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 a custom CUDA kernel for Manhattan distance with erf activation. Key optimizations:

Warp-level reduction: Uses __shfl_down_sync for efficient warp-wide sum reduction.

Shared memory for block reduction: Employs shared memory for cross-warp reduction within a block.

Grid-stride loop: Threads process multiple elements with stride blockDim.x for good load balancing.

Coalesced memory access: Linear memory layout and contiguous tensor inputs.

Minimal synchronization: Uses __syncthreads() only for shared memory coordination.

Fused operations: Combines Manhattan distance computation and erf activation in a single kernel.

The custom operator is compiled inline using PyTorch's C++/CUDA extension utilities for efficient GPU execution.



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:
        dist = torch.sum(torch.abs(x - self.target), dim=-1)
        return torch.erf(dist)

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]