```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_postprocess_cuda(torch::Tensor x, torch::Tensor addition);
"""

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

template <typename T>
__device__ __forceinline__ T activate(T x, T addition) {
    x = (x > T(0) ? x : T(0.2) * x) + addition;
    x = x < T(-1) ? T(-1) : x;
    x = x > T(1) ? T(1) : x;
    return T(0.5) * x * (T(1) + erf(x * T(0.7071067811865475244)));
}

template <>
__device__ __forceinline__ float activate<float>(float x, float addition) {
    x = (x > 0.0f ? x : 0.2f * x) + addition;
    x = x < -1.0f ? -1.0f : x;
    x = x > 1.0f ? 1.0f : x;
    return 0.5f * x * (1.0f + erff(x * 0.7071067811865475244f));
}

__global__ void fused_float4(
    float* __restrict__ x,
    const float* __restrict__ addition,
    int64_t vectors,
    int64_t spatial,
    int64_t channels
) {
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vectors;
         i += int64_t(blockDim.x) * gridDim.x) {
        float4 v = reinterpret_cast<float4*>(x)[i];
        const float a = addition[((i * 4) / spatial) % channels];
        v.x = activate(v.x, a);
        v.y = activate(v.y, a);
        v.z = activate(v.z, a);
        v.w = activate(v.w, a);
        reinterpret_cast<float4*>(x)[i] = v;
    }
}

template <typename scalar_t>
__global__ void fused_scalar(
    scalar_t* __restrict__ x,
    const scalar_t* __restrict__ addition,
    int64_t count,
    int64_t spatial,
    int64_t channels
) {
    using compute_t = at::opmath_type<scalar_t>;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count;
         i += int64_t(blockDim.x) * gridDim.x) {
        const compute_t value = static_cast<compute_t>(x[i]);
        const compute_t a =
            static_cast<compute_t>(addition[(i / spatial) % channels]);

        // Preserve intermediate rounding for reduced-precision tensors.
        const scalar_t leaky = static_cast<scalar_t>(
            value > compute_t(0) ? value : compute_t(0.2) * value);
        compute_t z = static_cast<compute_t>(
            static_cast<scalar_t>(static_cast<compute_t>(leaky) + a));
        z = z < compute_t(-1) ? compute_t(-1) : z;
        z = z > compute_t(1) ? compute_t(1) : z;
        x[i] = static_cast<scalar_t>(
            compute_t(0.5) * z *
            (compute_t(1) + erf(z * compute_t(0.7071067811865475244))));
    }
}

torch::Tensor fused_postprocess_cuda(
    torch::Tensor x,
    torch::Tensor addition
) {
    TORCH_CHECK(x.is_cuda() && addition.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(x.device() == addition.device(), "Device mismatch");
    TORCH_CHECK(x.scalar_type() == addition.scalar_type(), "Dtype mismatch");
    TORCH_CHECK(x.dim() == 5 && x.is_contiguous(), "Expected contiguous NCDHW");
    TORCH_CHECK(addition.is_contiguous(), "Expected contiguous addition");
    TORCH_CHECK(addition.numel() == x.size(1), "Expected one value per channel");

    const c10::cuda::CUDAGuard guard(x.device());
    const auto stream = c10::cuda::getCurrentCUDAStream(x.get_device());
    const int64_t count = x.numel();
    if (count == 0) return x;

    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const int64_t channels = x.size(1);
    constexpr int threads = 256;

    if (x.scalar_type() == at::kFloat && spatial % 4 == 0) {
        const int64_t vectors = count / 4;
        const int blocks = static_cast<int>(
            std::min<int64_t>((vectors + threads - 1) / threads, 65535));
        fused_float4<<<blocks, threads, 0, stream.stream()>>>(
            x.data_ptr<float>(), addition.data_ptr<float>(),
            vectors, spatial, channels);
    } else {
        const int blocks = static_cast<int>(
            std::min<int64_t>((count + threads - 1) / threads, 65535));
        AT_DISPATCH_FLOATING_TYPES_AND2(
            at::ScalarType::Half, at::ScalarType::BFloat16,
            x.scalar_type(), "fused_postprocess_cuda", [&] {
                fused_scalar<scalar_t><<<blocks, threads, 0, stream.stream()>>>(
                    x.data_ptr<scalar_t>(), addition.data_ptr<scalar_t>(),
                    count, spatial, channels);
            });
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return x;
}
"""

_fused_ops = load_inline(
    name="conv3d_fused_leaky_add_clamp_gelu",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_postprocess_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.sum_tensor = nn.Parameter(torch.randn(sum_tensor_shape))

    def forward(self, x):
        x = self.conv(x)
        if (
            x.is_cuda
            and x.dtype == self.sum_tensor.dtype
            and tuple(self.sum_tensor.shape) == (x.shape[1], 1, 1, 1)
        ):
            return _fused_ops.fused_postprocess_cuda(
                x.contiguous(), self.sum_tensor.contiguous()
            )

        x = torch.nn.functional.leaky_relu(x, negative_slope=0.2)
        x = torch.clamp(x + self.sum_tensor, min=-1.0, max=1.0)
        return torch.nn.functional.gelu(x)
```