  Stochastic gradient descent (SGD) is the main approach for training deep
networks: it moves towards the optimum of the cost function by iteratively
updating the parameters of a model in the direction of the gradient of the loss
evaluated on a minibatch. Several variants of SGD have been proposed to make
adaptive step sizes for each parameter (adaptive gradient) and take into
account the previous updates (momentum). Among several alternative of SGD the
most popular are AdaGrad, AdaDelta, RMSProp and Adam which scale coordinates of
the gradient by square roots of some form of averaging of the squared
coordinates in the past gradients and automatically adjust the learning rate on
a parameter basis. In this work, we compare Adam based variants based on the
difference between the present and the past gradients, the step size is
adjusted for each parameter. We run several tests benchmarking proposed methods
using medical image data. The experiments are performed using ResNet50
architecture neural network. Moreover, we have tested ensemble of networks and
the fusion with ResNet50 trained with stochastic gradient descent. To combine
the set of ResNet50 the simple sum rule has been applied. Proposed ensemble
obtains very high performance, it obtains accuracy comparable or better than
actual state of the art. To improve reproducibility and research efficiency the
MATLAB source code used for this research is available at GitHub:
https://github.com/LorisNanni.
