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 LogSigmoid activation with:

Memory Optimization:

Vectorized memory access using float4 for 4x bandwidth

Contiguous tensor inputs for coalesced memory access

Separate handling for vectorized main loop and scalar tail

Numerical Stability:

Numerically stable implementation using log1pf() and expf()

Branching for positive/negative values to prevent overflow

For x > 0: -log1pf(expf(-x))

For x ≤ 0: x - log1pf(expf(x))

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:

Fast math compilation flags for optimized transcendental functions

Inline function for LogSigmoid operation

Efficient numerical computation preventing precision loss

Work Distribution:

Vectorized main loop processes 4 elements per thread via float4

Scalar tail handles remaining elements (n % 4)

Each thread computes independent LogSigmoid operations

The implementation balances numerical accuracy with performance through stable logarithmic computations and vectorized memory access.

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().__init__()
        self.act = nn.LogSigmoid()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return self.act(x)

batch_size = 128
feature_dim = 512

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

def get_init_inputs():
    return []