Optimizing deep learning models using topological descriptors

Abstract

[en] The combination of persistent homology and deep learning has been used frequently in recent years in the state of the art. Some of the most important works in this combination are about explaining the behaviour of neural networks or the application to improve the segmentation of elements in images. This project studies an application of persistent homology, a tool that describes holes of a point cloud, which tries to optimize the topological structure of the neural network in the training process. Persistent homology is the most widely used mechanism in topological data analysis. Its main objective is to focus on the description of holes in a point cloud through a persistence diagram, this being a collection of these topological holes. Therefore, a topological descriptor can be obtained with such a diagram; a function whose main objective is to get a value that represents the complexity of the point cloud. For example, if a point cloud has multiple holes, a topological descriptor can get a number that represents them. Deep learning has been a cutting-edge field for the last decades. It can be set as the representation of the human brain computationally, which is the most potent model in artificial intelligence. But, in all deep learning and machine learning problems attempted (image classification, sentiment analysis, etc.), overfitting will always be a significant threat during model training. It remains a problem that currently has no solution. The proof-of-concept optimization framework of the project is to use differentiable topology and to show the viability of distinct topological descriptors that can optimize the network. Then, this could be used towards regularizing the learning of a network to improve its performance. This framework will become the first step towards my own attempt at avoiding the problem of overfitting and making networks learn rather than memorizing the training dataset.