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

SQNL (Square Nonlinearity) Function

Piecewise definition:

x > 2.0: 1.0

0 ≤ x ≤ 2.0: x - x²/4

-2.0 ≤ x < 0: x + x²/4

x < -2.0: -1.0

Quadratic approximation with hard saturation

Output bounded between [-1, 1]

Optimized Branching

Sequential if conditions for piecewise logic

Early returns for boundary cases

Precomputed 0.25f for multiplication

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

Inline function for SQNL computation

Mathematical Efficiency

Vectorized operations for 4 elements simultaneously

Simple arithmetic operations only

Early saturation for |x| > 2.0

Key Innovation: Vectorized Square Nonlinearity activation with efficient piecewise quadratic computation and hard saturation, optimized for bounded activation functions in 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):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x_abs = x.abs()

        y_mid = torch.where(
            x >= 0,
            x - x.pow(2) / 4.0,
            x + x.pow(2) / 4.0
        )

        y_saturated = torch.where(
            x > 2.0,
            torch.tensor(1.0, dtype=x.dtype, device=x.device),
            torch.where(
                x < -2.0,
                torch.tensor(-1.0, dtype=x.dtype, device=x.device),
                y_mid
            )
        )
        return y_saturated


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 []