Learning Combinations of Activation Functions

In the last decade, an active area of research has been devoted to design novel activation functions that are able to help deep neural networks to converge, obtaining better performance. The training procedure of these architectures usually involves optimization of the weights of their layers only, while non-linearities are generally pre-specified and their (possible) parameters are usually considered as hyper-parameters to be tuned manually. In this paper, we introduce two approaches to automatically learn different combinations of base activation functions (such as the identity function, ReLU, and tanh) during the training phase. We present a thorough comparison of our novel approaches with well-known architectures (such as LeNet-5, AlexNet, and ResNet-56) on three standard datasets (Fashion-MNIST, CIFAR-10, and ILSVRC-2012), showing substantial improvements in the overall performance, such as an increase in the top-1 accuracy for AlexNet on ILSVRC-2012 of 3.01 percentage points.Comment: 6 pages, 3 figures. Published as a conference paper at ICPR 2018. Code: https://bitbucket.org/francux/learning_combinations_of_activation_function

DANTE: Deep AlterNations for Training nEural networks

We present DANTE, a novel method for training neural networks using the alternating minimization principle. DANTE provides an alternate perspective to traditional gradient-based backpropagation techniques commonly used to train deep networks. It utilizes an adaptation of quasi-convexity to cast training a neural network as a bi-quasi-convex optimization problem. We show that for neural network configurations with both differentiable (e.g. sigmoid) and non-differentiable (e.g. ReLU) activation functions, we can perform the alternations effectively in this formulation. DANTE can also be extended to networks with multiple hidden layers. In experiments on standard datasets, neural networks trained using the proposed method were found to be promising and competitive to traditional backpropagation techniques, both in terms of quality of the solution, as well as training speed.Comment: 19 page

A survey on modern trainable activation functions

In neural networks literature, there is a strong interest in identifying and defining activation functions which can improve neural network performance. In recent years there has been a renovated interest of the scientific community in investigating activation functions which can be trained during the learning process, usually referred to as "trainable", "learnable" or "adaptable" activation functions. They appear to lead to better network performance. Diverse and heterogeneous models of trainable activation function have been proposed in the literature. In this paper, we present a survey of these models. Starting from a discussion on the use of the term "activation function" in literature, we propose a taxonomy of trainable activation functions, highlight common and distinctive proprieties of recent and past models, and discuss main advantages and limitations of this type of approach. We show that many of the proposed approaches are equivalent to adding neuron layers which use fixed (non-trainable) activation functions and some simple local rule that constraints the corresponding weight layers.Comment: Published in "Neural Networks" journal (Elsevier