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.

Just-In-Time (JIT) Compilation: CUDA kernel compiled at runtime via load_inline.

Vectorized Memory Access: Uses float4 for reading/writing 4 floats per instruction (coalesced memory).

Memory Coalescing: Contiguous memory access (x.contiguous()).

Kernel Grid/Block Optimization: Fixed 256 threads per block, grid size capped at 65535 blocks.

Fast Math Compiler Flags: --use_fast_math for faster approximate math (cosf, expf, sigmoid).

Restrict Pointers: __restrict__ to avoid pointer aliasing.

Read-Only Caching: __ldg() for cached constant memory reads.

Tail Processing: Handles leftover elements after vectorized loops.

Element-wise Custom Operator: CosLU function (x + alpha * cos(beta * x)) * sigmoid(x).

Inline Helper Functions: sigmoid_f and coslu_op marked __forceinline__.

Kernel Parameters: Passes alpha and beta as constants to the kernel.

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, alpha=1.0, beta=1.0):
        super().__init__()
        self.alpha = alpha
        self.beta = beta

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        term_cos = self.alpha * torch.cos(self.beta * x)
        return (x + term_cos) * torch.sigmoid(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 [1.0, 1.0]