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 KL divergence + Jensen-Shannon divergence + Swish activation with CUDA optimizations:

Dual parallel reduction - Warp shuffle for two sums: KL divergence in both directions.

Two shared memory buffers - Separate buffers for KL(X||M) and KL(T||M) sums.

Numerical stability - Adds ε=1e-8 to avoid log(0) and division issues.

Log reuse optimization - Computes log(m) once per element and reuses it.

Fused divergence chain - Computes symmetric JS divergence from two KL terms and applies Swish.

Grid-stride loop - Threads process multiple elements for load balancing.

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

Memory coalescing - Contiguous tensor access patterns.

Batch parallelism - One CUDA block per input row.

Single-pass computation - Computes both KL divergences in one memory traversal.



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, target):
        super(Model, self).__init__()
        self.target = nn.Parameter(target)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        eps = 1e-8

        m = 0.5 * (x + self.target)

        kl_x_m = torch.sum(x * (torch.log(x + eps) - torch.log(m + eps)), dim=-1)

        kl_t_m = torch.sum(self.target * (torch.log(self.target + eps) - torch.log(m + eps)), dim=-1)

        js_div = 0.5 * (kl_x_m + kl_t_m)

        return js_div * torch.sigmoid(js_div)


batch_size = 128
input_dim = 1024


def get_inputs():
    # Use softmax to ensure inputs are valid probability distributions (sum to 1, positive)
    x = torch.softmax(torch.randn(batch_size, input_dim), dim=-1)
    return [x]


def get_init_inputs():
    target = torch.softmax(torch.randn(input_dim), dim=-1)
    return [target]