Effects of Higher Order and Long-Range Synchronizations for Classification and Computing in Oscillator-Based Spiking Neural Networks

Development of artificial oscillator-based spiking neural networks (SNN), which are able to solve effectively various cybernetics problems including image recognition and adaptive control, is a key line of research. We have thoroughly explored the scheme of two thermally coupled $VO_2$ oscillators and found its effect of high order synchronization (HOS), which may be used to increase SNN classification capacity $N_s$. Phase-locking estimation method has been developed to determine values of subharmonic ratio SHR and synchronization effectiveness {\eta}. The experimental scheme has $N_s=12$ and SHR distributions are shaped as Arnold's tongues. In a model $N_s$ may reach maximum of $N_s>150$ at certain levels of coupling strength and noise. We demonstrate the long-range synchronization effect in a one-dimensional chain of oscillators and the phenomenon of synchronization transfer even at low values of {\eta} for intermediate links. The paper demonstrates realization of analogue operation of "multiplication", binary logic, and possibility of development of the interface between SNN and computer. The described effects increasing classification capacity of oscillator schemes and calculation principles based on the universal physical effect - HOS may be applied for any spiking type oscillators with any coupling type therefore enhancing practical value of the presented results to expand SNN capabilities.

[1]  Alexander Pergament,et al.  Electron beam modification of vanadium dioxide oscillators , 2016 .

[2]  S. Datta,et al.  Pairwise coupled hybrid vanadium dioxide-MOSFET (HVFET) oscillators for non-boolean associative computing , 2014, 2014 IEEE International Electron Devices Meeting.

[3]  Helge J. Ritter,et al.  Perceptual grouping through competition in coupled oscillator networks , 2014, ESANN.

[4]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[5]  Suman Datta,et al.  Computing with dynamical systems in the post-CMOS era , 2016, 2016 IEEE Photonics Society Summer Topical Meeting Series (SUM).

[6]  Jun Hu,et al.  Neuromorphic Cognitive Systems - A Learning and Memory Centered Approach , 2017, Intelligent Systems Reference Library.

[7]  Alexander Pergament,et al.  Thermal coupling and effect of subharmonic synchronization in a system of two VO2 based oscillators , 2020, ArXiv.

[8]  Nancy Kopell,et al.  Rapid synchronization through fast threshold modulation , 1993, Biological Cybernetics.

[9]  Roseli A. Francelin Romero,et al.  An object-based visual selection framework , 2016, Neurocomputing.

[10]  S. D. Khanin,et al.  Switching Channel Development Dynamics in Planar Structures on the Basis of Vanadium Dioxide , 2018 .

[11]  Vincent Cros,et al.  Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators , 2015, Scientific Reports.

[12]  T Kohonen,et al.  Associative memory and pattern recognition. , 1978, Medical biology.

[13]  S. Datta,et al.  Phase transition oxide neuron for spiking neural networks , 2016, 2016 74th Annual Device Research Conference (DRC).

[14]  T. Branco,et al.  The probability of neurotransmitter release: variability and feedback control at single synapses , 2009, Nature Reviews Neuroscience.

[15]  Paulo Barraza,et al.  Long-distance neural synchrony correlates with processing strategies to compare fractions , 2014, Neuroscience Letters.

[16]  Joël M. H. Karel,et al.  Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches , 2016, PloS one.

[17]  A Fukushima,et al.  Mutual synchronization of spin torque nano-oscillators through a long-range and tunable electrical coupling scheme , 2016, Nature Communications.

[18]  R. Matsumura,et al.  Unidirectional signal propagation in primary neurons micropatterned at a single-cell resolution. , 2016, Applied physics letters.

[19]  Damien Querlioz,et al.  A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network , 2017, Scientific Reports.

[20]  L. Pinneo.  On noise in the nervous system. , 1966, Psychological review.

[21]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[22]  Alexander Pergament,et al.  Deterministic noise in vanadium dioxide based structures , 2003 .

[23]  Kaushik Roy,et al.  Computing with coupled Spin Torque Nano Oscillators , 2016, 2016 21st Asia and South Pacific Design Automation Conference (ASP-DAC).

[24]  Suman Datta,et al.  Stochastic Insulator-to-Metal Phase Transition-Based True Random Number Generator , 2018, IEEE Electron Device Letters.

[25]  Suman Datta,et al.  Vertex coloring of graphs via phase dynamics of coupled oscillatory networks , 2016, Scientific Reports.

[26]  Vegard Flovik,et al.  Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model , 2016, Scientific Reports.

[27]  M. Pickett,et al.  A scalable neuristor built with Mott memristors. , 2013, Nature materials.

[28]  Tadashi Shibata,et al.  Coupled-Oscillator Associative Memory Array Operation for Pattern Recognition , 2015, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits.

[29]  Alexander Pergament,et al.  Modeling of thermal coupling in VO2-based oscillatory neural networks , 2018 .

[30]  Yan Fang,et al.  Pattern recognition with “materials that compute” , 2016, Science Advances.

[31]  Paolo Maffezzoni,et al.  Oscillator Array Models for Associative Memory and Pattern Recognition , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Vijaykrishnan Narayanan,et al.  Synchronized charge oscillations in correlated electron systems , 2014, Scientific Reports.

[33]  Julien Sylvestre,et al.  Computing with networks of nonlinear mechanical oscillators , 2017, PloS one.

[34]  B Krauskopf,et al.  Locking behavior of three coupled laser oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[36]  Maxim Volgushev,et al.  Precise Long-Range Synchronization of Activity and Silence in Neocortical Neurons during Slow-Wave Sleep , 2006, The Journal of Neuroscience.

[37]  Shuai Li,et al.  Coupling dynamics of Nb/Nb2O5 relaxation oscillators. , 2017, Nanotechnology.

[38]  Alexander Pergament,et al.  Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks , 2017, ArXiv.

[39]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[40]  S. Datta,et al.  Ultra low power coupled oscillator arrays for computer vision applications , 2016, 2016 IEEE Symposium on VLSI Technology.

[41]  Alexander Pergament,et al.  Relaxation oscillations in circuits containing sandwich switches based on vanadium dioxide , 2017 .

[42]  Suman Datta,et al.  A random number generator based on insulator-to-metal electronic phase transitions , 2017, 2017 75th Annual Device Research Conference (DRC).

[43]  Stephen Lynch,et al.  Binary Oscillator Computing , 2014 .

[45]  Shiro Saito,et al.  Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime , 2016, Nature Physics.

[46]  James A. Bain,et al.  Phase Coupling and Control of Oxide-Based Oscillators for Neuromorphic Computing , 2015, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits.

[47]  Jaijeet S. Roychowdhury,et al.  Boolean Computation Using Self-Sustaining Nonlinear Oscillators , 2014, Proceedings of the IEEE.

[48]  Emery N. Brown,et al.  Measuring the signal-to-noise ratio of a neuron , 2015, Proceedings of the National Academy of Sciences.

[49]  Wolfgang Porod,et al.  Computational Study of Spin-Torque Oscillator Interactions for Non-Boolean Computing Applications , 2013, IEEE Transactions on Magnetics.

[50]  Alexander Pergament,et al.  Electrical switching and oscillations in vanadium dioxide , 2017, 2001.01913.

[51]  Ankit Kumar,et al.  Autoassociative Memory and Pattern Recognition in Micromechanical Oscillator Network , 2017, Scientific Reports.