Oscillatory dynamics in complex recurrent neural networks
Spontaneous oscillations measured by Local field potentials (LFPs), electroencephalograms and magnetoencephalograms exhibits variety of oscillations spanning frequency band ($1-100$ Hz) in animals and humans. Both instantaneous power and phase of these ongoing oscillations have commonly been observed to correlate with pre-stimulus processing in animals and humans. However, despite of numerous attempts it is not fully clear whether the same mechanisms can give rise to a range of oscillations as observed in vivo during resting state spontaneous oscillatory activity of the brain. In the current paper we show how oscillatory activity can arise out of general recurrent on-center off-surround neural network. The current work shows (a) a complex valued input to a class of biologically inspired recurrent neural networks can be shown to be mathematically equivalent to a combination of real-valued recurrent network with real-valued feed forward network, (b) such a network can give rise to oscillatory signatures. We also validate the conjecture with results of simulation of complex valued additive recurrent neural network.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Deep Oscillatory Neural Network
We propose a novel, brain-inspired deep neural network model known as the Deep Oscillatory Neural Network (DONN). Deep neural networks like the Recurrent Neural Networks indeed possess sequence processing capabilities bu…
Nonlinear Neural Dynamics and Classification Accuracy in Reservoir Computing
Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic,…
Brain-inspired interpretable reservoir computing with resonant recurrent neural networks
Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by…
ClassificationInferring the dynamics of oscillatory systems using recurrent neural networks
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us…
Learning to Dissipate Energy in Oscillatory State-Space Models
State-space models (SSMs) are a class of networks for sequence learning that benefit from fixed state size and linear complexity with respect to sequence length, contrasting the quadratic scaling of typical attention mec…
State Space Models