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 SinuGaussian activation with the same three key optimizations as the previous sigmoid kernel:

Vectorized Memory Operations: Uses float4 loads/stores to process 4 elements per instruction, improving memory bandwidth utilization.

Coalesced Memory Access: Threads access contiguous memory locations via vectorized operations, enabling efficient memory coalescing.

Fast Math & Loop Unrolling: Compiler flags enable fast approximate math (sinf, expf) and implicit loop unrolling improves instruction-level parallelism.

Additional Optimization: The kernel precomputes beta * x * x to avoid redundant multiplication operations within the elementwise function.


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

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return torch.sin(x) * torch.exp(-self.beta * x.pow(2))


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]