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

ISRU (Inverse Square Root Unit) Function

Computes f(x) = x / √(1 + a * x²)

Smooth saturating activation with parameter a

Derivative: f'(x) = (1 + a*x²)^(-3/2)

Mathematical Optimization

Computes 1 + a*x*x term

Uses sqrtf for square root

Single division per element

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 ISRU computation

Numerical Properties

Bounded output: |f(x)| ≤ 1/√a

Smooth and differentiable everywhere

Saturates gracefully for large |x|

Key Innovation: Vectorized Inverse Square Root Unit activation with parametric control over saturation level, optimized for smooth, bounded nonlinearities.




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:
        # ISRU Formula: x / sqrt(1 + a * x^2)
        return x / torch.sqrt(1.0 + self.a * x.pow(2))


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():
    retu