The Gaussian Error Linear Unit, or GELU, is an activation function. The GELU activation function is $x\Phi(x)$, where $\Phi(x)$ the standard Gaussian cumulative distribution function. The GELU nonlinearity weights inputs by their percentile, rather than gates inputs by their sign as in ReLUs ($x\mathbf{1}_{x>0}$). Consequently the GELU can be thought of as a smoother ReLU.
$$\text{GELU}\left(x\right) = x{P}\left(X\leq{x}\right) = x\Phi\left(x\right) = x \cdot \frac{1}{2}\left[1 + \text{erf}(x/\sqrt{2})\right],$$ if $X\sim \mathcal{N}(0,1)$.
One can approximate the GELU with $0.5x\left(1+\tanh\left[\sqrt{2/\pi}\left(x + 0.044715x^{3}\right)\right]\right)$ or $x\sigma\left(1.702x\right),$ but PyTorch's exact implementation is sufficiently fast such that these approximations may be unnecessary. (See also the SiLU $x\sigma(x)$ which was also coined in the paper that introduced the GELU.)
GELUs are used in GPT3, BERT, and most other Transformers.
Source: Gaussian Error Linear Units (GELUs)Paper  Code  Results  Date  Stars 

Task  Papers  Share 

Retrieval  91  10.69% 
Language Modelling  71  8.34% 
Question Answering  52  6.11% 
Large Language Model  44  5.17% 
Text Generation  25  2.94% 
InContext Learning  21  2.47% 
Sentence  20  2.35% 
Information Retrieval  16  1.88% 
FewShot Learning  15  1.76% 
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