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 PSMish activation function with the following optimizations:
Double Precision Intermediate Calculation: Uses doubleprecision for the core mathematical operations (tanh, log, exp) to maintain numerical stability and precision, then converts back to floatfor storage, balancing accuracy with memory efficiency.
Tiled Kernel Design: Employs a block-based tiling approach where each thread processes elements within its assigned block, improving memory locality and cache efficiency.
Mathematical Function: Implements the PSMish activation: α * x * tanh(ln(1 + exp(β * x))), combining scaling factors with smooth gating behavior.
Memory Access Optimization: Uses __restrict__qualifiers and contiguous memory tensors to enable better compiler optimizations and reduce memory bank conflicts.
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.
Parameterized Activation: Supports learnable or configurable alphaand betaparameters passed directly to the CUDA kernel, allowing flexible activation behavior.
Inlined Device Function: The core mathematical operation is marked with __forceinline__to eliminate function call overhead within the kernel.
Numerical Stability: The use of double precision for intermediate calculations prevents precision loss in the complex exponential and logarithmic operations.

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

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        gate = torch.tanh(torch.log(1.0 + torch.exp(self.beta * x)))
        return self.alpha * x * gate


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]