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 Euclidean distance + erfc activation with CUDA optimizations:

Parallel reduction - Warp shuffle (__shfl_down_sync) for efficient warp-level sum.

Shared memory - Cross-warp reduction using shared memory for block-level sum.

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

Fused kernel - Combines squared difference computation, sum, sqrt, and erfc in single kernel.

Memory coalescing - Contiguous tensor layout and linear indexing.

CUDA math functions - Uses sqrtf() and erfcf() for hardware-accelerated operations.



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:
        dist = torch.sqrt(torch.sum((x - self.target) ** 2, dim=-1))
        return torch.erfc(dist)

batch_size = 128
input_dim = 1024

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

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