GELU

Perform the GELU (Gaussian Error Linear Unit) activation function on an input matrix:

$$C[i][j] = \text{GELU}(A[i][j])$$

The GELU function is defined as:

$$\text{GELU}(x) = x \cdot \Phi(x)$$

where $\Phi(x)$ is the cumulative distribution function of the standard normal distribution.

A common approximation for GELU is:

$$\text{GELU}(x) \approx 0.5x \cdot (1 + \tanh(\sqrt{2/\pi} \cdot (x + 0.044715x^3)))$$

Input:

• Matrix $A$ of size $M \times N$ containing floating-point values

Output:

• Matrix $C$ of size $M \times N$ containing the GELU activation values

Notes:

• Both matrices $\text{A}$ and $\text{C}$ are stored in row-major order
• You should implement the approximation formula for GELU defined above
• GELU is commonly used in modern transformer-based neural networks like BERT and GPT