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We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle.

At the same time that artificial intelligence is becoming popular, concern and the need for regulation is growing, including among other requirements the data privacy. In this context, Federated Learning is proposed as a solution to data privacy concerns derived from different source data scenarios due to its distributed learning. The defense mechanisms proposed in literature are just focused on defending against adversarial attacks and the performance, leaving aside other important qualities such as explainability, fairness to poor quality clients, dynamism in terms of attacks configuration and generality in terms of being resilient against different kinds of attacks. In this work, we propose RAB$^2$-DEF, a $\textbf{r}$esilient $\textbf{a}$gainst $\textbf{b}\text{yzantine}$ and $\textbf{b}$ackdoor attacks which is $\textbf{d}$ynamic, $\textbf{e}$xplainable and $\textbf{f}$air to poor clients using local linear explanations. We test the performance of RAB$^2$-DEF in image datasets and both byzantine and backdoor attacks considering the state-of-the-art defenses and achieve that RAB$^2$-DEF is a proper defense at the same time that it boosts the other qualities towards trustworthy artificial intelligence.

Transformers have become the leading choice in natural language processing over other deep learning architectures. This trend has also permeated the field of time series analysis, especially for long-horizon forecasting, showcasing promising results both in performance and running time. In this paper, we introduce Local Attention Mechanism (LAM), an efficient attention mechanism tailored for time series analysis. This mechanism exploits the continuity properties of time series to reduce the number of attention scores computed. We present an algorithm for implementing LAM in tensor algebra that runs in time and memory O(nlogn), significantly improving upon the O(n^2) time and memory complexity of traditional attention mechanisms. We also note the lack of proper datasets to evaluate long-horizon forecast models. Thus, we propose a novel set of datasets to improve the evaluation of models addressing long-horizon forecasting challenges. Our experimental analysis demonstrates that the vanilla transformer architecture magnified with LAM surpasses state-of-the-art models, including the vanilla attention mechanism. These results confirm the effectiveness of our approach and highlight a range of future challenges in long-sequence time series forecasting.

In the last few years, the formulation of real-world optimization problems and their efficient solution via metaheuristic algorithms has been a catalyst for a myriad of research studies. In spite of decades of historical advancements on the design and use of metaheuristics, large difficulties still remain in regards to the understandability, algorithmic design uprightness, and performance verifiability of new technical achievements. A clear example stems from the scarce replicability of works dealing with metaheuristics used for optimization, which is often infeasible due to ambiguity and lack of detail in the presentation of the methods to be reproduced. Additionally, in many cases, there is a questionable statistical significance of their reported results. This work aims at providing the audience with a proposal of good practices which should be embraced when conducting studies about metaheuristics methods used for optimization in order to provide scientific rigor, value and transparency. To this end, we introduce a step by step methodology covering every research phase that should be followed when addressing this scientific field. Specifically, frequently overlooked yet crucial aspects and useful recommendations will be discussed in regards to the formulation of the problem, solution encoding, implementation of search operators, evaluation metrics, design of experiments, and considerations for real-world performance, among others. Finally, we will outline important considerations, challenges, and research directions for the success of newly developed optimization metaheuristics in their deployment and operation over real-world application environments.

Early detection of diseases in crops is essential to prevent harvest losses and improve the quality of the final product. In this context, the combination of machine learning and proximity sensors is emerging as a technique capable of achieving this detection efficiently and effectively. For example, this machine learning approach has been applied to potato crops -- to detect late blight (Phytophthora infestans) -- and grapevine crops -- to detect downy mildew. However, most of these AI models found in the specialised literature have been developed using leaf-by-leaf images taken in the lab, which does not represent field conditions and limits their applicability. In this study, we present the first machine learning model capable of detecting mild symptoms of late blight in potato crops through the analysis of high-resolution RGB images captured directly in the field, overcoming the limitations of other publications in the literature and presenting real-world applicability. Our proposal exploits the availability of high-resolution images via the concept of patching, and is based on deep convolutional neural networks with a focal loss function, which makes the model to focus on the complex patterns that arise in field conditions. Additionally, we present a data augmentation scheme that facilitates the training of these neural networks with few high-resolution images, which allows for development of models under the small data paradigm. Our model correctly detects all cases of late blight in the test dataset, demonstrating a high level of accuracy and effectiveness in identifying early symptoms. These promising results reinforce the potential use of machine learning for the early detection of diseases and pests in agriculture, enabling better treatment and reducing their impact on crops., Comment: 9 pages

One of the key issues regarding classification problems in Trustworthy Artificial Intelligence is ensuring Fairness in the prediction of different classes when protected (sensitive) features are present. Data quality is critical in these cases, as biases in training data can be reflected in machine learning, impacting human lives and failing to comply with current regulations. One strategy to improve data quality and avoid these problems is preprocessing the dataset. Instance selection via undersampling can foster balanced learning of classes and protected feature values. Performing undersampling in class overlap areas close to the decision boundary should bolster the impact on the classifier. This work proposes Fair Overlap Number of Balls (Fair-ONB), an undersampling method that harnesses the data morphology of the different data groups (obtained from the combination of classes and protected feature values) to perform guided undersampling in overlap areas. It employs attributes of the ball coverage of the groups, such as the radius, number of covered instances and density, to select the most suitable areas for undersampling and reduce bias. Results show that the Fair-ONB method improves model Fairness with low impact on the classifier's predictive performance., Comment: 14 pages, 5 tables, 8 figures

Significant advancements in the field of wood species identification are needed worldwide to support sustainable timber trade. In this work we contribute to automate the identification of wood species via high-resolution macroscopic images of timber. The main challenge of this problem is that fine-grained patterns in timber are crucial in order to accurately identify wood species, and these patterns are not properly learned by traditional convolutional neural networks (CNNs) trained on low/medium resolution images. We propose a Timber Deep Learning Identification with Patch-based Inference Voting methodology, abbreviated TDLI-PIV methodology. Our proposal exploits the concept of patching and the availability of high-resolution macroscopic images of timber in order to overcome the inherent challenges that CNNs face in timber identification. The TDLI-PIV methodology is able to capture fine-grained patterns in timber and, moreover, boosts robustness and prediction accuracy via a collaborative voting inference process. In this work we also introduce a new data set of marcroscopic images of timber, called GOIMAI-Phase-I, which has been obtained using optical magnification in order to capture fine-grained details, which contrasts to the other datasets that are publicly available. More concretely, images in GOIMAI-Phase-I are taken with a smartphone with a 24x magnifying lens attached to the camera. Our data set contains 2120 images of timber and covers 37 legally protected wood species. Our experiments have assessed the performance of the TDLI-PIV methodology, involving the comparison with other methodologies available in the literature, exploration of data augmentation methods and the effect that the dataset size has on the accuracy of TDLI-PIV., Comment: 17 pages and 6 figures

In Artificial Intelligence, there is an increasing demand for adaptive models capable of dealing with a diverse spectrum of learning tasks, surpassing the limitations of systems devised to cope with a single task. The recent emergence of General-Purpose Artificial Intelligence Systems (GPAIS) poses model configuration and adaptability challenges at far greater complexity scales than the optimal design of traditional Machine Learning models. Evolutionary Computation (EC) has been a useful tool for both the design and optimization of Machine Learning models, endowing them with the capability to configure and/or adapt themselves to the task under consideration. Therefore, their application to GPAIS is a natural choice. This paper aims to analyze the role of EC in the field of GPAIS, exploring the use of EC for their design or enrichment. We also match GPAIS properties to Machine Learning areas in which EC has had a notable contribution, highlighting recent milestones of EC for GPAIS. Furthermore, we discuss the challenges of harnessing the benefits of EC for GPAIS, presenting different strategies to both design and improve GPAIS with EC, covering tangential areas, identifying research niches, and outlining potential research directions for EC and GPAIS.

Motivated by work of Dolgopyat and N\'andori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions. Building on previous work of Al-Saqban and Forni, we apply this method to obtain mixing limit theorems for particular subbundles of the Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar these results are applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces., Comment: 45 pages

Explainable Artificial Intelligence (XAI) is a pivotal research domain aimed at understanding the operational mechanisms of AI systems, particularly those considered ``black boxes'' due to their complex, opaque nature. XAI seeks to make these AI systems more understandable and trustworthy, providing insight into their decision-making processes. By producing clear and comprehensible explanations, XAI enables users, practitioners, and stakeholders to trust a model's decisions. This work analyses the value of data morphology strategies in generating counterfactual explanations. It introduces the Overlap Number of Balls Model-Agnostic CounterFactuals (ONB-MACF) method, a model-agnostic counterfactual generator that leverages data morphology to estimate a model's decision boundaries. The ONB-MACF method constructs hyperspheres in the data space whose covered points share a class, mapping the decision boundary. Counterfactuals are then generated by incrementally adjusting an instance's attributes towards the nearest alternate-class hypersphere, crossing the decision boundary with minimal modifications. By design, the ONB-MACF method generates feasible and sparse counterfactuals that follow the data distribution. Our comprehensive benchmark from a double perspective (quantitative and qualitative) shows that the ONB-MACF method outperforms existing state-of-the-art counterfactual generation methods across multiple quality metrics on diverse tabular datasets. This supports our hypothesis, showcasing the potential of data-morphology-based explainability strategies for trustworthy AI., Comment: 21 pages, 6 figures. Submitted to Information Sciences

In the realm of Artificial Intelligence (AI), the need for privacy and security in data processing has become paramount. As AI applications continue to expand, the collection and handling of sensitive data raise concerns about individual privacy protection. Federated Learning (FL) emerges as a promising solution to address these challenges by enabling decentralized model training on local devices, thus preserving data privacy. This paper introduces FLEX: a FLEXible Federated Learning Framework designed to provide maximum flexibility in FL research experiments. By offering customizable features for data distribution, privacy parameters, and communication strategies, FLEX empowers researchers to innovate and develop novel FL techniques. The framework also includes libraries for specific FL implementations including: (1) anomalies, (2) blockchain, (3) adversarial attacks and defences, (4) natural language processing and (5) decision trees, enhancing its versatility and applicability in various domains. Overall, FLEX represents a significant advancement in FL research, facilitating the development of robust and efficient FL applications., Comment: Submitted to Information Fusion

As Artificial Intelligence systems become integral across domains, the demand for explainability grows. While the effort by the scientific community is focused on obtaining a better explanation for the model, it is important not to ignore the potential of this explanation process to improve training as well. While existing efforts primarily focus on generating and evaluating explanations for black-box models, there remains a critical gap in directly enhancing models through these evaluations. This paper introduces SHIELD (Selective Hidden Input Evaluation for Learning Dynamics), a regularization technique for explainable artificial intelligence designed to improve model quality by concealing portions of input data and assessing the resulting discrepancy in predictions. In contrast to conventional approaches, SHIELD regularization seamlessly integrates into the objective function, enhancing model explainability while also improving performance. Experimental validation on benchmark datasets underscores SHIELD's effectiveness in improving Artificial Intelligence model explainability and overall performance. This establishes SHIELD regularization as a promising pathway for developing transparent and reliable Artificial Intelligence regularization techniques., Comment: 18 pages, 8 figures

Trustworthy Artificial Intelligence solutions are essential in today's data-driven applications, prioritizing principles such as robustness, safety, transparency, explainability, and privacy among others. This has led to the emergence of Federated Learning as a solution for privacy and distributed machine learning. While decision trees, as self-explanatory models, are ideal for collaborative model training across multiple devices in resource-constrained environments such as federated learning environments for injecting interpretability in these models. Decision tree structure makes the aggregation in a federated learning environment not trivial. They require techniques that can merge their decision paths without introducing bias or overfitting while keeping the aggregated decision trees robust and generalizable. In this paper, we propose an Interpretable Client Decision Tree Aggregation process for Federated Learning scenarios that keeps the interpretability and the precision of the base decision trees used for the aggregation. This model is based on aggregating multiple decision paths of the decision trees and can be used on different decision tree types, such as ID3 and CART. We carry out the experiments within four datasets, and the analysis shows that the tree built with the model improves the local models, and outperforms the state-of-the-art., Comment: Submitted to Information Science Journal

Social Media and Internet have the potential to be exploited as a source of opinion to enrich Decision Making solutions. Crowd Decision Making (CDM) is a methodology able to infer opinions and decisions from plain texts, such as reviews published in social media platforms, by means of Sentiment Analysis. Currently, the emergence and potential of Large Language Models (LLMs) lead us to explore new scenarios of automatically understand written texts, also known as natural language processing. This paper analyzes the use of ChatGPT based on prompt design strategies to assist in CDM processes to extract opinions and make decisions. We integrate ChatGPT in CDM processes as a flexible tool that infer the opinions expressed in texts, providing numerical or linguistic evaluations where the decision making models are based on the prompt design strategies. We include a multi-criteria decision making scenario with a category ontology for criteria. We also consider ChatGPT as an end-to-end CDM model able to provide a general opinion and score on the alternatives. We conduct empirical experiments on real data extracted from TripAdvisor, the TripR-2020Large dataset. The analysis of results show a promising branch for developing quality decision making models using ChatGPT. Finally, we discuss the challenges of consistency, sensitivity and explainability associated to the use of LLMs in CDM processes, raising open questions for future studies.

Classic Delphi and Fuzzy Delphi methods are used to test content validity of a data collection tools such as questionnaires. Fuzzy Delphi takes the opinion issued by judges from a linguistic perspective reducing ambiguity in opinions by using fuzzy numbers. We propose an extension named 2-Tuple Fuzzy Linguistic Delphi method to deal with scenarios in which judges show different expertise degrees by using fuzzy multigranular semantics of the linguistic terms and to obtain intermediate and final results expressed by 2-tuple linguistic values. The key idea of our proposal is to validate the full questionnaire by means of the evaluation of its parts, defining the validity of each item as a Decision Making problem. Taking the opinion of experts, we measure the degree of consensus, the degree of consistency, and the linguistic score of each item, in order to detect those items that affect, positively or negatively, the quality of the instrument. Considering the real need to evaluate a b-learning educational experience with a consensual questionnaire, we present a Decision Making model for questionnaire validation that solve it. Additionally, we contribute to this consensus reaching problem by developing an online tool under GPL v3 license. The software visualizes the collective valuations for each iteration and assists to determine which parts of the questionnaire should be modified to reach a consensual solution., Comment: project at https://github.com/rosanamontes/teranga.go. arXiv admin note: substantial text overlap with arXiv:2402.01775