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 Radial Basis Function (RBF) activation with the following optimizations:
Vectorization: Uses float4memory operations to process 4 elements per thread, significantly increasing memory throughput by leveraging vector loads/stores.
Cache Optimization: Employs __ldg()intrinsic for read-only data to leverage GPU's texture cache and improve memory access patterns.
Memory Coalescing: Accesses contiguous memory blocks through vector operations, optimizing GPU memory bandwidth utilization.
Grid-Stride Loop: Handles arbitrary-sized tensors efficiently by having threads process multiple elements with strided indexing.
Tail Processing: Separately handles non-multiple-of-4 elements after vectorized operations to ensure complete data processing.
Fast Math Optimization: Uses --use_fast_mathcompiler flag and expf()intrinsic for optimized exponential calculations.
Mathematical Function: Implements Gaussian RBF activation: f(x) = exp(-β × (x - μ)²), providing a bell-shaped response centered at μwith spread controlled by β.
Parameterized Function: Supports configurable beta(inverse width) and mu(center) parameters passed directly to the CUDA kernel, enabling flexible RBF shaping.
Numerical Efficiency: Computes the squared difference efficiently as diff * diffrather than powf(diff, 2).
Occupancy Optimization: Configures 256 threads per block and dynamically calculates grid size based on vectorized element count (threads × 4) to maximize GPU occupancy.
Compiler Optimizations: Enabled with -O3flag for aggressive performance optimization.
Inlined Device Function: The core RBF operation is marked with __forceinline__to eliminate function call overhead within 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, beta=1.0, mu=0.0):
        super().__init__()
        self.beta = beta
        self.mu = mu

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return torch.exp(-self.beta * (x - self.mu).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, 0.0]]