  The design of activation functions is a growing research area in the field of
neural networks. In particular, instead of using fixed point-wise functions
(e.g., the rectified linear unit), several authors have proposed ways of
learning these functions directly from the data in a non-parametric fashion. In
this paper we focus on the kernel activation function (KAF), a recently
proposed framework wherein each function is modeled as a one-dimensional kernel
model, whose weights are adapted through standard backpropagation-based
optimization. One drawback of KAFs is the need to select a single kernel
function and its eventual hyper-parameters. To partially overcome this problem,
we motivate an extension of the KAF model, in which multiple kernels are
linearly combined at every neuron, inspired by the literature on multiple
kernel learning. We provide an application of the resulting multi-KAF on a
realistic use case, specifically handwritten Latin OCR, on a large dataset
collected in the context of the `In Codice Ratio' project. Results show that
multi-KAFs can improve the accuracy of the convolutional networks previously
developed for the task, with faster convergence, even with a smaller number of
overall parameters.
