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

ISRLU (Inverse Square Root Linear Unit) Function

Piecewise definition:

x ≥ 0: x (ReLU-like)

x < 0: x / √(1 + a * x²) (ISRU-like)

Combines ReLU for positives with ISRU for negatives

Parameter a controls negative saturation

Optimized Branching

Simple if (x >= 0) condition

Early return for positive branch

Negative branch uses ISRU computation

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 ISRLU computation

Numerical Properties

Non-negative for x ≥ 0

Smoothly saturates for negative inputs

Differentiable everywhere except origin

Key Innovation: Vectorized Inverse Square Root Linear Unit activation combining ReLU's simplicity for positives with ISRU's smooth saturation for negatives, optimized with efficient branching and mathematical computation.

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, a=1.0):
        super().__init__()
        self.a = a

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # ISRLU Formula: x if x >= 0, else x / sqrt(1 + a * x^2)
        y_neg = x / torch.sqrt(1.0 + self.a * x.pow(2))

        return torch.where(x >= 0, x, y_neg)


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 [1.0