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 dot product + MSE + tanh activation with CUDA optimizations:

Parallel reduction - Warp shuffle for two simultaneous sums: dot product and squared differences.

Dual shared memory buffers - Separate buffers for dot and MSE sums to avoid bank conflicts.

Fused operations - Combines dot product, MSE calculation, and tanh activation in one kernel.

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

Single-pass computation - Computes both dot product and squared differences in one memory traversal.

Memory coalescing - Contiguous tensor access patterns.

Batch parallelism - One CUDA block per input row.



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)
        mse = torch.mean((x - self.target) ** 2, dim=-1)
        return torch.tanh(dot - mse)

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]