NAIL OR
Logit-space OR-gate (Normalized Approximate Independent Logit)
**NAIL OR** is a two-dimensional activation function which takes two logits as input and produces a single output. It is a piece-wise linear approximation of the probabilistic OR operator in logit-space.
$$\begin{equation}
    \text{OR_{AIL}}(x, y) :=
        \begin{cases}
            x + y, & x > 0, \, y > 0 \\
            \max(x, y), & \text{otherwise}
        \end{cases}
\end{equation}
$$
Logical Activation Functions: Logit-space equivalents of Probabilistic Boolean Operators
https://paperswithcode.com/paper/logical-activation-functions-logit-space-1
Logical Activation Functions: Logit-space equivalents of Probabilistic Boolean Operators