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:

Grid-Stride Loop

Processes all elements with grid-stride pattern

Handles arbitrary tensor sizes efficiently

Better GPU utilization for large tensors

Two-Level Reduction

Block-level reduction with warp shuffles

Partial results stored in shared memory

Final reduction on PyTorch side

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Grid-stride enables coalesced access

Performance Tuning

Fixed 256 threads per block

Block count capped at 2048 for occupancy

Compiler flag: -O3

Numerical Optimization

Precompute eps_sq outside kernel

Double precision accumulation

Single sqrtf per element



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, eps=1e-3):
        super().__init__()
        self.eps = eps

    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        diff = x - y
        loss = torch.sqrt(diff * diff + self.eps * self.eps)
        return torch.mean(loss)

batch_size = 1024
feature_dim = 512

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

def get_init_inputs():
    return [1e-3]