float* Bs = reinterpret_cast<float*>(dynsmem) + STAGES * TILE_K * LDA; // [STAGES][TILE_K][LDB]
    float* Cs = reinterpret_cast<float*>(dynsmem);                       // reused at epilogue

    __shared__ int soff[TILE_M][4];
    __shared__ long long sbase[TILE_M];
    __shared__ long long sorow[TILE_M];
    __shared__ float scomb[TILE_N];

    const int phase = blockIdx.x;
    const int po = phase >> 1, pq = phase & 1;
    const int Hp = (Ho - po + 1) >> 1;
    const int Wp2 = (Wo - pq + 1) >> 1;
    const long M = (long)N * Hp * Wp2;
    const long row0 = (long)blockIdx.y * TILE_M;
    if (row0 >= M) return;

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

    if (tid < TILE_M) {
        long row = row0 + tid;
        if (row < M) {
            long hw = (long)Hp * Wp2;
            long n = row / hw;
            long rem = row - n * hw;
            int oh2 = (int)(rem / Wp2);
            int ow2 = (int)(rem - (long)oh2 * Wp2);
            sbase[tid] = (long long)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][ab] = v ? (ih * W + iw) : -1;
            }
            int oh = 2 * oh2 + po;
            int ow = 2 * ow2 + pq;
            sorow[tid] = (long long)n * ytn + (long)oh * Wo + ow;
        } else {
            sbase[tid] = 0;
            #pragma unroll
            for (int ab = 0; ab < 4; ++ab) soff[tid][ab] = -1;
            sorow[tid] = -1;
        }
    }
    if (tid < TILE_N) scomb[tid] = __ldg(comb + tid);
    __syncthreads();

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

    auto stage = [&](int ks) {
        float* Asb = As + (ks % STAGES) * (TILE_K * LDA);
        float* Bsb = Bs + (ks % STAGES) * (TILE_K * LDB);
        int kbase = ks * TILE_K;
        #pragma unroll
        for (int it = 0; it < (TILE_K * TILE_M) / NTHREADS; ++it) {  // 16
            int idx = tid + it * NTHREADS;
            int m  = idx & (TILE_M - 1);
            int kk = idx >> 7;
            int kg = kbase + kk;
            int ci = kg >> 2;
            int ab = kg & 3;
            int off = soff[m][ab];
            const float* src = x + (sbase[m] + (long)ci * xsc + (off >= 0 ? off : 0));
            cp_async4(&Asb[kk * LDA + m], src, off >= 0);
        }
        #pragma unroll
        for (int it = 0; it < (TILE_K * TILE_N) / (NTHREADS * 4); ++it) {  // 4
            int idx = tid + it * NTHREADS;   // 0..1023
            int co4 = (idx & 15) * 4;
            int kk  = idx >> 4;
            cp_async16(&Bsb[kk * LDB + co4], wphase + (long)(kbase + kk) * 64 + co4);
        }
        cp_commit();
    };

    #pragma unroll
    for (int s = 0; s < STAGES - 1; ++s) stage(s);

    const int warp = tid >> 5;
    const int lane = tid & 31;
    const int m_off = (warp & 3) * 32;
    const int n_off = (warp >> 2) * 32;
    const int gid = lane >> 2;
    const int tig = lane & 3;

    float acc[8][4];
    #pragma unroll
    for (int i = 0; i < 8; ++i)
        #pragma unroll
        for (int e = 0; e < 4; ++e) acc[i][e] = 0.0f;

    cp_wait<STAGES - 2>();
    __syncthreads();

    #pragma unroll
    for (int ks = 0; ks < KTILES; ++ks) {
        if (ks + STAGES - 1 < KTILES) stage(ks + STAGES - 1);

        const float* Asb = As + (ks % STAGES) * (TILE_K * LDA);
        const float* Bsb = Bs + (ks % STAGES) * (TILE_K * LDB);

        #pragma unroll
        for (int k8 = 0; k8 < TILE_K / 8; ++k8) {
            int kb = k8 * 8;
            float af[2][4], bf[4][2];
            #pragma unroll
            for (int e = 0; e < 4; ++e) {
                int kk = kb + tig + 4 * (e >> 1);
                int mm = gid + 8 * (e & 1);
                af[0][e] = to_tf32(Asb[kk * LDA + m_off + mm]);
                af[1][e] = to_tf32(Asb[kk * LDA + m_off + 16 + mm]);
            }
            #pragma unroll
            for (int j = 0; j < 4; ++j) {
                #pragma unroll
                for (int e = 0; e < 2; ++e) {
                    bf[j][e] = Bsb[(kb + tig + 4 * e) * LDB + n_off + j * 8 + gid];
                }
            }
            #pragma unroll
            for (int i = 0; i < 2; ++i)
                #pragma unroll
                for (int j = 0; j < 4; ++j)
                    mma_tf32(acc[i * 4 + j], af[i], bf[j]);
        }

        cp_wait<STAGES - 2>();
        __syncthreads();
    }

    // epilogue: store accumulators to smem as [co][m]
    __syncthreads();
    #pragma unroll
    for (int i = 0; i < 2; ++i) {
        #pragma unroll
        for (int j = 0; j < 4; ++j) {
            float* a8 = acc[i * 4 + j];
            int m0 = m_off + i * 16 + gid;
            int c0 = n_off + j * 8 + 2 * tig;
            Cs[c0 * LDC + m0]         = a8[0];
            Cs[(c0 + 1) * LDC + m0]   = a8[1];
            Cs[c0 * LDC + m0 + 8]     = a8[2];
            Cs[(c0 + 1) * LDC + m0 + 8] = a8[3];
        }
    }
    __syncthreads();

    // fused bias-subtract + tanh, write out (m fastest for coalescing;
    // phase CTAs are adjacent in gridDim.x so lines merge in L2)
    const int me = tid & (TILE_M - 1);
    const int cg = tid >> 7;   // 0 or 1
    const long long orow = sorow[me];
    if (orow >= 0) {
        #pragma unroll
        for (int it = 0; it < (TILE_M * TILE_N) / NTHREADS; ++it) {  // 32
            int co = 2 * it + cg;
            float v = Cs[co * LDC + me] + scomb[co];
            y[orow + (long long)co * ytc] = tanhf(v);
        }
    }
}

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

static bool g_smem_set = 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 long Ho = (long)(H - 1) * stride - 2 * padding + KH + output_padding;
    const long Wo = (long)(W - 1) * stride - 2 * padding + KW + 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;
    }

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

    bool fast = (CI == 64) && (CO == 64) && (KH == 4) && (KW == 4) &&
                (stride == 2) && (padding == 1) && (output_padding == 1) &&
                (Ho <= INT_MAX) && (Wo <= INT_MAX) &&
                ((Ho & 1) == 0) && ((Wo & 1) == 0);

    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 = Ho * Wo;
        int threads = 256;
        long blocks = (total + threads - 1) / threads;
        fused_bias_tanh_kernel<<<(unsigned)blocks, threads, 0, stream>>>(
            tmp.data_ptr<float>(), bc.data_ptr<float>(), y.data_ptr<float>(),
            HW, total, CO);
        return y;
    }

    if (!g_smem_set) {
        cudaFuncSetAttribute(deconv_fused_tc_kernel,
                             cudaFuncAttributeMaxDynamicSharedMemorySize, DYN_SMEM);
        g_smem_set = true;
    }

    auto wp = torch::empty({4 * 256 * 64}, xc.options());
    auto comb = torch::empty({64}, xc.options());
    rearrange_weight_kernel<<<257, 256, 0, stream>>>(
        wc.data_ptr<float>(), cb_ptr, bc.data_ptr<float>(),
        wp.data_ptr<float>(), comb.data_ptr<float>(), has_cb);

    long maxM = 0;
    for (int p = 0; p < 4; ++p) {
        int po = p >> 1, pq = p & 1;
        long Hp = (Ho - po + 1) >> 1;
        long Wp2 = (Wo - pq + 1) >> 1;
        long Mp = (long)N * Hp * Wp2;
        if (Mp > maxM) maxM = Mp;
    }
    long tiles = (maxM + TILE_M - 1) / TILE_M;

    dim3 grid(4, (unsigned)tiles, 1);
    deconv_fused_tc_kernel<<<grid, NTHREADS, DYN_SMEM, stream>>>(
        xc.data_ptr<float>(), wp.data_ptr<float>(), comb.data_ptr<float>(),
        y.data_ptr<float>(), N, H, W, (int)Ho, (int)Wo);
    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_tf32_mma",
    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 fused TF32 tensor-core
    implicit-GEMM CUDA kernel (mma.sync m16n8k8, 3-stage cp.async pipeline)
    with (+conv_bias, -bias, tanh) fused in the epilogue.  The 4 parity-phase
    CTAs of a tile are adjacent in the launch grid so their interleaved
    writes merge in L2 and input reads are shared.  Falls back to ATen
    conv_transpose2d + a fused elementwise kernel for other configurations.
    """
    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 is correct on the test inputs. Mean runtime 15.8 ms; the PyTorch reference (with TF32 enabled) takes 18.6 ms; speedup 1.177x.
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_ | 4715.2 | 1 |
| fused_bias_tanh_kernel(float const*, float const*, float*, long, long, int) | 3636.9 | 1 |
| void cudnn::engines_precompiled::nhwcToNchwKernel<float, float, float, true, false, (cudnn | 3392.7 | 1 |
| void at::native::elementwise_kernel<128, 2, at::native::gpu_kernel_impl_nocast<at::native: | 3208.0 | 2 |
| void cudnn::engines_precompiled::nchwToNhwcKernel<float, float, float, false, true, (cudnn | 811.0 | 2 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_3<xmma__5x_ | 191.3 | 1 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_1<xmma__5x_ | 4.8 | 1 |
| void xmma__5x_cudnn::implicit_gemm::strided_dgrad_indexed::kernel_helper_stage_2<xmma__5x_ | 3.7 | 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.


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().
