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:

Two-Kernel Approach

Kernel 1: Compute squared norm with parallel reduction

Kernel 2: Apply scaling factor with vectorized operations

Separates reduction from scaling for better performance

Vectorized Memory Access + ILP

Uses float4 for 4-element vector loads/stores

Instruction-Level Parallelism (ILP): Processes 2 vectors (8 elements) per loop iteration

Increases computational density in scaling kernel

Double Precision Reduction

Custom atomicAddDouble for 64-bit atomic operations

Double precision accumulation for numerical accuracy

Warp shuffle and shared memory reduction

Numerical Stability

Adds 1e-6 to denominator to prevent division by zero

Clips clip_coef to maximum of 1.0

Square root calculation for L2 norm

Grid-Stride Loop

Processes elements with grid-stride pattern in both kernels

Handles arbitrary tensor sizes efficiently

Better GPU utilization

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

Key Innovation: Two-kernel design with ILP-optimized scaling, separating norm computation from gradient scaling for optimal performance and numerical stability.



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

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        total_norm = torch.norm(x, p=2)
        clip_coef = self.max_norm / (total_norm + 1e-6)
        clip_coef = torch.clamp(clip_coef, max=1.0)
        return x * clip_coef

batch_size = 128
feature_dim = 256

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

def get_init_inputs():
    return [1.0]