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 rank‑based normalization with scaling

Bitonic sort in shared memory with value‑index pairs (s_val, s_idx)

Stable tie‑breaking using original index when values are equal

Rank calculation after sorting: rank = tid (0‑based position)

Normalization: rank / (width‑1) scaled by scale parameter

In‑place reordering to restore original element positions

Fixed block size of 1024 threads; width must be ≤ 1024

Block‑per‑sample processing (one block per batch row)

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):
        super(Model, self).__init__()
        self.scale = 10.0

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        ranks = x.argsort(dim=-1).argsort(dim=-1).float()
        n = x.size(-1)
        if n > 1:
            norm = ranks / (n - 1)
        else:
            norm = torch.zeros_like(ranks)
        return norm * self.scale

batch_size = 128
input_dim = 1024

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

def get_init_inputs():
    return