  Success of deep neural networks in diverse tasks across domains of computer
vision, speech recognition and natural language processing, has necessitated
understanding the dynamics of training process and also working of trained
models. Two independent contributions of this paper are 1) Novel activation
function for faster training convergence 2) Systematic pruning of filters of
models trained irrespective of activation function. We analyze the topological
transformation of the space of training samples as it gets transformed by each
successive layer during training, by changing the activation function. The
impact of changing activation function on the convergence during training is
reported for the task of binary classification. A novel activation function
aimed at faster convergence for classification tasks is proposed. Here, Betti
numbers are used to quantify topological complexity of data. Results of
experiments on popular synthetic binary classification datasets with large
Betti numbers(>150) using MLPs are reported. Results show that the proposed
activation function results in faster convergence requiring fewer epochs by a
factor of 1.5 to 2, since Betti numbers reduce faster across layers with the
proposed activation function. The proposed methodology was verified on
benchmark image datasets: fashion MNIST, CIFAR-10 and cat-vs-dog images, using
CNNs. Based on empirical results, we propose a novel method for pruning a
trained model. The trained model was pruned by eliminating filters that
transform data to a topological space with large Betti numbers. All filters
with Betti numbers greater than 300 were removed from each layer without
significant reduction in accuracy. This resulted in faster prediction time and
reduced memory size of the model.
