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Mostrando ítems 1-10 de 13
Artículo
Topology-based representative datasets to reduce neural network training resources
(Springer, 2022)
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. ...
Artículo
Representative Datasets: The Perceptron Case
(Cornell University, 2019)
One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such training process consists in an iterative change of parameters trying to minimize a loss function. ...
Artículo
Two-hidden-layer feed-forward networks are universal approximators: A constructive approach
(ScienceDirect, 2020-11)
It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, given a continuous function on a compact set embedded in an n-dimensional space, there exists a ...
Artículo
Simplicial-Map Neural Networks Robust to Adversarial Examples
(MDPI [Commercial Publisher], 2021-01-15)
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent ...
Artículo
Optimizing the Simplicial-Map Neural Network Architecture
(MDPI, 2021)
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators ...
Artículo
Approximating lower-star persistence via 2D combinatorial map simplification
(Elsevier, 2020)
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm ...
Artículo
Emotion recognition in talking-face videos using persistent entropy and neural networks
(American Institute of Mathematical Sciences (AIMS), 2022)
The automatic recognition of a person’s emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vi sion, or psychology, ...
Artículo
Towards a Philological Metric through a Topological Data Analysis Approach
(Cornell University, 2019)
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives of the poetry of this epoch are Francisco de Quevedo and Luis de Góngora y Argote. They are ...
Artículo
Strong Euler well-composedness
(Springer, 2021)
In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed ...
Artículo
Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
(Cornell University, 2019)
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer ...