You write custom CUDA kernels to replace the pytorch operators in the given GeGLU 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 chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.

This code implements Structural Similarity Index (SSIM) + Softplus activation with CUDA optimizations:

Per-batch parallelism - One CUDA block processes one batch element with all threads cooperating.

Five simultaneous reductions - Computes sums for: x, y, x², y², xy in parallel.

Shared memory reduction - Uses 5×256-element shared memory arrays for parallel reduction.

Tree reduction - Binary tree reduction within shared memory for all five statistics.

SSIM computation - Calculates SSIM with means (μ), variances (σ²), and covariance (σxy).

Numerical stability constants - Uses C1=0.0001 and C2=0.0009 for stable division.

Softplus activation - Applies log(1+exp(x)) via log1pf(expf(ssim)) for numerical accuracy.

Memory coalescing - Threads stride through vector elements for efficient memory access.

Single-pass statistics - Computes all necessary statistics in one traversal.

Large shared memory allocation - 5×256 floats (5KB) for simultaneous reduction buffers.



Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:
import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()

    def forward(self, x, y):
        C1 = 0.01 ** 2
        C2 = 0.03 ** 2

        mu_x = x.mean(dim=1, keepdim=True)
        mu_y = y.mean(dim=1, keepdim=True)

        sigma_x = ((x - mu_x) ** 2).mean(dim=1, keepdim=True)
        sigma_y = ((y - mu_y) ** 2).mean(dim=1, keepdim=True)
        sigma_xy = ((x - mu_x) * (y - mu_y)).mean(dim=1, keepdim=True)

        numerator = (2 * mu_x * mu_y + C1) * (2 * sigma_xy + C2)
        denominator = (mu_x ** 2 + mu_y ** 2 + C1) * (sigma_x + sigma_y + C2)

        ssim = numerator / denominator
        return F.softplus(ssim).mean()


batch_size = 16
input_dim = 1024


def get_inputs():
    x = torch.rand(batch_size, input_dim)
    y = torch.rand(batch_size, input_dim)
    return [x, y]


def get_init_inputs():
    return []