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 L1 (Hamming‑like) distance with GELU activation

Element‑wise absolute differences: |x[i] – target[i]| accumulated across features

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

GELU activation: dist × 0.5 × (1 + erf(dist / √2)) using CUDA erff

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
import torch.nn.functional as F

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.sum(torch.abs(x - self.target), dim=-1)
        return F.gelu(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]