```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>
#include <cstdint>

constexpr int REDUCE_THREADS = 256;
constexpr int FINISH_THREADS = 128;
constexpr int TILE = 16384;

__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 value;
}

__device__ __forceinline__ float warp_max(float value) {
    #pragma unroll
    for (int offset = 16; offset > 0; offset >>= 1)
        value = fmaxf(value, __shfl_down_sync(0xffffffff, value, offset));
    return value;
}

// Independent input and weight reductions share one kernel launch.
template<bool VECTORIZED>
__global__ void prepare_kernel(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    float* __restrict__ partials,
    float* __restrict__ weight_sums,
    int64_t spatial,
    int parts,
    int kernel_elements,
    int64_t input_blocks,
    int64_t weight_count,
    int64_t total_blocks
) {
    __shared__ float reduction[8];
    const int tid = threadIdx.x;

    for (int64_t block = blockIdx.x;
         block < total_blocks;
         block += gridDim.x) {
        if (block >= input_blocks) {
            const int64_t index =
                (block - input_blocks) * REDUCE_THREADS + tid;

            if (index < weight_count) {
                const float* w = weight + index * kernel_elements;
                float value = 0.0f;
                if (kernel_elements == 9) {
                    #pragma unroll
                    for (int k = 0; k < 9; ++k)
                        value += w[k];
                } else {
                    for (int k = 0; k < kernel_elements; ++k)
                        value += w[k];
                }
                weight_sums[index] = value;
            }
        } else {
            const int64_t plane = block / parts;
            const int part = block % parts;
            const int64_t start = int64_t(part) * TILE;
            float value = 0.0f;

            if constexpr (VECTORIZED) {
                const float4* x = reinterpret_cast<const float4*>(
                    input + plane * spatial
                );
                float a = 0.0f;
                float b = 0.0f;
                float c = 0.0f;
                float d = 0.0f;

                #pragma unroll
                for (int j = 0; j < TILE / (4 * REDUCE_THREADS); ++j) {
                    const int64_t index =
                        start / 4 + tid + j * REDUCE_THREADS;
                    if (index < spatial / 4) {
                        const float4 v = x[index];
                        a += v.x;
                        b += v.y;
                        c += v.z;
                        d += v.w;
                    }
                }
                value = (a + b) + (c + d);
            } else {
                #pragma unroll
                for (int j = 0; j < TILE / REDUCE_THREADS; ++j) {
                    const int64_t index =
                        start + tid + j * REDUCE_THREADS;
                    if (index < spatial)
                        value += input[plane * spatial + index];
                }
            }

            value = warp_sum(value);
            if ((tid & 31) == 0)
                reduction[tid >> 5] = value;
            __syncthreads();

            if (tid < 32) {
                value = tid < 8 ? reduction[tid] : 0.0f;
                value = warp_sum(value);
                if (tid == 0)
                    partials[block] = value;
            }
            __syncthreads();
        }
    }
}

__global__ void finish_kernel(
    const float* __restrict__ partials,
    const float* __restrict__ weight_sums,
    const float* __restrict__ conv_bias,
    const float* __restrict__ extra_bias,
    float* __restrict__ output,
    int in_channels,
    int out_channels,
    int parts,
    float inverse_output_area
) {
    extern __shared__ float storage[];
    float* input_sums = storage;
    float* logits = input_sums + in_channels;
    float* reduction = logits + out_channels;

    const int batch = blockIdx.x;
    const int tid = threadIdx.x;
    const int lane = tid & 31;
    const int warp = tid >> 5;
    const float negative_infinity = -CUDART_INF_F;

    for (int i = tid; i < in_channels; i += FINISH_THREADS) {
        const int64_t base = (int64_t(batch) * in_channels + i) * parts;
        float value = 0.0f;
        for (int p = 0; p < parts; ++p)
            value += partials[base + p];
        input_sums[i] = value * inverse_output_area;
    }
    __syncthreads();

    float local_max = negative_infinity;
    for (int c = tid; c < out_channels; c += FINISH_THREADS) {
        float value = 0.0f;
        for (int i = 0; i < in_channels; ++i) {
            value = fmaf(
                input_sums[i],
                weight_sums[int64_t(i) * out_channels + c],
                value
            );
        }
        value = (value + conv_bias[c]) + extra_bias[c];
        logits[c] = value;
        local_max = fmaxf(local_max, value);
    }

    local_max = warp_max(local_max);
    if (lane == 0)
        reduction[warp] = local_max;
    __syncthreads();

    if (warp == 0) {
        float value = lane < 4 ? reduction[lane] : negative_infinity;
        value = warp_max(value);
        if (lane == 0)
            reduction[4] = value;
    }
    __syncthreads();

    const float maximum = reduction[4];
    float local_sum = 0.0f;
    for (int c = tid; c < out_channels; c += FINISH_THREADS)
        local_sum += expf(logits[c] - maximum);

    local_sum = warp_sum(local_sum);
    if (lane == 0)
        reduction[warp] = local_sum;
    __syncthreads();

    if (warp == 0) {
        float value = lane < 4 ? reduction[lane] : 0.0f;
        value = warp_sum(value);
        if (lane == 0) {
            output[batch] = isinf(maximum)
                ? 10.0f * maximum
                : 10.0f * (maximum + logf(value));
        }
    }
}

torch::Tensor pooled_transpose_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor conv_bias,
    torch::Tensor extra_bias
) {
    const c10::cuda::CUDAGuard device_guard(x.device());

    const int batch = x.size(0);
    const int in_channels = x.size(1);
    const int out_channels = weight.size(1);
    const int kh = weight.size(2);
    const int kw = weight.size(3);
    const int64_t spatial = x.size(2) * x.size(3);
    const int parts = (spatial + TILE - 1) / TILE;

    auto output = torch::empty({batch, 1}, x.options());
    if (batch == 0)
        return output;

    const int64_t input_blocks = int64_t(batch) * in_channels * parts;
    const int64_t weight_count = int64_t(in_channels) * out_channels;
    const int64_t weight_blocks =
        (weight_count + REDUCE_THREADS - 1) / REDUCE_THREADS;
    const int64_t total_blocks = input_blocks + weight_blocks;
    const int blocks = int(total_blocks < 65535 ? total_blocks : 65535);

    auto scratch = torch::empty(
        {input_blocks + weight_count}, x.options()
    );
    float* partials = scratch.data_ptr<float>();
    float* weight_sums = partials + input_blocks;

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

    if (spatial % 4 == 0 &&
        reinterpret_cast<uintptr_t>(x.data_ptr<float>()) % 16 == 0) {
        prepare_kernel<true><<<blocks, REDUCE_THREADS, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(),
            partials, weight_sums, spatial, parts, kh * kw,
            input_blocks, weight_count, total_blocks
        );
    } else {
        prepare_kernel<false><<<blocks, REDUCE_THREADS, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(),
            partials, weight_sums, spatial, parts, kh * kw,
            input_blocks, weight_count, total_blocks
        );
    }
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    const int64_t output_area =
        (x.size(2) + kh - 1) * (x.size(3) + kw - 1);
    const size_t shared_bytes =
        size_t(in_channels + out_channels + 5) * sizeof(float);

    finish_kernel<<<batch, FINISH_THREADS, shared_bytes, stream>>>(
        partials, weight_sums,
        conv_bias.data_ptr<float>(), extra_bias.data_ptr<float>(),
        output.data_ptr<float>(),
        in_channels, out_channels, parts,
        1.0f / float(output_area)
    );
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return output;
}
"""

_extension = load_inline(
    name="fused_transpose_global_pool_lse_v3",
    cpp_sources=r"""
#include <torch/extension.h>
torch::Tensor pooled_transpose_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor conv_bias,
    torch::Tensor extra_bias
);
""",
    cuda_sources=_cuda_source,
    functions=["pooled_transpose_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, bias_shape):
        super().__init__()
        self.conv_transpose = nn.ConvTranspose2d(
            in_channels, out_channels, kernel_size
        )
        self.bias = nn.Parameter(torch.randn(bias_shape))

    def forward(self, x):
        conv = self.conv_transpose
        use_custom = (
            x.is_cuda
            and x.dtype == torch.float32
            and conv.weight.dtype == torch.float32
            and conv.bias is not None
            and conv.bias.dtype == torch.float32
            and self.bias.dtype == torch.float32
            and x.device == conv.weight.device == conv.bias.device == self.bias.device
            and x.ndim == 4
            and x.shape[1] == conv.in_channels
            and x.shape[2] > 0
            and x.shape[3] > 0
            and conv.groups == 1
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.output_padding == (0, 0)
            and conv.dilation == (1, 1)
            and tuple(self.bias.shape) == (conv.out_channels, 1, 1)
            and conv.in_channels + conv.out_channels + 5 <= 12000
            and not torch.is_autocast_enabled()
        )

        if use_custom:
            return _extension.pooled_transpose_cuda(
                x.contiguous(),
                conv.weight.contiguous(),
                conv.bias.contiguous(),
                self.bias.contiguous(),
            )

        x = conv(x)
        x = x.mean(dim=(2, 3), keepdim=True)
        x = x + self.bias
        x = torch.logsumexp(x, dim=1, keepdim=True)
        return x.sum(dim=(2, 3)) * 10.0
```