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 with #pragma unroll

Shared memory for block-level reduction

Double precision accumulation

Numerical Stability

Adds eps=1e-12f to prevent division by zero

Uses fabsf for absolute values

Double precision for summation

Kernel Design

One block per batch sample

256 threads per block for feature processing

Vectorized main loop + scalar tail handling

Memory Access

contiguous() tensors for coalescing

__restrict__ pointers

Sequential row-based access

Performance Optimization

Compiler flags: -O3, --use_fast_math

Single thread handles remainder elements

Efficient grid configuration

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().__init__()

    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        abs_diff = torch.abs(x - y)
        abs_sum = torch.abs(x) + torch.abs(y)
        return torch.sum(abs_diff / (abs_sum + 1e-12), dim=1)

batch_size = 1024
feature_dim = 4096

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 []n []