Gaussian Error Gated Linear Unit

题面

Implement the Gaussian Error Gated Linear Unit (GEGLU) 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.

GEGLU is defined as follows. Given an input vector $x$, split it into two halves $x_1$ and $x_2$:

1. Compute GELU on the second half $x_2$:

   $$\text{GELU}(x_2) = \frac{1}{2} x_2 \left(1 + \text{erf}\left(\frac{x_2}{\sqrt{2}}\right)\right)$$

2. Compute the GEGLU output:

   $$\text{GEGLU}(x_1, x_2) = x_1 \cdot \text{GELU}(x_2)$$

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, 1.0]  (N=2)
Output: [0.8413447]

Example 2:

Input:  [2.0, -1.0, 1.0, 0.5]  (N=4)
Output: [1.6826895, -0.3457312]

Constraints

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