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.
CUDA C++ kernel for Hellinger‑Bhattacharyya composite distance

Element‑wise square‑root differences: (√|x[i]| – √|target[i]|)²

Two‑level parallel reduction: warp‑level (__shfl_down_sync) + shared‑memory reduction

Hellinger distance: √∑diff² × 1/√2 (scale factor 0.70710678)

Bhattacharyya coefficient approximation: 1 – H² (distance‑to‑similarity conversion)

Negative logarithm of the coefficient to obtain divergence, with epsilon for stability

Grid‑stride loops for coalesced memory access across feature dimension

Block‑per‑sample processing with 256 threads per block

PyTorch inline C++/CUDA extension via load_inline




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:
        sqrt_x = torch.sqrt(torch.abs(x))
        sqrt_target = torch.sqrt(torch.abs(self.target))
        euclidean_dist = torch.sqrt(torch.sum((sqrt_x - sqrt_target) ** 2, dim=-1))
        hellinger_dist = euclidean_dist / 1.41421356
        return -torch.log(torch.abs(1.0 - hellinger_dist ** 2) + 1e-6)

batch_size = 128
input_dim = 1024

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

def get_init_inputs():
    target = torch.abs(torch.randn(input_dim))
    return [target]