Homological Neural Networks: A Sparse Architecture for Multivariate
  Complexity
Yuanrong Wang Antonio Briola Tomaso Aste
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.