Title: Kafnets: kernel-based non-parametric activation functions for neural networks,
Abstract: Neural networks are generally built by interleaving (adaptable) linear layers
with (fixed) nonlinear activation functions. To increase their flexibility,
several authors have proposed methods for adapting the activation functions
themselves, endowing them with varying degrees of flexibility. None of these
approaches, however, have gained wide acceptance in practice, and research in
this topic remains open. In this paper, we introduce a novel family of flexible
activation functions that are based on an inexpensive kernel expansion at every
neuron. Leveraging over several properties of kernel-based models, we propose
multiple variations for designing and initializing these kernel activation
functions (KAFs), including a multidimensional scheme allowing to nonlinearly
combine information from different paths in the network. The resulting KAFs can
approximate any mapping defined over a subset of the real line, either convex
or nonconvex. Furthermore, they are smooth over their entire domain, linear in
their parameters, and they can be regularized using any known scheme, including
the use of $\ell_1$ penalties to enforce sparseness. To the best of our
knowledge, no other known model satisfies all these properties simultaneously.
In addition, we provide a relatively complete overview on alternative
techniques for adapting the activation functions, which is currently lacking in
the literature. A large set of experiments validates our proposal.