Miguel A. Gutiérrez-Naranjo

Elvin Somón, Miguel A. Gutiérrez-Naranjo

We conducted a reproducibility-oriented re-evaluation of prior migraine classification studies, correcting for data leakage and metric bias. We then introduced (i) a clinically motivated aggregation of two hemiplegic subtypes following ICHD-3 §1.2.3, (ii) a class-dependent hybrid augmentation strategy that assigns generation methods based on per-class sample size, and (iii) the concept of fidelity asymmetry, motivating proportionally constrained growth as an alternative to full class balance. Experiments were performed on a dataset of 400 patients across seven migraine subtypes under a two-stage protocol, including the six-class configuration described above. Models were evaluated using stratified 5-fold cross-validation with macro-averaged F1 as the primary metric. Correcting methodological flaws reduces previously inflated performance estimates, with the corrected macro-F1 baseline standing at 0.71. The proposed framework consistently outperformed individual augmenters in macro-F1 averaged across the eight evaluated classifiers (0.862 vs. 0.836 for Gaussian Copula, 0.815 for CTGAN, and 0.801 for the no-augmentation baseline), and achieved its peak result of 0.914 with FT-Transformer under proportional augmentation. The no-augmentation FT-Transformer baseline (0.896) shows that, at the per-classifier ceiling, clinically motivated class aggregation accounts for most of the absolute improvement; the framework's principal measurable contribution is the gain in average robustness across classifiers, highlighting the dominant role of problem formulation.

Eduardo Sanchez-Karhunen, Jose F. Quesada-Moreno, Miguel A. Gutiérrez-Naranjo

Intent detection is a text classification task whose aim is to recognize and label the semantics behind a users query. It plays a critical role in various business applications. The output of the intent detection module strongly conditions the behavior of the whole system. This sequence analysis task is mainly tackled using deep learning techniques. Despite the widespread use of these techniques, the internal mechanisms used by networks to solve the problem are poorly understood. Recent lines of work have analyzed the computational mechanisms learned by RNNs from a dynamical systems perspective. In this work, we investigate how different RNN architectures solve the SNIPS intent detection problem. Sentences injected into trained networks can be interpreted as trajectories traversing a hidden state space. This space is constrained to a low-dimensional manifold whose dimensionality is related to the embedding and hidden layer sizes. To generate predictions, RNN steers the trajectories towards concrete regions, spatially aligned with the output layer matrix rows directions. Underlying the system dynamics, an unexpected fixed point topology has been identified with a limited number of attractors. Our results provide new insights into the inner workings of networks that solve the intent detection task.

Eduardo Sanchez-Karhunen, Jose F. Quesada-Moreno, Miguel A. Gutiérrez-Naranjo

Intent detection, a fundamental text classification task, aims to identify and label the semantics of user queries, playing a vital role in numerous business applications. Despite the dominance of deep learning techniques in this field, the internal mechanisms enabling Recurrent Neural Networks (RNNs) to solve intent detection tasks are poorly understood. In this work, we apply dynamical systems theory to analyze how RNN architectures address this problem, using both the balanced SNIPS and the imbalanced ATIS datasets. By interpreting sentences as trajectories in the hidden state space, we first show that on the balanced SNIPS dataset, the network learns an ideal solution: the state space, constrained to a low-dimensional manifold, is partitioned into distinct clusters corresponding to each intent. The application of this framework to the imbalanced ATIS dataset then reveals how this ideal geometric solution is distorted by class imbalance, causing the clusters for low-frequency intents to degrade. Our framework decouples geometric separation from readout alignment, providing a novel, mechanistic explanation for real world performance disparities. These findings provide new insights into RNN dynamics, offering a geometric interpretation of how dataset properties directly shape a network's computational solution.

Victor Toscano-Duran, Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo

While artificial neural networks are known as universal approximators for continuous functions, many modern approaches rely on overparameterized architectures with high computational cost. In this work, we introduce the Barycentric Neural Network (BNN): a compact shallow architecture that encodes both structure and parameters through a fixed set of base points and their associated barycentric coordinates. We show that the BNN enables the exact representation of continuous piecewise linear functions (CPLFs), ensuring strict continuity across segments. Given that any continuous function on a compact domain can be uniformly approximated by CPLFs, the BNN emerges as a flexible and interpretable tool for function approximation. To enhance geometric fidelity in low-resource scenarios, such as those with few base points to create BNNs or limited training epochs, we propose length-weighted persistent entropy (LWPE): a stable variant of persistent entropy. Our approach integrates the BNN with a loss function based on LWPE to optimize the base points that define the BNN, rather than its internal parameters. Experimental results show that our approach achieves superior and faster approximation performance compared to standard losses (MSE, RMSE, MAE and LogCosh), offering a computationally sustainable alternative for function approximation.

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 of Simplicial-Map Neural Networks (SMNNs), an explainable neural network based on support sets and simplicial maps (functions used in topology to transform shapes while preserving their structural connectivity). The novelty of the methodology proposed in this paper is two-fold: Firstly, SIMAP layers work in combination with other deep learning architectures as an interpretable layer substituting classic dense final layers. Secondly, unlike SMNNs, the support set is based on a fixed maximal simplex, the barycentric subdivision being efficiently computed with a matrix-based multiplication algorithm.

Eduardo Paluzo-Hidalgo, Miguel A. Gutiérrez-Naranjo, Rocio Gonzalez-Diaz

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and an effective implementation are also newly introduced in this paper.

Alejandro Luque-Cerpa, Miguel A. Gutiérrez-Naranjo, Miguel Cárdenas-Montes

The improvement of air-quality in urban areas is one of the main concerns of public government bodies. This concern emerges from the evidence between the air quality and the public health. Major efforts from government bodies in this area include monitoring and forecasting systems, banning more pollutant motor vehicles, and traffic limitations during the periods of low-quality air. In this work, a proposal for dynamic prices in regulated parking services is presented. The dynamic prices in parking service must discourage motor vehicles parking when low-quality episodes are predicted. For this purpose, diverse deep learning strategies are evaluated. They have in common the use of collective air-quality measurements for forecasting labels about air quality in the city. The proposal is evaluated by using economic parameters and deep learning quality criteria at Madrid (Spain).

Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo

In this paper, we use topological data analysis (TDA) tools such as persistent homology, persistent entropy and bottleneck distance, to provide a {\it TDA-based summary} of any given set of texts and a general method for computing a distance between any two literary styles, authors or periods. To this aim, deep-learning word-embedding techniques are combined with these tools in order to study the topological properties of texts embedded in a metric space. As a case of study, we use the written texts of three poets of the Spanish Golden Age: Francisco de Quevedo, Luis de Góngora and Lope de Vega. As far as we know, this is the first time that word embedding, bottleneck distance, persistent homology and persistent entropy are used together to characterize texts and to compare different literary styles.

Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo, Eduardo Paluzo-Hidalgo

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 feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.

Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo, Eduardo Paluzo-Hidalgo

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. These changes are driven by a dataset, which can be seen as a set of labelled points in an n-dimensional space. In this paper, we explore the concept of are representative dataset which is a dataset smaller than the original one, satisfying a nearness condition independent of isometric transformations. Representativeness is measured using persistence diagrams (a computational topology tool) due to its computational efficiency. We prove that the accuracy of the learning process of a neural network on a representative dataset is "similar" to the accuracy on the original dataset when the neural network architecture is a perceptron and the loss function is the mean squared error. These theoretical results accompanied by experimentation open a door to reducing the size of the dataset to gain time in the training process of any neural network.

Daniel Rodríguez-Chavarría, Miguel A. Gutiérrez-Naranjo, Joaquín Borrego-Díaz

Nowadays, the success of neural networks as reasoning systems is doubtless. Nonetheless, one of the drawbacks of such reasoning systems is that they work as black-boxes and the acquired knowledge is not human readable. In this paper, we present a new step in order to close the gap between connectionist and logic based reasoning systems. We show that two of the most used inference rules for obtaining negative information in rule based reasoning systems, the so-called Closed World Assumption and Negation as Finite Failure can be characterized by means of spiking neural P systems, a formal model of the third generation of neural networks born in the framework of membrane computing.