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 CUDA kernel implements a custom activation function (SERF - Scaled Error Function) with the following optimizations:
Tiled Kernel Design: Uses a block-based tiling approach where each thread processes elements within its assigned block, improving memory locality and cache efficiency.
Mathematical Function: Implements a complex activation: x * erf(ln(1 + exp(x))), combining error function, logarithmic, and exponential operations.
Memory Access Optimization: Employs __restrict__qualifiers and contiguous memory tensors to enable better compiler optimizations.
Compiler Optimizations: Enabled with -O3flag for aggressive performance optimization of the generated code.
Occupancy Optimization: Configures 256 threads per block and dynamically calculates grid size (up to 65535 blocks) to maximize GPU occupancy.
Inlined Device Function: The core mathematical operation is marked with __forceinline__to eliminate function call overhead within the kernel.
Numerical Stability: Uses standard math functions (erff, logf, expf) with careful composition to maintain numerical stability.

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
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return x * torch.erf(torch.log(1 + torch.exp(x)))


batch_size = 128
feature_dim = 512


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


def get_init_inputs():
    return []