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.

This code implements Jaccard similarity + Dice coefficient + sqrt activation with CUDA optimizations:

Triple parallel reduction - Warp shuffle for three sums: dot product, x², t².

Three shared memory buffers - Separate buffers to avoid bank conflicts.

Fused similarity metrics - Combines Jaccard and Dice coefficient calculations in one kernel.

Numerical stability - Adds 1e-6 to denominator to prevent division by zero.

Grid-stride loop - Threads process multiple elements for load balancing.

CUDA math function - Uses sqrtf() for hardware-accelerated square root.

Memory coalescing - Contiguous tensor access patterns.

Batch parallelism - One CUDA block per input row.

Single-pass computation - Computes all three sums simultaneously in one memory traversal.



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, target):
        super(Model, self).__init__()
        self.target = nn.Parameter(target)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        dot = torch.sum(x * self.target, dim=-1)
        norm_x_sq = torch.sum(x * x, dim=-1)
        norm_target_sq = torch.sum(self.target * self.target, dim=-1)

        jaccard = dot / (norm_x_sq + norm_target_sq - dot + 1e-6)
        dice = 2.0 * jaccard / (1.0 + jaccard)
        return torch.sqrt(dice)


batch_size = 128
input_dim = 1024


def get_inputs():
    x = torch.abs(torch.randn(batch_size, input_dim))
    return [x]


def get_init_inputs():
    target = torch.abs(torch.randn(input_dim))
    return [target]