This study presents a general trainable network of Hopf oscillators to model high-dimensional electroencephalogram (EEG) signals across different sleep stages. The proposed architecture consists of two main components: a layer of interconnected oscillators and a complex-valued feed-forward network designed with and without a hidden layer. Incorporating a hidden layer in the feed-forward network leads to lower reconstruction errors than the simpler version without it. Our model reconstructs EEG signals across all five sleep stages and predicts the subsequent 5 s of EEG activity. The predicted data closely aligns with the empirical EEG regarding mean absolute error, power spectral similarity, and complexity measures. We propose three models, each representing a stage of increasing complexity from initial training to architectures with and without hidden layers. In these models, the oscillators initially lack spatial localization. However, we introduce spatial constraints in the final two models by superimposing spherical shells and rectangular geometries onto the oscillator network. Overall, the proposed model represents a step toward constructing a large-scale, biologically inspired model of brain dynamics.

Extracting information from EEG signals in the human brain with the help of deep learning tools is a topic that is rapidly gaining popularity. Specifically, recognition of visual stimulus from brain Electroencephalography (EEG) signals has immense applications in the field of brain-computer interfacing. We propose a deep learning system for decoding visual stimuli from EEG signals. The proposed system comprises a classifier and a decoder. For the classifier module, we use a Deep Oscillatory Neural Network (DONN), which has hidden layers consisting of nonlinear neural oscillators. The features obtained from the last hidden layer of the classifier module are provided as input to the Decoder network which is a static feedforward network. The proposed system is trained on ThoughtViz EEG datasets. The proposed architecture exhibits superior classification performance compared to the performance reported in the literature.

Deep neural networks applied to signal processing problems will have to incorporate various architectural features to remember the history of the input signals, e.g., loops between the layers, “gated” neurons, and tapped delay lines. But real brains have rich dynamics expressed in terms of various frequency bands (alpha, beta, gamma, delta), exhibiting dynamical phenomena like phase locking, synchronization, etc. A typical Recurrent Neural Network or RNN-type model has serious shortcomings in representing these dynamic aspects of the brain. In this paper, we propose a novel class of bio-inspired deep neural network models known as deep oscillatory neural networks. There are deep networks of nonlinear oscillators trained on lines similar to a deep network. We present two variations of the models − the Deep Oscillatory Neural Network (DONN) and a convolutional variation of it named Oscillatory Convolutional Neural Network (OCNN) – and apply the models to a variety of problems involving classification and prediction of Electroencephalogram (EEG) signals: prediction of nearby EEG channels, classification of single-channel EEG data, and classification of spatiotemporal topographical images of EEG signal. Simulations show that the proposed oscillatory neural networks yield superior or comparable classification and prediction accuracy levels compared to published models, while requiring substantially smaller number of trainable parameters. The potential for creating energy-efficient hardware realizations of oscillator networks suggests an added incentive to intensify study of oscillator networks for classification problems.

We propose the Deep Oscillatory Neural Network (DONN), a brain-inspired network architecture that incorporates oscillatory dynamics into learning. Unlike conventional neural networks with static internal states, DONN neurons exhibit brain-like oscillatory activity through neural Hopf oscillators operating in the complex domain. The network combines neural oscillators with traditional sigmoid and ReLU neurons, all employing complex-valued weights and activations. Input signals can be presented to oscillators in three modes: resonator, amplitude modulation, and frequency modulation. Training uses complex backpropagation to minimize the output error. We extend this approach to convolutional architectures, creating Oscillatory Convolutional Neural Networks (OCNNs). Evaluation on benchmark signal and image processing tasks demonstrates comparable or improved performance over baseline methods. Interestingly, the network exhibits emergent phenomena such as feature and temporal binding during image classification, a key characteristic of biological visual processing, and exhibit STDP (Spike Timing Dependent Plasticity) kernel when trained using Hebbain learning. These phenomena with explicit oscillatory dynamics enhance the interpretability of internal representations.

We present a general, trainable oscillatory neural network as a large-scale model of brain dynamics. The model has a cascade of two stages - an oscillatory stage and a complex-valued feedforward stage - for modelling the relationship between structural connectivity and functional connectivity from neuroimaging data under resting brain conditions. Earlier works of large-scale brain dynamics that used Hopf oscillators used linear coupling of oscillators. A distinctive feature of the proposed model employs a novel form of coupling known as power coupling. Oscillatory networks based on power coupling can accurately model arbitrary multi-dimensional signals. Training the lateral connections in the oscillator layer is done by a modified form of Hebbian learning, whereas a variation of the complex backpropagation algorithm does training in the second stage. The proposed model can not only model the empirical functional connectivity with remarkable accuracy (correlation coefficient between simulated and empirical functional connectivity- 0.99) but also identify default mode network regions. In addition, we also inspected how structural loss in the brain can cause significant aberration in simulated functional connectivity and functional connectivity dynamics; and how it can be restored with optimized model parameters by an in silico perturbational study.

A large-scale model of brain dynamics, as it is manifested in functional neuroimaging data, is presented in this study. The model is built around a general trainable network of Hopf oscillators, the dynamics of which are described in the complex domain. It was shown earlier that when a pair of Hopf oscillators are coupled by power coupling with a complex coupling strength, it is possible to stabilize the normal phase difference at a value related to the angle of the complex coupling strength. In the present model, the magnitudes of the complex coupling weights are set using the Structural Connectivity information obtained from Diffusion Tensor Imaging (DTI). The complex-valued outputs of the oscillator network are transformed by a complex-valued feedforward network with a single hidden layer. The entire model is trained in 2 stages: in the 1 st stage, the intrinsic frequencies of the oscillators in the oscillator network are trained, whereas in the 2 nd stage, the weights of the feedforward network are trained using the complex backpropagation algorithm. The Functional Connectivity Matrix (FCM) obtained from the network’s output is compared with empirical Functional Connectivity Matrix, a comparison that resulted in a correlation of 0.99 averaged over 5 subjects.