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.

Technologies Used in This Code
Core Libraries
PyTorch: Deep learning framework

CUDA: NVIDIA GPU parallel computing

C++: Kernel implementation

CUDA Components
CUDA kernel: sqrt_reciprocal_rsqrt_kernel

CUDA math intrinsics: sqrtf(), rsqrtf()

Element-wise parallelism: One thread per element

Mathematical Operations
Square root: sqrtf(x)

Reciprocal: 1.0f / y (where y = sqrt(x))

Reciprocal square root: rsqrtf(z) (where z = 1/sqrt(x))

Numerical identity: rsqrtf(1/sqrt(x)) = sqrt(sqrt(x)) (mathematically)

Efficient math: Using CUDA intrinsics for performance

Architecture
Standard 1D grid: Simple block/grid configuration

Element-wise computation: Independent processing per element

Memory pattern: Coalesced memory access

CUDA Math Functions
sqrtf(): Single-precision square root

rsqrtf(): Single-precision reciprocal square root (fast approximation)

Division: Standard floating-point division

Performance Features
GPU acceleration: Parallel computation across all elements

Intrinsic usage: rsqrtf() is often hardware-accelerated

Simple operations: Low computational cost per element

Numerical considerations: Input should be non-negative for sqrt

Unique Mathematical Property
Composite function: Computes sqrt(sqrt(x)) via three operations

Potential numerical differences: rsqrtf() may be approximate

Input constraints: x ≥ 0 required for real-valued results



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(Model, self).__init__()

    def forward(self, x):
        return torch.rsqrt(torch.reciprocal(torch.sqrt(x)))

batch_size = 1024
dim = 1024

def get_inputs():
    x = torch.rand(batch_size, dim) + 0.1
    return [x]

def get_init_inputs():
    return []