Symmetric simplicial neural networks

Abstract

Convolutional Neural Networks are capable of perform many complex tasks such as image classification. Recently morphological functions where introduced as a replacement of the first convolutional layers in any net, using their non-linearities to achieve better accuracy for classification Neural Networks, but in most cases the functions are fixed beforehand and can not be trained. We propose the use of Symmetric Simplicial algorithm that can be trained to perform many morphological computations and even more complex functions. We present the training of a certain topology that uses Symmetric Simplicials instead of morphological functions and the classification accuracy achieved during the training process.