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 CUDA kernel implements optimized Double Gated Linear Unit (Double GLU) with:

Memory Optimization:

Vectorized memory access using float4 for 4x bandwidth

Contiguous tensor inputs for coalesced memory access

Processes two GLU pairs simultaneously per thread

Parallelization Strategy:

Grid-stride loop for efficient workload distribution

256 threads per block optimal configuration

Automatic grid size calculation with 65535 block limit

Computational Optimization:

Double GLU: Two parallel GLU operations sigmoid(gate) * activation

Optimized sigmoid: 1.0f / (1.0f + expf(-x))

Fast math compilation flags for optimized exponential

Efficient indexing for four input chunks (G1, X1, G2, X2)

Work Distribution:

Each thread processes 8 total elements (4 per GLU pair) via float4

Processes two independent GLU operations simultaneously

Input divided into four equal chunks, output into two chunks

Requires input feature dimension divisible by 16 for optimal performance

The implementation maximizes throughput by processing two GLU operations in parallel through vectorization and efficient memory access patterns.

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):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        g1, x1, g2, x2 = x.chunk(4, dim=-1)
        return torch.cat([torch.sigmoid(g1) * x1, torch.sigmoid(g2) * x2], dim=-1)

batch_size = 128
feature_dim = 4096

def get_inputs():
    x = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    return [x]

def get_init_inputs():
    return []