235. GeLU (PyTorch)

Implement GeLU (exact form) in PyTorch using primitive tensor ops only.

Signature: def gelu(x: torch.Tensor) -> torch.Tensor

The rule: you may NOT call F.gelu, nn.GELU, or torch.nn.functional.gelu. We verify your output matches F.gelu(x) (the exact erf form, the PyTorch default).

Allowed primitives: torch.special.erf, basic arithmetic, math.sqrt.

Formula (exact):

GeLU(x) = 0.5 * x * (1 + erf(x / sqrt(2)))

PyTorch idioms vs the NumPy version:

• The NumPy reference imports from scipy.special import erf. In PyTorch, the same function lives at torch.special.erf — note the .special namespace, mirroring SciPy. There is no top-level torch.erf shortcut for the version you want; torch.erf exists but torch.special.erf is the canonical name and matches SciPy semantics exactly.
• Use math.sqrt(2) (a Python float) rather than torch.sqrt(torch.tensor(2.0)) — the math module gives a constant the JIT compiler can fold.