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The universal approximation theorem ensures that any continuous real-valued function defined on a compact subset can be approximated with arbitrary precision by a single hidden layer neural network. Similarly, Arena et al. proved in 1996 that any continuous quaternion-valued function on a compact can be approximated with arbitrary precision by a single hidden layer quaternion-valued neural network whose hidden units are equipped with the so-called split activation function. Quaternions are four-dimensional hypercomplex numbers widely used to describe spatial rotations. Like quaternions, tessarines are four-dimensional hypercomplex numbers. However, in contrast quaternion algebra, the product of tessarines is commutative. The commutativity of tessarine&#39;s product may be advantageous for the design of neural networks because synaptic weights and neuron inputs can interchange their roles. In this paper, we show that the universal approximation theorem also holds for tessarine-valued neural networks. Precisely, we show that that any continuous tessarine-valued function can be approximated with arbitrary precision by a single hidden layer tessarine-valued neural network with split activation functions in the hidden layer. A simple numerical example, confirming the theoretical result and revealing the superior performance of a tessarine-valued neural network over a real-valued model for interpolating a vector-valued function, is presented in the paper.

BRACIS 2021

Universal Approximation Theorem for Tessarine-Valued Neural Networks

hypercomplex neural networks

fundamentals of artificial intelligence

artificial neural networks

**BRACIS** originated from the combination of the two most important scientific events in Brazil in Artificial Intelligence (AI) and Computational Intelligence (CI): the Brazilian Symposium on Artificial Intelligence – **SBIA** (22 editions), and the Brazilian Symposium on Neural Networks – **SBRN** (13 editions). **ENIAC** is a national forum for researchers, practitioners, educators and students to present and discuss innovations, trends, experiences, developments and work in progress in the fields of Artificial and Computational Intelligence. **STIL** is the bi-annual Language Technology event.
All events are supported by the Brazilian Computer Society – Special Interest Groups: **CE-IA**, **CE-IC** and **CE-PLN**.

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BRACIS originated from the combination of the two most important scientific events in Brazil in Artificial Intelligence (AI) and Computational Intelligence (CI): the Brazilian Symposium on Artificial Intelligence – SBIA (22 editions), and the Brazilian Symposium on Neural Networks – SBRN (13 editions). 
ENIAC is a national forum for researchers, practitioners, educators and students to present and discuss innovations, trends, experiences, developments and work in progress in the fields of Artificial and Computational Intelligence. 
STIL is the bi-annual Language Technology event.
All events are supported by the Brazilian Computer Society – Special Interest Groups: CE-IA, CE-IC and CE-PLN

The universal approximation theorem ensures that any continuous real-valued function defined on a compact subset can be approximated with arbitrary precision by a single hidden layer neural network. Similarly, Arena et al. proved in 1996 that any continuous quaternion-valued function on a compact can be approximated with arbitrary precision by a single hidden layer quaternion-valued neural network whose hidden units are equipped with the so-called split activation function. Quaternions are four-dimensional hypercomplex numbers widely used to describe spatial rotations. Like quaternions, tessarines are four-dimensional hypercomplex numbers. However, in contrast quaternion algebra, the product of tessarines is commutative. The commutativity of tessarine's product may be advantageous for the design of neural networks because synaptic weights and neuron inputs can interchange their roles. In this paper, we show that the universal approximation theorem also holds for tessarine-valued neural networks. Precisely, we show that that any continuous tessarine-valued function can be approximated with arbitrary precision by a single hidden layer tessarine-valued neural network with split activation functions in the hidden layer. A simple numerical example, confirming the theoretical result and revealing the superior performance of a tessarine-valued neural network over a real-valued model for interpolating a vector-valued function, is presented in the paper.

technical paper

The judicial system is composed of numerous court documents. These documents may contain relevant information that supports decision-making in future processes. However, collecting this information is not a trivial task. This article proposes the use of clustering techniques to group similar court lawsuits and facilitate the collection of information. In this way, different approaches were evaluated for identifying the most appropriate to perform this task. The approaches were applied to a database composed of 1515 facts of initial petitions. These approaches were evaluated using internal metrics and texts of the grouped court lawsuits. The results showed that the best approach to grouping court lawsuits is composed of the K-Means algorithm and the TF-IDF representation technique in combination with the PCA technique.

Assessment of text clustering approaches for legal documents

A propagação de desinformação trouxe e ainda traz diversos problemas para a sociedade, sendo 
considerada uma infodemia pela Organização Mundial da Saúde (OMS). A grande maioria dos trabalhos 
desenvolvidos para lidar com desinformação são focados para a língua inglesa. A fim de preencher 
essa lacuna, este trabalho investiga estratégias baseadas em aprendizado de máquina supervisionado 
para detectar desinformação em tweets escritos na língua portuguesa. Além disso, criou-se um 
corpus que foi manualmente anotado para esta tarefa, a fim de avaliar as abordagens 
desenvolvidas e compará-las com trabalhos relacionados. Os resultados alcançados são competitivos 
com trabalhos correlatos, indicando que a abordagem produz um interessante baseline para o 
corpus construído.


Detecting Misinformation in Tweets Related to COVID-19

Fake news propagation has been a problem noted in several areas of society, for example, in the fight against the pandemic caused by the new coronavirus (Sars-Cov-2). Combating misinformation, especially on social networks, is fundamental to control the spread of the virus and, consequently, the pandemic. Therefore, this work built supervised learning models focused on identifying fake news about the Sars-Cov-2. As a result, 18 models were built and rated, their reached 0.62%, 0.82%, and 0.47% f-score for the labels considered (news, opinion, and fake).

Fake news detection about Covid-19 in the Portuguese language

We present and make available pre-trained language models (Phraser, Word2Vec, Doc2Vec, FastText, and BERT) for the Brazilian legal language, a Python package with functions to facilitate their use, and a set of demonstrations/tutorials containing some applications involving them. Given that our material is built upon legal texts coming from several Brazilian courts, this initiative is extremely helpful for the Brazilian legal field, which lacks other open and specific tools and language models. Our main objective is to catalyze the use of natural language processing tools for legal texts analysis by the Brazilian industry, government, and academia, providing the necessary tools and accessible material.

LegalNLP - Natural Language Processing methods for the Brazilian Legal Language

Curriculum learning consists of training strategies for machinelearning techniques in which the easiest observations are presented first, progressing into more difficult cases as training proceeds. For assemblingthe curriculum, it is necessary to order the observations a dataset has ac-cording to their difficulty. This work investigates how instance hardnessmeasures, which can be used to assess the difficulty level of each obser-vation in a dataset from different perspectives, can be used to assemble acurriculum. Experiments with four CIFAR-100 sub-problems have demon-strated the feasibility of using the instance hardness measures, the mainadvantage is on convergence speed and some datasets accuracy gains canalso be verified.

Using instance hardness measures in curriculum learning

Predicting the stance of social media users on a topic can be challenging, especially for unsupervised cases. In this work, retweeted posts were used as elements of user interaction, to calculate the similarities between the most active within a discussion. Stance detection for these users was performed using dimensionality reduction and clustering techniques, topic modeling using contextual embeddings, and automatic cluster labeling based on recurring terms in each group. This approach produced a small number of user clusters (between 2 and 3), with uniformity in user labeling in different bases greater than 98%.

Automatic Twitter Stance Detection on Politically Controversial Issues: A Study on Covid-19's CPI

The development of new communication networks to offer
innovative services has increased the volume of data. With the introduction of
Deep Reinforcement Learning and Service Function Chaining architecture,
new research opportunities have emerged to propose solutions to the new
challenges. This work proposes a model to demonstrate through
computational simulations how these techniques can be applied. The model
was evaluated using two variations of the Deep Q-Network algorithm over the
CIC-Darknet dataset. Results showed that both variations are a promising
mechanism to make the networks more autonomous and intelligent.

A Model for Traffic Forwarding through Service Function Chaining using Deep Reinforcement Learning Techniques

Events are phenomena that occur at a specific time and place. Its detection can bring benefits to society since it is possible to extract knowledge from these events. Event detection is a multimodal task since these events have textual, geographical, and temporal components. Most multimodal research in the literature uses the concatenation of the components to represent the events. These approaches use multi-class or binary learning to detect events of interest which intensifies the user's labeling effort, where the user should label event classes even if there is no interest in detecting them. In this paper, we present the Triple-VAE approach that learns a unified representation from textual, spatial, and density modalities through a variational autoencoder, which is one of the state-of-the-art in representation learning. Our proposed Triple-VAE obtains suitable event representations for one-class classification, where users provide labels only for events of interest, thereby reducing the labeling effort. We carried out an experimental evaluation with ten real-world event datasets, four multimodal representation methods, and five evaluation metrics. Triple-VAE outperforms and presents a statistically significant difference considering the other three representation methods in all datasets. Therefore, Triple-VAE proved to be promising to represent the events in the one-class event detection scenario.

Triple-VAE: A Triple Variational Autoencoder to Represent Events in One-Class Event Detection

Wikipedia is an important free source of intelligible knowledge. Despite that, Brazilian Portuguese Wikipedia still lacks descriptions for many subjects. In an effort to expand the Brazilian Wikipedia, we contribute PLSum, a framework for generating wiki-like abstractive summaries from multiple descriptive websites. The framework has an extractive stage followed by an abstractive one. In particular, for the abstractive stage, we fine-tune and compare two recent variations of the Transformer neural network, PTT5, and Longformer. To fine-tune and evaluate the model, we created a dataset with thousands of examples, linking reference websites to Wikipedia. Our results show that it is possible to generate meaningful abstractive summaries from Brazilian Portuguese web content.

PLSUM: Generating PT-BR Wikipedia by Summarizing Multiple Websites

In this work we propose a selection Hyper-Heuristic (HH) based onthe Thompson Sampling (TS) approach to the solution of Quadratic AssignmentProblem (QAP). The QAP aims to allocate facilities in a set of possible knownlocations, in order to minimize the total cost of all movements between facili-ties. The proposed HH is applied in the automatic configuration of a memeticalgorithm, acting on the selection of a combination of low-level heuristics. Eachcombination involves the selection of a recombination heuristic, a local searchstrategy and a mutation heuristic. The algorithm was tested in 15 instances ofNug benchmark and the performance of HH is superior to that obtained by anycombination of heuristics applied in isolation, demonstrating its efficiency inthe automatic configuration of the algorithm. Experiments show that TS per-formance is affected by the quality of the set of low-level heuristics. The bestversion of HH obtains the optimal solution in 9 instances and the mean percen-tage deviation of the optimal solution (gap), considering all 15 instances, was 8.6%, with the largest gaps found for the three largest instances.

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Universal Approximation Theorem for Tessarine-Valued Neural Networks

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