```python
import torch
import torch.nn as nn
import torch.nn.functional as F
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 sum_tensor);
"""

_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 <algorithm>
#include <cstdint>

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

__global__ void fused_vector_kernel(
    const float4* __restrict__ x,
    const float* __restrict__ bias,
    float4* __restrict__ out,
    int64_t vector_count,
    int64_t spatial_vectors,
    int64_t channels)
{
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vector_count; i += stride) {
        const int64_t channel = (i / spatial_vectors) % channels;
        const float b = bias[channel];
        const float4 v = x[i];

        float4 result;
        result.x = postprocess(v.x, b);
        result.y = postprocess(v.y, b);
        result.z = postprocess(v.z, b);
        result.w = postprocess(v.w, b);
        out[i] = result;
    }
}

__global__ void fused_scalar_kernel(
    const float* __restrict__ x,
    const float* __restrict__ bias,
    float* __restrict__ out,
    int64_t count,
    int64_t spatial,
    int64_t channels)
{
    const int64_t stride = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count; i += stride) {
        const int64_t channel = (i / spatial) % channels;
        out[i] = postprocess(x[i], bias[channel]);
    }
}

torch::Tensor fused_postprocess_cuda(
    torch::Tensor x,
    torch::Tensor sum_tensor)
{
    TORCH_CHECK(x.is_cuda() && sum_tensor.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.device() == sum_tensor.device(),
                "Tensors must share a device");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                sum_tensor.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.dim() == 5 && x.is_contiguous() &&
                sum_tensor.is_contiguous(),
                "Expected contiguous NCDHW input and contiguous bias");
    TORCH_CHECK(sum_tensor.numel() == x.size(1),
                "Expected one bias value per output channel");

    const c10::cuda::CUDAGuard device_guard(x.device());
    auto out = torch::empty_like(x);
    const int64_t count = x.numel();
    if (count == 0) {
        return out;
    }

    const int64_t channels = x.size(1);
    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const auto stream = at::cuda::getCurrentCUDAStream();
    constexpr int threads = 256;

    const bool vectorized =
        spatial % 4 == 0 &&
        reinterpret_cast<uintptr_t>(x.data_ptr<float>()) % 16 == 0 &&
        reinterpret_cast<uintptr_t>(out.data_ptr<float>()) % 16 == 0;

    if (vectorized) {
        const int64_t vector_count = count / 4;
        const int blocks = static_cast<int>(
            std::min<int64_t>((vector_count + threads - 1) / threads, 65535));

        fused_vector_kernel<<<blocks, threads, 0, stream>>>(
            reinterpret_cast<const float4*>(x.data_ptr<float>()),
            sum_tensor.data_ptr<float>(),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            vector_count,
            spatial / 4,
            channels);
    } else {
        const int blocks = static_cast<int>(
            std::min<int64_t>((count + threads - 1) / threads, 65535));

        fused_scalar_kernel<<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(),
            sum_tensor.data_ptr<float>(),
            out.data_ptr<float>(),
            count,
            spatial,
            channels);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return out;
}
"""

_fused_ops = load_inline(
    name="conv3d_leaky_add_clamp_gelu_fused_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_postprocess_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    verbose=False,
)


class _FusedPostprocess(torch.autograd.Function):
    @staticmethod
    def forward(ctx, x, sum_tensor):
        if ctx.needs_input_grad[0] or ctx.needs_input_grad[1]:
            ctx.save_for_backward(x, sum_tensor)
        return _fused_ops.fused_postprocess_cuda(x, sum_tensor)

    @staticmethod
    def backward(ctx, grad_output):
        x, sum_tensor = ctx.saved_tensors
        pre_clamp = F.leaky_relu(x, negative_slope=0.2) + sum_tensor
        z = pre_clamp.clamp(-1.0, 1.0)

        gelu_grad = (
            0.5 * (1.0 + torch.erf(z * 0.7071067811865476))
            + z * torch.exp(-0.5 * z.square()) * 0.3989422804014327
        )
        grad = grad_output * gelu_grad
        grad = grad * ((pre_clamp >= -1.0) & (pre_clamp <= 1.0))

        grad_x = None
        grad_sum = None
        if ctx.needs_input_grad[0]:
            grad_x = grad * torch.where(x > 0.0, 1.0, 0.2)
        if ctx.needs_input_grad[1]:
            grad_sum = grad.sum(dim=(0, 2, 3, 4)).reshape_as(sum_tensor)

        return grad_x, grad_sum


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 == torch.float32
            and self.sum_tensor.dtype == torch.float32
            and x.is_contiguous()
            and self.sum_tensor.is_contiguous()
            and self.sum_tensor.device == x.device
            and tuple(self.sum_tensor.shape) == (x.size(1), 1, 1, 1)
        ):
            return _FusedPostprocess.apply(x, self.sum_tensor)

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