Recurrent neural networks with associative memory properties are typically based on fixed-point dynamics, which is fundamentally distinct from the oscillatory dynamics of the brain. There have been proposals for oscillatory associative memories, but here too, in the majority of cases, only binary patterns are stored as oscillatory states in the network. Oscillatory neural network models typically operate at a single/common frequency. At multiple frequencies, even a pair of oscillators with real coupling exhibits rich dynamics of Arnold tongues, not easily harnessed to achieve reliable memory storage and retrieval. Since real brain dynamics comprises of a wide range of spectral components, there is a need for oscillatory neural network models that operate at multiple frequencies. We propose an oscillatory neural network that can model multiple time series simultaneously by performing a Fourier-like decomposition of the signals. We show that these enhanced properties of a network of Hopf oscillators become possible by operating in the complex-variable domain. In this model, the single neural oscillator is modeled as a Hopf oscillator, with adaptive frequency and dynamics described over the complex domain. We propose a novel form of coupling, dubbed “power coupling,” between complex Hopf oscillators. With power coupling, expressed naturally only in the complex-variable domain, it is possible to achieve stable (normalized) phase relationships in a network of multifrequency oscillators. Network connections are trained either by Hebb-like learning or by delta rule, adapted to the complex domain. The network is capable of modeling N-channel electroencephalogram time series with high accuracy and shows the potential as an effective model of large-scale brain dynamics.
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Dr. David Lowemann, M.Sc, Ph.D., is a co-founder of the Institute for the Future of Human Potential, where he leads the charge in pioneering Self-Enhancement Science for the Success of Society. With a keen interest in exploring the untapped potential of the human mind, Dr. Lowemann has dedicated his career to pushing the boundaries of human capabilities and understanding.
Armed with a Master of Science degree and a Ph.D. in his field, Dr. Lowemann has consistently been at the forefront of research and innovation, delving into ways to optimize human performance, cognition, and overall well-being. His work at the Institute revolves around a profound commitment to harnessing cutting-edge science and technology to help individuals lead more fulfilling and intelligent lives.
Dr. Lowemann’s influence extends to the educational platform BetterSmarter.me, where he shares his insights, findings, and personal development strategies with a broader audience. His ongoing mission is shaping the way we perceive and leverage the vast capacities of the human mind, offering invaluable contributions to society’s overall success and collective well-being.