Abstract :

Oscillatory phenomena are ubiquitous in the brain. Although there are oscillator-based models of brain dynamics, they do not seem to enjoy the universal computational properties of rate-coded and spiking neuron network models. Use of oscillator-based models is often limited to special phenomena like locomotor rhythms and oscillatory attractor-based memories. If neuronal ensembles are taken to be the basic functional units of brain dynamics, it is desirable to develop oscillator-based models that can explain a wide variety of neural phenomena. To this end, we aim to develop a generalized network of oscillatory neurons. Specifically we propose a novel neural network architecture consisting of Hopf oscillators described in the complex domain. The oscillators can adapt their intrinsic frequencies by tracking the frequency components of the input signals. The oscillators are also laterally connected with each other through a special form of coupling we labeled as “power coupling”. Power coupling allows two oscillators with arbitrarily different intrinsic frequencies to interact at a constant normalized phase difference. The network can be operated in two phases. In the encoding phase the oscillators comprising the network perform a Fourier-like decomposition of the input signal(s). In the reconstruction phase, outputs the trained oscillators are combined to reconstruct the training signals. As a salient example, the network can be trained to reconstruct Electroencephalogram (EEG) signals, paving the way to an exciting class of large scale brain models.