Write a custom CUDA kernel to optimize `SAAF` (Shape Autotuning Activation Function).

Formula: f(x) = (alpha * x) / (1 + exp(-beta * x))

This is a two-parameter generalization of the Swish/SiLU activation function.

Problem Analysis:
1. Memory Bound: This is an element-wise activation. Performance is limited by memory bandwidth.
2. Operator Chaining: The PyTorch implementation involves multiple element-wise operations (mul, exp, add, div), creating intermediate tensors.

Optimization Strategy: Fused Element-wise Kernel with Vectorization

1. One-Thread-per-Element: Map each element to a CUDA thread.

2. Vectorized Loads (float4): Use `float4` to process 128 bits per memory transaction.

3. Fused In-Register Math:
   - For each element `x`:
     `denom = 1.0f + __expf(-beta * x)`
     `result = (alpha * x) / denom`
   - All computations are fused in registers.

4. One-Pass: Fuse all steps into a single read-compute-write kernel. 
  
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
```python
import torch
import torch.nn as nn

BATCH_SIZE = 4096
HIDDEN_DIM = 4096
SHAPE = (BATCH_SIZE, HIDDEN_DIM)

# SAAF 初始参数
ALPHA_INIT = 1.0
BETA_INIT = 1.0

class SAAF(nn.Module):
    """
    Zhou Y, Li D, Huo S, Kung SY (2021) Shape autotuning activation function [Formula presented]. 
    Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.114534
    Formula: f(x) = (alpha * x) / (1 + exp(-beta * x))
    """
    def __init__(self, alpha_init=1.0, beta_init=1.0):
        super(SAAF, self).__init__()
        self.alpha = nn.Parameter(torch.tensor(alpha_init))
        self.beta = nn.Parameter(torch.tensor(beta_init))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return self.alpha * x * torch.sigmoid(self.beta * x)

class Model(nn.Module):
    def __init__(self, alpha_init=1.0, beta_init=1.0):
        super(Model, self).__init__()
        self.act = SAAF(alpha_init, beta_init)
    
    def forward(self, x):
        return self.act(x)

def get_inputs():
    input_tensor = torch.randn(SHAPE, dtype=torch.float32)
    return [input_tensor.contiguous()]

def get_init_inputs():
    return [ALPHA_INIT, BETA_INIT]