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

Triple Reduction

Simultaneously computes intersection, sum_x, and sum_y

Warp shuffle with #pragma unroll

Shared memory for block-level reduction

Numerical Stability

Adds eps to denominator to prevent division by zero

Double precision accumulation for accuracy

Compiler flag: --use_fast_math

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

Row-based sequential access pattern

Performance Optimization

Compiler flag: -O3

Single thread handles remainder elements

Efficient Dice coefficient calculation









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-6):
        super().__init__()
        self.eps = eps

    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        intersection = (x * y).sum(dim=1)
        sum_x = x.sum(dim=1)
        sum_y = y.sum(dim=1)
        return (2.0 * intersection) / (sum_x + sum_y + self.eps)

batch_size = 128
feature_dim = 512

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

def get_init_inputs():
    return [1e-6]