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

Reduces memory instructions by 4x

Better memory bandwidth utilization

Parallel Reduction

Warp shuffle operations with #pragma unroll

Shared memory for block-level reduction

Double precision accumulation for accuracy

Grid-Stride Loop

Processes elements with grid-stride pattern

Handles arbitrary tensor sizes efficiently

Better GPU utilization

L2 Regularization Calculation

Computes squared L2 norm: sum(x^2)

Applies weight decay: 0.5 * decay * sum(x^2)

Efficient mathematical formulation

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Coalesced memory access patterns

Performance Tuning

Fixed 256 threads per block

Block count capped at 1024

Compiler flag: -O3

Two-Level Reduction

Block-level reduction in CUDA kernel

Final reduction on PyTorch side with .sum()

Efficient for both small and large tensors

Key Innovation: Vectorized L2 norm computation with parallel reduction, optimized for weight decay regularization in training algorithms.


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, decay=1e-4):
        super().__init__()
        self.decay = decay

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return 0.5 * self.decay * torch.sum(x ** 2)

batch_size = 1024
feature_dim = 4096

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

def get_init_inputs():
    return [1e-4]