Unification of popular artificial neural network activation functions
This work addresses a foundational problem in machine learning by providing a unified, adaptive approach to activation functions, though it appears incremental as it builds on existing functions rather than introducing a new paradigm.
The authors tackled the problem of unifying popular neural network activation functions by proposing a flexible representation using Mittag-Leffler functions, which can interpolate between different functions and mitigate issues like vanishing and exploding gradients, demonstrating its effectiveness as an affordable alternative to built-in implementations across various datasets and network complexities.
We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.