Homological Neural Networks: A Sparse Architecture for Multivariate Complexity

TL;DR

This paper introduces Homological Neural Networks, a sparse higher-order architecture leveraging data's topological structure, which improves efficiency and effectiveness in complex data tasks like tabular data and time series regression.

Contribution

The paper presents a novel neural network architecture based on homological data structures, enhancing interpretability and efficiency over traditional models.

Findings

Achieves comparable or better results than state-of-the-art models with fewer parameters.

Effective in challenging domains like tabular data and time series regression.

Demonstrates advantages of topological data analysis in neural network design.

Abstract

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced network-based information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters.