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Implement GELU Activation (Gaussian Error Linear Unit)

Activation Functions

Medium

Compute the exact Gaussian Error Linear Unit for every input value:

\operatorname{GELU}(x) = \frac{x}{2}\left(1 + \operatorname{erf}\left(\frac{x}{\sqrt{2}}\right)\right)

Here, $x$ is an input value and $\operatorname{erf}$ is the Gaussian error function. Apply the formula elementwise and return a NumPy array with the same shape as the input.

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Examples

Input: x = [-1.0, 0.0, 1.0]

Output: [-0.158655, 0.0, 0.841345]

Explanation: The exact GELU formula scales negative values toward zero while retaining most of a positive value.

Input: x = [[-2.0, -1.0], [0.0, 1.0]]

Output: [[-0.0455, -0.158655], [0.0, 0.841345]]

Hint 1

Use np.asarray(x, dtype=float) before applying the formula.

Hint 2

Use np.vectorize(math.erf) to apply the scalar error function elementwise.

Requirements

Apply the exact error-function formula elementwise
Preserve the input shape
Return a NumPy array of floating-point values

Constraints

x is a nonempty finite numeric list of any depth
x contains at most $10^6$ values
Use NumPy and the Python standard library only

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