Swish-Gated Linear Unit

题面

Implement the Swish-Gated Linear Unit (SWiGLU) activation function forward pass for 1D input vectors. Given an input tensor of shape [N] where N is the number of elements, compute the output using the elementwise formula. The input and output tensor must be of type float32.

SWiGLU is defined as:

• Split input 𝑥 into two halves: 𝑥₁ and 𝑥₂
• Compute SiLU on the first half: SiLU(𝑥₁) = 𝑥₁ ⋅ σ(𝑥₁), σ(𝑥) = 1 / (1 + e^{-𝑥})
• Compute the SWiGLU output: SWiGLU(𝑥₁, 𝑥₂) = SiLU(𝑥₁) ⋅ 𝑥₂

Implementation Requirements

• Use only native features (external libraries are not permitted)
• The solve function signature must remain unchanged
• The final result must be stored in the output tensor

Examples

Example 1:

Input:  [1.0, 2.0, 3.0, 4.0]  (N=4)
Output: [2.1931758, 7.0463767]

Example 2:

Input:  [0.5, 1.0]  (N=2)
Output: [0.31122968]

Constraints

• 1 ≤ N ≤ 100,000
• N is an even number
• -100.0 ≤ input values ≤ 100.0
• Performance is measured with N = 100,000