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 Kullback-Leibler divergence + LayerNorm with CUDA optimizations:

Element-wise parallelism - Each thread processes one element independently (no reduction).

Numerical stability - Adds ε=1e-8 to absolute values to avoid log(0).

Fused KL computation - Computes ylog(y/x) = y(log(y)-log(x)) in single kernel.

Simple grid-stride mapping - Standard 1D grid/block for element-wise operations.

CUDA math functions - Uses fabsf() and logf() for hardware acceleration.

Memory coalescing - Contiguous memory access patterns.

No shared memory - Pure element-wise computation without synchronization.

Post-processing - Applies PyTorch's LayerNorm to KL divergence elements.

Batch processing - Handles all elements in parallel regardless of shape.

Efficient log difference - Computes log(y)-log(x) instead of log(y/x) for numerical accuracy.



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


class Model(nn.Module):
    def __init__(self, dim):
        super(Model, self).__init__()
        self.ln = nn.LayerNorm(dim)

    def forward(self, x, y):
        eps = 1e-8

        x_safe = torch.abs(x) + eps
        y_safe = torch.abs(y) + eps

        kl_elem = y_safe * (torch.log(y_safe) - torch.log(x_safe))
        out = self.ln(kl_elem)
        return out.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 [input_dim]