Continuously Differentiable Exponential Linear Units
This work provides a technical improvement for deep learning practitioners by enhancing the usability and stability of ELU activations, though it is incremental in nature.
The paper addresses the issue that Exponential Linear Units (ELUs) are not continuously differentiable for all shape parameter values, presenting an alternative parametrization that ensures C1 continuity, making it easier to tune and reason about, with additional properties like bounded derivatives and inclusion of linear and ReLU functions as special cases.
Exponential Linear Units (ELUs) are a useful rectifier for constructing deep learning architectures, as they may speed up and otherwise improve learning by virtue of not have vanishing gradients and by having mean activations near zero. However, the ELU activation as parametrized in [1] is not continuously differentiable with respect to its input when the shape parameter alpha is not equal to 1. We present an alternative parametrization which is C1 continuous for all values of alpha, making the rectifier easier to reason about and making alpha easier to tune. This alternative parametrization has several other useful properties that the original parametrization of ELU does not: 1) its derivative with respect to x is bounded, 2) it contains both the linear transfer function and ReLU as special cases, and 3) it is scale-similar with respect to alpha.