Sincronização por acoplamento de osciladores e a sua aplicação em aprendizado semi-supervisionado
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Data
2021-09-09
Autores
Toso, Guilherme Marino [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
As redes neurais biológicas são objetos de estudo que envolvem diversos campos de pesquisa científica, desde biólogos e neurocientistas até físicos, matemáticos e cientistas da computação. Durante décadas muito se descobriu sobre suas unidades básicas, os neurônios, por exemplo, a propagação da informação em forma de impulso nervoso proveniente de um neurônio pré-sináptico para uma célula pós-sináptica, sendo que às vezes, esta transmissão é quase simultânea. Este fenômeno síncrono conhecido como sincronização neural pode explicar o aprendizado, bem como a atenção visual e a coordenação motora. A sincronização envolve a correlação temporal dos disparos neurais e esta eventualidade pode ser a representação dos atributos de um objeto. Em sistemas artificiais, este fenômeno já foi aplicado para realizar segmentação de imagens, onde os pixels são representados por uma grade de osciladores, assim, os elementos de uma grade com características semelhantes sincronizam suas oscilações, segmentando os objetos de uma imagem ao longo do tempo. Desse modo, esta dissertação tem como objetivo estudar a possibilidade de sincronização da dinâmica espaço-temporal dos modelos neurais, tanto em sistemas caóticos quanto estocásticos, mediante um termo de acoplamento que controla a sincronização dos osciladores e possui a capacidade de segmentar a dinâmica neural no tempo. Como prova de conceito, foi desenvolvido um modelo de aprendizado de máquina semi-supervisionado para representar exemplos supervisionados como osciladores sincronizados e amostras não-supervisionadas como neurônios dessincronizados. O processo de treinamento ocorre através da criação de conexões entre os neurônios Para tanto, foram estudados modelos estocásticos de tempo contínuo e caóticos de tempo discreto. Em seguida, foi realizada a análise de sincronização e segmentação de trajetórias, logo desenvolveu-se o algoritmo de Complexo Simplicial Propagando Rótulos em que foram testados os parâmetros e a acurácia em alguns conjuntos de dados. Como resultado, o modelo de rotulação e a dinâmica neural foram unificados para representar a classificação através dos disparos neurais que transitam do estado estocástico ou caótico para uma organização temporal nos disparos neurais e a segmentação dos osciladores com rótulos dissemelhantes. Por fim, o modelo foi desenvolvido para adaptar a força de acoplamento para lidar com competição pela sincronização neural.
Biological neural networks are objects of study that involve several fields of scientific research, from biologists and neuroscientists to physicists, mathematicians, and computer scientists. For decades, much has been discovered about its basic unit, neurons, for example, the propagation of information in the form of a nerve impulse from a presynaptic neuron to a postsynaptic cell, and sometimes this transmission is almost simultaneous This synchronous phenomenon known as neural synchronization can explain learning, as well as visual attention and motor coordination. Synchronization involves the temporal correlation of neural triggers and this eventuality can be the representation of an object's attributes. In artificial systems, this phenomenon has already been applied to perform image segmentation, where pixels are represented by a grid of oscillators, thus the elements of a grid with similar characteristics synchronize their oscillations, segmenting the objects of an image over time. Thereby, this dissertation aims to study the possibility of synchronizing the space-time dynamics of neural models, both in chaotic and stochastic systems, through a coupling term that controls the synchronization of oscillators and has the ability to segment the neural dynamics in time. As a proof of concept, a semi-supervised machine learning model was developed to represent supervised examples as synchronized oscillators and unsupervised samples as desynchronized neurons. The training process takes place through the creation of connections between neurons. Therefore, continuous-time stochastic and discrete-time chaotic models were studied. Then, the analysis of trajectories' synchronization and segmentation was performed, nextly the Simplicial Complex Propagating Labels' algorithm was developed and were tested the parameters and accuracy in some data sets. As a result, the labeling model and neural dynamics were unified to represent the classification through the neural activity that transition from the stochastic or chaotic state to a temporal organization in neural triggers and the segmentation of oscillators with dissimilar labels. Finally, the model was developed to adapt the coupling force to deal with competition for neural synchronization.
Biological neural networks are objects of study that involve several fields of scientific research, from biologists and neuroscientists to physicists, mathematicians, and computer scientists. For decades, much has been discovered about its basic unit, neurons, for example, the propagation of information in the form of a nerve impulse from a presynaptic neuron to a postsynaptic cell, and sometimes this transmission is almost simultaneous This synchronous phenomenon known as neural synchronization can explain learning, as well as visual attention and motor coordination. Synchronization involves the temporal correlation of neural triggers and this eventuality can be the representation of an object's attributes. In artificial systems, this phenomenon has already been applied to perform image segmentation, where pixels are represented by a grid of oscillators, thus the elements of a grid with similar characteristics synchronize their oscillations, segmenting the objects of an image over time. Thereby, this dissertation aims to study the possibility of synchronizing the space-time dynamics of neural models, both in chaotic and stochastic systems, through a coupling term that controls the synchronization of oscillators and has the ability to segment the neural dynamics in time. As a proof of concept, a semi-supervised machine learning model was developed to represent supervised examples as synchronized oscillators and unsupervised samples as desynchronized neurons. The training process takes place through the creation of connections between neurons. Therefore, continuous-time stochastic and discrete-time chaotic models were studied. Then, the analysis of trajectories' synchronization and segmentation was performed, nextly the Simplicial Complex Propagating Labels' algorithm was developed and were tested the parameters and accuracy in some data sets. As a result, the labeling model and neural dynamics were unified to represent the classification through the neural activity that transition from the stochastic or chaotic state to a temporal organization in neural triggers and the segmentation of oscillators with dissimilar labels. Finally, the model was developed to adapt the coupling force to deal with competition for neural synchronization.
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Palavras-chave
Neurônios, Sincronização, Aprendizado semi-supervisionado, Fenomenologia, Corpo-próprio, GeoGebra, Calculadora 3D, GeoGebra AR, Cálculo diferencial, Cálculo integral, Phenomenology, Living-body, 3D calculator, Differential calculus, Integral calculus