A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing

The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 * 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.Comment: 26 pages, 24 figure

Learning and recognition by a dynamical system with a plastic velocity field

Learning is a mechanism intrinsic to all sentient biological systems. Despite the diverse range of paradigms that exist, it appears that an artificial system has yet to be developed that can emulate learning with a comparable degree of accuracy or efficiency to the human brain. With the development of new approaches comes the opportunity to reduce this disparity in performance. A model presented by Janson and Marsden [arXiv:1107.0674 (2011)] (Memory foam model) redefines the critical features that an intelligent system should demonstrate. Rather than focussing on the topological constraints of the rigid neuron structure, the emphasis is placed on the on-line, unsupervised, classification, retention and recognition of stimuli. In contrast to traditional AI approaches, the system s memory is not plagued by spurious attractors or the curse of dimensionality. The ability to continuously learn, whilst simultaneously recognising aspects of a stimuli ensures that this model more closely embodies the operations occurring in the brain than many other AI approaches. Here we consider the pertinent deficiencies of classical artificial learning models before introducing and developing this memory foam self-shaping system. As this model is relatively new, its limitations are not yet apparent. These must be established by testing the model in various complex environments. Here we consider its ability to learn and recognize the RGB colours composing cartoons as observed via a web-camera. The self-shaping vector field of the system is shown to adjust its composition to reflect the distribution of three-dimensional inputs. The model builds a memory of its experiences and is shown to recognize unfamiliar colours by locating the most appropriate class with which to associate a stimuli. In addition, we discuss a method to map a three-dimensional RGB input onto a line spectrum of colours. The corresponding reduction of the models dimensions is shown to dramatically improve computational speed, however, the model is then restricted to a much smaller set of representable colours. This models prototype offers a gradient description of recognition, it is evident that a more complex, non-linear alternative may be used to better characterize the classes of the system. It is postulated that non-linear attractors may be utilized to convey the concept of hierarchy that relates the different classes of the system. We relate the dynamics of the van der Pol oscillator to this plastic self-shaping system, first demonstrating the recognition of stimuli with limit cycle trajectories. The location and frequency of each cycle is dependent on the topology of the systems energy potential. For a one-dimensional stimuli the dynamics are restricted to the cycle, the extension of the model to an N dimensional stimuli is approached via the coupling of N oscillators. Here we study systems of up to three mutually coupled oscillators and relate limit cycles, fixed points and quasi-periodic orbits to the recognition of stimuli

Resonate and Fire Neuron with Fixed Magnetic Skyrmions

In the brain, the membrane potential of many neurons oscillates in a subthreshold damped fashion and fire when excited by an input frequency that nearly equals their eigen frequency. In this work, we investigate theoretically the artificial implementation of such "resonate-and-fire" neurons by utilizing the magnetization dynamics of a fixed magnetic skyrmion in the free layer of a magnetic tunnel junction (MTJ). To realize firing of this nanomagnetic implementation of an artificial neuron, we propose to employ voltage control of magnetic anisotropy or voltage generated strain as an input (spike or sinusoidal) signal, which modulates the perpendicular magnetic anisotropy (PMA). This results in continual expansion and shrinking (i.e. breathing) of a skyrmion core that mimics the subthreshold oscillation. Any subsequent input pulse having an interval close to the breathing period or a sinusoidal input close to the eigen frequency drives the magnetization dynamics of the fixed skyrmion in a resonant manner. The time varying electrical resistance of the MTJ layer due to this resonant oscillation of the skyrmion core is used to drive a Complementary Metal Oxide Semiconductor (CMOS) buffer circuit, which produces spike outputs. By rigorous micromagnetic simulation, we investigate the interspike timing dependence and response to different excitatory and inhibitory incoming input pulses. Finally, we show that such resonate and fire neurons have potential application in coupled nanomagnetic oscillator based associative memory arrays

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure