7 papers
Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases
Eduardo Paluzo-Hidalgo, Yuichi Ike
We introduce a theoretical framework that connects multi-chart autoencoders in manifold learning with the classical theory of vector bundles and characteristic classes. Rather than…
Latent Space Topology Evolution in Multilayer Perceptrons
Eduardo Paluzo-Hidalgo
This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplic…
Topological Quality of Subsets via Persistence Matching Diagrams
Ãlvaro Torras-Casas, Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset…
Application of the representative measure approach to assess the reliability of decision trees in dealing with unseen vehicle collision data
Javier Perera-Lago, VÃctor Toscano-Durán, Eduardo Paluzo-Hidalgo +2
Machine learning algorithms are fundamental components of novel data-informed Artificial Intelligence architecture. In this domain, the imperative role of representative datasets i…
An In-Depth Analysis of Data Reduction Methods for Sustainable Deep Learning
VÃctor Toscano-Durán, Javier Perera-Lago, Eduardo Paluzo-Hidalgo +3
In recent years, Deep Learning has gained popularity for its ability to solve complex classification tasks, increasingly delivering better results thanks to the development of more…
SIMAP: A simplicial-map layer for neural networks
Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo, Eduardo Paluzo-Hidalgo
In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version o…