Oscillatory Neural Systems

The brain, while being small, low-power, and robust, performs complex computations that we cannot yet replicate or fully understand. Oscillatory signals are ubiquitously observed in the brain across multiple scales, e.g., from individual neural membranes to large-scale averages measured in electroencephalograms. Explaining the computational function and generation of brain oscillations is an active area in neuroscience. Computation with oscillatory signals is also interesting from an engineering standpoint in the field of analog computing. Digital computing represents objects with discrete, Boolean variables. In contrast, analog computing investigates how to use the continuous dynamics of physical systems to perform fast, energy-efficient computing. The potential advantage of analog computing has been hard to realize due to the challenges of working with analog systems and competing with rapid advances in digital computing. Recently, neuromorphic computers and coupled oscillator networks have shown potential as efficient analog computers for certain applications. Thus, motivated by neuroscience as well as engineering, here we explore computations in oscillatory systems that efficiently perform specific functions. Our results demonstrate that models of computation using oscillator neural networks can be used as tools for neuroscience and as the basis of efficient analog computers. Specifically, we investigate inference in feedforward deep neural networks, the analog implementation of associative memories, and optimization performed through the dynamics of coupled oscillator networks. Presumably, the function of a brain critically relies on a combination of continuous and discrete signals, e.g., membrane voltages in neurons and their averages, local field potentials, and action potentials or spikes. Neuromorphic computers that use this combination of signaling are emerging as alternatives to traditional computers for certain tasks. How information is encoded by spikin