```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cpp_source = r"""
#include <torch/extension.h>
torch::Tensor fused_pool_activation_cuda(
    torch::Tensor x, torch::Tensor subtract);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <stdint.h>

__global__ void fused_pool_activation_kernel(
    const float* __restrict__ x,
    const float* __restrict__ subtract,
    float* __restrict__ output,
    int D, int H, int W,
    int OD, int OH, int OW,
    int64_t spatial_out,
    int64_t total_out)
{
    const int64_t index =
        static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
    if (index >= total_out) return;

    const int64_t n = index / spatial_out;
    const int64_t spatial_index = index - n * spatial_out;
    const int ow = spatial_index % OW;
    const int oh = (spatial_index / OW) % OH;
    const int od = spatial_index / (static_cast<int64_t>(OH) * OW);

    const int64_t plane = static_cast<int64_t>(H) * W;
    const int64_t volume = static_cast<int64_t>(D) * plane;
    const int64_t base =
        n * 16 * volume + (2 * od) * plane + (2 * oh) * W + 2 * ow;

    float values[16];
    float channel_max = -CUDART_INF_F;

    #pragma unroll
    for (int c = 0; c < 16; ++c) {
        const float* p = x + base + c * volume;
        float pooled = -CUDART_INF_F;

        #pragma unroll
        for (int dz = 0; dz < 2; ++dz) {
            #pragma unroll
            for (int dy = 0; dy < 2; ++dy) {
                #pragma unroll
                for (int dx = 0; dx < 2; ++dx) {
                    const float v = p[dz * plane + dy * W + dx];
                    pooled = isnan(v) ? v :
                             (isnan(pooled) ? pooled : fmaxf(pooled, v));
                }
            }
        }

        values[c] = pooled;
        channel_max = fmaxf(channel_max, pooled);
    }

    float denominator = 0.0f;
    #pragma unroll
    for (int c = 0; c < 16; ++c) {
        values[c] = expf(values[c] - channel_max);
        denominator += values[c];
    }

    const float inv_denominator = 1.0f / denominator;
    float result = -CUDART_INF_F;

    #pragma unroll
    for (int c = 0; c < 16; ++c) {
        const float shifted = values[c] * inv_denominator - subtract[c];
        const float activated = shifted / (1.0f + expf(-shifted));
        result = isnan(activated) ? activated :
                 (isnan(result) ? result : fmaxf(result, activated));
    }

    output[index] = result;
}

torch::Tensor fused_pool_activation_cuda(
    torch::Tensor x, torch::Tensor subtract)
{
    TORCH_CHECK(x.is_cuda() && subtract.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.device() == subtract.device(),
                "Tensors must be on the same device");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                subtract.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.is_contiguous() && subtract.is_contiguous(),
                "Expected contiguous tensors");
    TORCH_CHECK(x.dim() == 5 && x.size(1) == 16 &&
                subtract.numel() == 16,
                "Expected 16 channels");

    const c10::cuda::CUDAGuard guard(x.device());

    const int D = x.size(2);
    const int H = x.size(3);
    const int W = x.size(4);
    const int OD = D / 2;
    const int OH = H / 2;
    const int OW = W / 2;

    TORCH_CHECK(OD > 0 && OH > 0 && OW > 0,
                "Pooling output dimensions must be positive");

    auto output = torch::empty({x.size(0), OD, OH, OW}, x.options());
    const int64_t spatial_out = static_cast<int64_t>(OD) * OH * OW;
    const int64_t total_out = x.size(0) * spatial_out;

    if (total_out > 0) {
        constexpr int threads = 128;
        const int blocks = (total_out + threads - 1) / threads;
        const auto stream =
            c10::cuda::getCurrentCUDAStream(x.get_device());

        fused_pool_activation_kernel<<<blocks, threads, 0, stream.stream()>>>(
            x.data_ptr<float>(),
            subtract.data_ptr<float>(),
            output.data_ptr<float>(),
            D, H, W, OD, OH, OW, spatial_out, total_out);

        C10_CUDA_KERNEL_LAUNCH_CHECK();
    }

    return output;
}
"""

_fused_ops = load_inline(
    name="convtranspose3d_fused_pool_swish_max_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_pool_activation_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


def _triple(value):
    if isinstance(value, (tuple, list)):
        return tuple(value)
    return (value, value, value)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels,
        out_channels,
        kernel_size,
        stride,
        padding,
        output_padding,
        pool_kernel_size,
        pool_stride,
        pool_padding,
    ):
        super().__init__()
        self.conv_transpose = nn.ConvTranspose3d(
            in_channels,
            out_channels,
            kernel_size,
            stride=stride,
            padding=padding,
            output_padding=output_padding,
        )
        self.max_pool = nn.MaxPool3d(
            kernel_size=pool_kernel_size,
            stride=pool_stride,
            padding=pool_padding,
        )
        self.subtract = nn.Parameter(torch.randn(out_channels))

        effective_pool_stride = (
            pool_kernel_size if pool_stride is None else pool_stride
        )
        self._use_fused_pool = (
            out_channels == 16
            and _triple(pool_kernel_size) == (2, 2, 2)
            and _triple(effective_pool_stride) == (2, 2, 2)
            and _triple(pool_padding) == (0, 0, 0)
        )

    def forward(self, x):
        x = self.conv_transpose(x)

        if (
            self._use_fused_pool
            and x.is_cuda
            and x.dtype == torch.float32
            and x.is_contiguous()
            and self.subtract.dtype == torch.float32
            and self.subtract.is_contiguous()
            and not (
                torch.is_grad_enabled()
                and (x.requires_grad or self.subtract.requires_grad)
            )
        ):
            return _fused_ops.fused_pool_activation_cuda(x, self.subtract)

        x = self.max_pool(x)
        x = torch.softmax(x, dim=1)
        x = x - self.subtract.view(1, -1, 1, 1, 1)
        x = torch.sigmoid(x) * x
        return torch.max(x, dim=1)[0]
```