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 Jensen-Shannon divergence + GroupNorm with CUDA optimizations:

Element-wise parallelism - Each thread computes JS divergence for one pair of p[i], q[i] independently.

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

Intermediate reuse - Computes m = 0.5*(p+q) once and reuses for both KL terms.

Fused JS computation - Combines two KL divergence calculations and JS averaging in single kernel.

Memory coalescing - Contiguous memory access patterns.

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

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

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

Post-processing - Applies PyTorch's GroupNorm to JS divergence elements.

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



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, num_channels, num_groups=32):
        super(Model, self).__init__()
        self.gn = nn.GroupNorm(num_groups, num_channels)

    def forward(self, x, y):
        eps = 1e-8
        p = torch.abs(x) + eps
        q = torch.abs(y) + eps
        m = 0.5 * (p + q)

        kl_p = p * (torch.log(p) - torch.log(m))
        kl_q = q * (torch.log(q) - torch.log(m))

        js_elem = 0.5 * (kl_p + kl_q)
        out = self.gn(js_elem)
        return out.mean()


batch_size = 16
input_dim = 1024


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


def get_init_inputs():
    return [input_dim]