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 Optimization Strategies:

Vectorized Memory Access

Uses float4 for 4-element vector loads/stores

__ldg() for read-only caching through texture memory

Bit shifts for division (>> 2, << 2) for efficiency

AHAF Activation Function

Adaptive Hyperbolic Activation: β * x * sigmoid(γ * x)

Parametric activation with β and γ parameters

Combines linear scaling with sigmoid gating

Optimized Sigmoid

Uses expf(-x) for sigmoid computation

Inline function for reusability

Standard sigmoid: 1 / (1 + exp(-x))

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Grid-stride loop for arbitrary sizes

Performance Optimization

Compiler flags: -O3, --use_fast_math

Efficient kernel launch configuration

Block count limited to 65535

Precomputed parameter application

Mathematical Efficiency

Vectorized operations for 4 elements simultaneously

Single exponential per element

Parameterized scaling in single pass

Key Innovation: Vectorized AHAF (Adaptive Hyperbolic Activation Function) with parametric control over both linear scaling (β) and sigmoid steepness (γ), optimized for adaptive neural networks.

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, beta=1.0, gamma=1.0):
        super().__init__()
        self.beta = beta
        self.gamma = gamma

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # AHAF Formula: beta * x * sigmoid(gamma * x)
        return self.beta * x * torch.sigmoid(self.gamma * x)


batch_size = 1024
feature_dim = 1024


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


def get_init_inputs():
    return [1.0, 1.0]