A Structural Interpretation of GELU and Threshold-Transmission Activations via the First-Order Loss Function

תקציר מקורי באנגליתarXiv:2607.03664v3 Announce Type: replace Abstract: The Gaussian Error Linear Unit is usually motivated as the expected output of an input-dependent Bernoulli gate. This work gives an alternative interpretation: GELU is the expected output of a hard linear gate with a Gaussian random threshold. This view provides a generative interpretation for the Bernoulli gate: the gate opens once the input clears a latent Gaussian threshold. This interpretation stems from a decomposition based on well-known results in stochastic inventory theory and leads to a threshold-transmission family that includes ReLU, GELU, SiLU/Swish, and hard swish as special cases. By considering a latent uniform threshold, we recover a hard-swish-like piecewise-polynomial gate whose nonlinear transition is confined to a fin