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 Hamming-like XOR + AND operation with CUDA optimizations:

Fused bitwise simulation - Uses fabsf(a-b) to simulate XOR (difference) and multiplies with target for AND.

Single parallel reduction - Warp shuffle for sum reduction of AND results.

Shared memory reduction - Standard warp/block reduction pattern.

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

Memory coalescing - Contiguous tensor access patterns.

Batch parallelism - One CUDA block per input row.

Lightweight kernel - Minimal arithmetic operations per element.

Floating-point emulation - Simulates boolean logic using floating-point arithmetic for differentiable operations.



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:
        xor_soft = torch.abs(x - self.target)
        xor_and = xor_soft * self.target
        return torch.sum(xor_and, dim=-1)


batch_size = 128
input_dim = 1024


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


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