A Capsule-unified Framework of Deep Neural Networks for Graphical Programming

TL;DR

This paper introduces a unified mathematical framework for deep neural networks using capsules, enabling standardized graphical programming and providing a universal training algorithm for capsule networks.

Contribution

It formalizes neural networks mathematically, extends them with capsules, and develops a universal backpropagation algorithm within a unified framework.

Findings

Mathematical formalization of neural networks as directed graphs

Development of a capsule-based unified framework for deep learning

Introduction of a universal backpropagation algorithm for capsule networks

Abstract

Recently, the growth of deep learning has produced a large number of deep neural networks. How to describe these networks unifiedly is becoming an important issue. We first formalize neural networks in a mathematical definition, give their directed graph representations, and prove a generation theorem about the induced networks of connected directed acyclic graphs. Then, using the concept of capsule to extend neural networks, we set up a capsule-unified framework for deep learning, including a mathematical definition of capsules, an induced model for capsule networks and a universal backpropagation algorithm for training them. Finally, we discuss potential applications of the framework to graphical programming with standard graphical symbols of capsules, neurons, and connections.