Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

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