Write a custom CUDA kernel to optimize `DSiLU` (Double Sigmoid Linear Unit).

Formula: f(x) = x * sigmoid(x * sigmoid(x))

Problem Analysis:
1. Computationally Intensive & Memory Bound: The operation is element-wise but involves a nested chain of transcendental functions (two sigmoids, which means two exp calls).
2. Operator Chaining: A PyTorch implementation creates multiple intermediate tensors for the inner sigmoid, the product, and the outer sigmoid.

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`:
     `inner_sig = 1.0f / (1.0f + __expf(-x))`
     `silu_val = x * inner_sig`
     `outer_sig = 1.0f / (1.0f + __expf(-silu_val))`
     `result = x * outer_sig`
   - 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)

class DSiLU(nn.Module):
    """
    Double Sigmoid Linear Unit (DSiLU).
    Revisiting activation functions: empirical evaluation for image understanding and classification
    https://link.springer.com/article/10.1007/s11042-023-16159-2
    Formula: f(x) = x * sigmoid(x * sigmoid(x))
    """
    def __init__(self):
        super(DSiLU, self).__init__()

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

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.act = DSiLU()
    
    def forward(self, x):
        return self.act(x)

def get_inputs():
    input_tensor = torch.randn(SHAPE, dtype=torch.float32) * 5.0
    return [input_tensor.contiguous()]

def get_init_inputs():
    return []