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):
    """
    Performs a transposed 2D convolution operation with asymmetric input and kernel size.

    Args:
        in_channels (int): Number of channels in the input tensor.
        out_channels (int): Number of channels produced by the convolution.
        kernel_size (tuple): Tuple of integers representing the kernel size (height, width).
        stride (tuple, optional): Tuple of integers representing the stride of the convolution. Defaults to (1, 1).
        padding (tuple, optional): Tuple of integers representing the padding applied to the input. Defaults to (0, 0).
        output_padding (tuple, optional): Tuple of integers representing the additional size added to one side of the output shape. Defaults to (0, 0).
        dilation (tuple, optional): Tuple of integers representing the spacing between kernel elements. Defaults to (1, 1).
        groups (int, optional): Number of blocked connections from input channels to output channels. Defaults to 1.
        bias (bool, optional): If `True`, adds a learnable bias to the output. Defaults to `False`.
    """
    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple, stride: tuple = (1, 1), padding: tuple = (0, 0), output_padding: tuple = (0, 0), dilation: tuple = (1, 1), groups: int = 1, bias: bool = False):
        super(Model, self).__init__()
        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding, dilation=dilation, groups=groups, bias=bias)
        
    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Performs the transposed 2D convolution.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_channels, height_in, width_in).

        Returns:
            torch.Tensor: Output tensor of shape (batch_size, out_channels, height_out, width_out).
        """
        return self.conv_transpose2d(x)

# Test code
batch_size = 64
in_channels = 64
out_channels = 128
kernel_size = (3, 5)
height_in = 128
width_in = 256

def get_inputs():
    x = torch.rand(batch_size, in_channels, height_in, width_in)
    return [x]

def get_init_inputs():
    return [in_channels, out_channels, kernel_size]  # Provide in_channels, out_channels, kernel_size for initialization
    ```
    
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 3 of 6 for this task. Your previous solution (turn 2) 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>

#define BM 64
#define BN 128
#define BK 32
#define NTHREADS 256
#define MAXK 1024

// TF32 rounding: destination register of cvt.rna.tf32.f32 must be .b32
__device__ __forceinline__ float to_tf32(float v) {
    unsigned u;
    asm volatile("cvt.rna.tf32.f32 %0, %1;\n" : "=r"(u) : "f"(v));
    return __uint_as_float(u);
}

// ---------------------------------------------------------------------------
// Repack ConvTranspose2d weight (C_in, C_out, kh, kw) into BgT[C_out][K] with
// k = ic*kh*kw + ky*kw + kx, pre-rounded to TF32.
// ---------------------------------------------------------------------------
__global__ void repack_weight_kernel(const float* __restrict__ w,
                                     float* __restrict__ BgT,
                                     int C_in, int C_out, int kh, int kw) {
    int k = blockIdx.x * blockDim.x + threadIdx.x;
    int K = C_in * kh * kw;
    if (k >= K) return;
    int kwkh = kh * kw;
    int ic = k / kwkh;
    int ky = (k % kwkh) / kw;
    int kx = k % kw;
    const float* wp = w + ((long)ic * C_out) * kwkh + ky * kw + kx;
    float* bp = BgT + k;
    for (int oc = 0; oc < C_out; ++oc) {
        *bp = to_tf32(*wp);
        wp += kwkh;
        bp += K;
    }
}

// ---------------------------------------------------------------------------
// Implicit-GEMM transposed convolution (stride=1, pad=0, dilation=1, groups=1)
//   out[n, oc, y, x] = sum_{ic,ky,kx} w[ic,oc,ky,kx] * in[n,ic,y-ky,x-kx]
//   M = N*H_out*W_out, N = C_out, K = C_in*kh*kw
// TF32 tensor cores (mma.m16n8k8), fp32 accumulation, fp32 output.
// ---------------------------------------------------------------------------
__global__ __launch_bounds__(NTHREADS)
void tconv_implicit_gemm_kernel(const float* __restrict__ input,
                                const float* __restrict__ BgT,
                                const float* __restrict__ bias,
                                float* __restrict__ output,
                                int N_batch, int C_in, int H_in, int W_in,
                                int H_out, int W_out, int C_out,
                                int kh, int kw, int K, long M) {
    constexpr int SMEM_MAIN = BK * (BM + 4) + BN * (BK + 4);
    constexpr int SMEM_EPI  = BM * (BN + 4);
    constexpr int SMEM_F    = SMEM_MAIN > SMEM_EPI ? SMEM_MAIN : SMEM_EPI;
    __shared__ float smem[SMEM_F];
    __shared__ int s_koff[MAXK];
    __shared__ int s_kk[MAXK];
    __shared__ int s_base[BM];
    __shared__ int s_yx[BM];
    __shared__ long s_obase[BM];

    float* As = smem;                     // [BK][BM+4]
    float* Bs = smem + BK * (BM + 4);     // [BN][BK+4]

    const int tid = threadIdx.x;
    const int lane = tid & 31;
    const int warp = tid >> 5;
    const int warp_m = warp >> 2;         // 0..1
    const int warp_n = warp & 3;          // 0..3
    const int cr = lane & 3;
    const int cg = lane >> 2;
    const long m0 = (long)blockIdx.x * BM;
    const int HW = H_in * W_in;
    const long HWo = (long)H_out * W_out;
    const int kwkh = kh * kw;

    // per-m lookup tables
    if (tid < BM) {
        long m = m0 + tid;
        if (m < M) {
            int spatial = (int)(m % HWo);
            int n = (int)(m / HWo);
            int y = spatial / W_out;
            int x = spatial % W_out;
            s_base[tid] = n * (C_in * HW) + y * W_in + x;
            s_yx[tid] = (y << 16) | x;
            s_obase[tid] = (long)n * C_out * HWo + spatial;
        } else {
            s_base[tid] = -1;
            s_yx[tid] = 0;
            s_obase[tid] = 0;
        }
    }
    // full-K lookup tables (div/mod done once per kernel)
    for (int i = tid; i < K; i += NTHREADS) {
        int ic = i / kwkh;
        int ky = (i % kwkh) / kw;
        int kx = i % kw;
        s_koff[i] = ic * HW - ky * W_in - kx;
        s_kk[i] = (ky << 8) | kx;
    }
    __syncthreads();

    float acc[2][4][4];
    #pragma unroll
    for (int i = 0; i < 2; ++i)
        #pragma unroll
        for (int j = 0; j < 4; ++j)
            #pragma unroll
            for (int r = 0; r < 4; ++r) acc[i][j][r] = 0.0f;

    for (int k0 = 0; k0 < K; k0 += BK) {
        // stage A tile (implicit im2col gather)
        #pragma unroll
        for (int r = 0; r < (BK * BM) / NTHREADS; ++r) {
            int idx = r * NTHREADS + tid;
            int kl = idx >> 6;            // / BM
            int ml = idx & (BM - 1);
            int k = k0 + kl;
            float v = 0.0f;
            int base = s_base[ml];
            if (k < K && base >= 0) {
                int kk = s_kk[k];
                int yx = s_yx[ml];
                int iy = (yx >> 16) - (kk >> 8);
                int ix = (yx & 0xffff) - (kk & 0xff);
                if ((unsigned)iy < (unsigned)H_in && (unsigned)ix < (unsigned)W_in)
                    v = input[base + s_koff[k]];
            }
            As[kl * (BM + 4) + ml] = to_tf32(v);
        }
        // stage B tile
        #pragma unroll
        for (int r = 0; r < (BK * BN) / NTHREADS; ++r) {
            int idx = r * NTHREADS + tid;
            int kl = idx & (BK - 1);
            int nl = idx >> 5;            // / BK
            int k = k0 + kl;
            float v = (k < K && nl < C_out) ? BgT[(long)nl * K + k] : 0.0f;
            Bs[nl * (BK + 4) + kl] = v;
        }
        __syncthreads();

        #pragma unroll
        for (int ks = 0; ks < BK; ks += 8) {
            float a[2][4], b[4][2];
            #pragma unroll
            for (int i = 0; i < 2; ++i) {
                const float* Ap = As + ks * (BM + 4) + warp_m * 32 + i * 16;
                a[i][0] = Ap[cr * (BM + 4) + cg];
                a[i][1] = Ap[cr * (BM + 4) + cg + 8];
                a[i][2] = Ap[(cr + 4) * (BM + 4) + cg];
                a[i][3] = Ap[(cr + 4) * (BM + 4) + cg + 8];
            }
            #pragma unroll
            for (int j = 0; j < 4; ++j) {
                const float* Bp = Bs + (warp_n * 32 + j * 8) * (BK + 4) + ks;
                b[j][0] = Bp[cg * (BK + 4) + cr];
                b[j][1] = Bp[cg * (BK + 4) + cr + 4];
            }
            #pragma unroll
            for (int i = 0; i < 2; ++i) {
                #pragma unroll
                for (int j = 0; j < 4; ++j) {
                    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"(acc[i][j][0]), "+f"(acc[i][j][1]),
                          "+f"(acc[i][j][2]), "+f"(acc[i][j][3])
                        : "r"(__float_as_uint(a[i][0])), "r"(__float_as_uint(a[i][1])),
                          "r"(__float_as_uint(a[i][2])), "r"(__float_as_uint(a[i][3])),
                          "r"(__float_as_uint(b[j][0])), "r"(__float_as_uint(b[j][1])));
                }
            }
        }
        __syncthreads();
    }

    // stage accumulators (+bias) into shared tile for coalesced NCHW writeout
    float* Cs = smem;                     // [BM][BN+4]
    #pragma unroll
    for (int i = 0; i < 2; ++i) {
        #pragma unroll
        for (int j = 0; j < 4; ++j) {
            int nl = warp_n * 32 + j * 8 + 2 * cr;
            #pragma unroll
            for (int rr = 0; rr < 2; ++rr) {
                int ml = warp_m * 32 + i * 16 + cg + rr * 8;
                if (nl + 1 < C_out) {
                    float b0 = bias ? bias[nl] : 0.0f;
                    float b1 = bias ? bias[nl + 1] : 0.0f;
                    Cs[ml * (BN + 4) + nl]     = acc[i][j][2 * rr] + b0;
                    Cs[ml * (BN + 4) + nl + 1] = acc[i][j][2 * rr + 1] + b1;
                } else if (nl < C_out) {
                    float b0 = bias ? bias[nl] : 0.0f;
                    Cs[ml * (BN + 4) + nl] = acc[i][j][2 * rr] + b0;
                }
            }
        }
    }
    __syncthreads();

    #pragma unroll
    for (int r = 0; r < (BM * BN) / NTHREADS; ++r) {
        int idx = r * NTHREADS + tid;
        int oc = idx >> 6;                // / BM
        int ml = idx & (BM - 1);
        long m = m0 + ml;
        if (m < M && oc < C_out)
            output[s_obase[ml] + (long)oc * HWo] = Cs[ml * (BN + 4) + oc];
    }
}

// ---------------------------------------------------------------------------
// Reference-style fallback kernel (any GPU, any shape): fp32 direct tconv.
// ---------------------------------------------------------------------------
__global__ void tconv_direct_kernel(const float* __restrict__ input,
                                    const float* __restrict__ weight,
                                    const float* __restrict__ bias,
                                    float* __restrict__ output,
                                    int N_batch, int C_in, int H_in, int W_in,
                                    int H_out, int W_out, int C_out,
                                    int kh, int kw, long total) {
    long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (idx >= total) return;
    int x = idx % W_out;
    int y = (idx / W_out) % H_out;
    int oc = (idx / ((long)W_out * H_out)) % C_out;
    int n = idx / ((long)W_out * H_out * C_out);

    float sum = bias ? bias[oc] : 0.0f;
    int kwkh = kh * kw;
    for (int ic = 0; ic < C_in; ++ic) {
        const float* ip = input + ((long)n * C_in + ic) * H_in * W_in;
        const float* wp = weight + ((long)ic * C_out + oc) * kwkh;
        for (int ky = 0; ky < kh; ++ky) {
            int iy = y - ky;
            if ((unsigned)iy >= (unsigned)H_in) continue;
            for (int kx = 0; kx < kw; ++kx) {
                int ix = x - kx;
                if ((unsigned)ix >= (unsigned)W_in) continue;
                sum += ip[iy * W_in + ix] * wp[ky * kw + kx];
            }
        }
    }
    output[idx] = sum;
}

// ---------------------------------------------------------------------------
torch::Tensor tconv_forward(torch::Tensor input, torch::Tensor weight,
                            torch::Tensor bias, long kh, long kw) {
    TORCH_CHECK(input.is_cuda() && weight.is_cuda(), "inputs must be CUDA");
    TORCH_CHECK(input.dtype() == torch::kFloat32, "fp32 expected");
    auto x = input.contiguous();
    auto w = weight.contiguous();

    const int N_batch = x.size(0);
    const int C_in = x.size(1);
    const int H_in = x.size(2);
    const int W_in = x.size(3);
    const int C_out = w.size(1);
    const int H_out = H_in + (int)kh - 1;
    const int W_out = W_in + (int)kw - 1;
    const int K = C_in * (int)(kh * kw);
    const long M = (long)N_batch * H_out * W_out;

    auto out = torch::empty({N_batch, C_out, H_out, W_out}, x.options());
    auto stream = at::cuda::getCurrentCUDAStream();

    const float* bias_ptr = nullptr;
    if (bias.defined() && bias.numel() > 0) bias_ptr = bias.contiguous().data_ptr<float>();

    const cudaDeviceProp* prop = at::cuda::getCurrentDeviceProperties();

    bool fast = prop->major >= 8 && (M % BM) == 0 && K > 0 && K <= MAXK &&
                C_in <= 65535 && kh <= 255 && kw <= 255 &&
                H_out <= 65535 && W_out <= 65535 &&
                x.numel() < 2147483647L;

    if (fast) {
        auto BgT = torch::empty({C_out, K}, x.options());
        int threads = 256;
        int blocks = (K + threads - 1) / threads;
        repack_weight_kernel<<<blocks, threads, 0, stream>>>(
            w.data_ptr<float>(), BgT.data_ptr<float>(), C_in, C_out, (int)kh, (int)kw);

        long grid = M / BM;
        tconv_implicit_gemm_kernel<<<(unsigned)grid, NTHREADS, 0, stream>>>(
            x.data_ptr<float>(), BgT.data_ptr<float>(), bias_ptr,
            out.data_ptr<float>(), N_batch, C_in, H_in, W_in, H_out, W_out,
            C_out, (int)kh, (int)kw, K, M);
    } else {
        long total = M * (long)C_out;
        int threads = 256;
        long blocks = (total + threads - 1) / threads;
        tconv_direct_kernel<<<(unsigned)blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), w.data_ptr<float>(), bias_ptr,
            out.data_ptr<float>(), N_batch, C_in, H_in, W_in, H_out, W_out,
            C_out, (int)kh, (int)kw, total);
    }
    return out;
}
"""

cpp_source = "torch::Tensor tconv_forward(torch::Tensor input, torch::Tensor weight, torch::Tensor bias, long kh, long kw);"

tconv_ext = load_inline(
    name="tconv_implicit_gemm_v2",
    cpp_sources=cpp_source,
    cuda_sources=cuda_source,
    functions=["tconv_forward"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,
                 stride: tuple = (1, 1), padding: tuple = (0, 0),
                 output_padding: tuple = (0, 0), dilation: tuple = (1, 1),
                 groups: int = 1, bias: bool = False):
        super(ModelNew, self).__init__()
        self.conv_transpose2d = nn.ConvTranspose2d(
            in_channels, out_channels, kernel_size, stride=stride,
            padding=padding, output_padding=output_padding, dilation=dilation,
            groups=groups, bias=bias)
        # fast path supported only for this configuration
        s = tuple(stride) if hasattr(stride, "__len__") else (stride, stride)
        p = tuple(padding) if hasattr(padding, "__len__") else (padding, padding)
        op = tuple(output_padding) if hasattr(output_padding, "__len__") else (output_padding, output_padding)
        d = tuple(dilation) if hasattr(dilation, "__len__") else (dilation, dilation)
        self._fast = (s == (1, 1) and p == (0, 0) and op == (0, 0)
                      and d == (1, 1) and groups == 1)
        k = kernel_size if hasattr(kernel_size, "__len__") else (kernel_size, kernel_size)
        self._kh, self._kw = int(k[0]), int(k[1])

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        if self._fast and x.is_cuda and x.dtype == torch.float32:
            w = self.conv_transpose2d.weight
            b = self.conv_transpose2d.bias
            if b is None:
                b = x.new_empty(0)
            return tconv_ext.tconv_forward(x, w, b, self._kh, self._kw)
        return self.conv_transpose2d(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 20.7 ms; the PyTorch reference (with TF32 enabled) takes 6.69 ms; speedup 0.323x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| tconv_implicit_gemm_kernel(float const*, float const*, float const*, float*, int, int, int | 20615.0 | 1 |
| repack_weight_kernel(float const*, float*, int, int, int, int) | 15.1 | 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.


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().
