Improvising the Learning of Neural Networks on Hyperspherical Manifold

The impact of convolution neural networks (CNNs) in the supervised settings provided tremendous increment in performance. The representations learned from CNN's operated on hyperspherical manifold led to insightful outcomes in face recognition, face identification and other supervised tasks. A broad range of activation functions is developed with hypersphere intuition which performs superior to softmax in euclidean space. The main motive of this research is to provide insights. First, the stereographic projection is implied to transform data from Euclidean space ($\mathbb{R}^{n}$) to hyperspherical manifold ($\mathbb{S}^{n}$) to analyze the performance of angular margin losses. Secondly, proving both theoretically and practically that decision boundaries constructed on hypersphere using stereographic projection obliges the learning of neural networks. Experiments have proved that applying stereographic projection on existing state-of-the-art angular margin objective functions led to improve performance for standard image classification data sets (CIFAR-10,100). The code is publicly available at: https://github.com/barulalithb/stereo-angular-margin.