- Letter
- Published:
- Suhas Kumar1,
- John Paul Strachan1 &
- R. Stanley Williams1
Nature volume548,pages 318–321 (2017)Cite this article
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- Electronic devices
- Nonlinear phenomena
Abstract
At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos1 that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains2,3,4,5,6,7. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos2, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems8. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos9,10,11,12, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking5,6,13. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal–insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator14 and observe a tunable range of periodic and chaotic self-oscillations15. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.
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Acknowledgements
The research is in part based on work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via contract number 2017-17013000002. We thank L. O. Chua for reviewing the manuscript, discussions and data analysis. We also thank G. Gibson for discussions and insights.
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Hewlett Packard Labs, 1501 Page Mill Road, Palo Alto, 94304, California, USA
Suhas Kumar,John Paul Strachan&R. Stanley Williams
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- Suhas Kumar
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Contributions
All authors contributed to the conception of the idea, design of experiments, construction of the model, data analysis and writing of the manuscript. S.K. primarily set up experiments and collected experimental data. S.K. and J.P.S. together ran the simulations of the models. R.S.W. conceptualized the static model, the inclusion of thermal noise in the dynamical model, and determined the relevance of chaos in computational systems. J.P.S. had the specific idea of using chaos for accelerating solutions in Hopfield networks.
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Correspondence to Suhas Kumar or R. Stanley Williams.
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Reviewer Information Nature thanks W. Ditto, Z. Toroczkai and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Kumar, S., Strachan, J. & Williams, R. Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing. Nature 548, 318–321 (2017). https://doi.org/10.1038/nature23307
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Editorial Summary
Computing at the edge of chaos
In recent years, grids of memristor devices, with their synapse-like dynamics and adaptable conductivity, have demonstrated neural-network-type implementations of analogue (non-Boolean) computing. Suhas Kumar et al. now explore the possibility of exploiting chaotic dynamics in highly nonlinear niobium dioxide memristor devices. This idea is inspired by the theory that biological neurons operate in a regime called 'the edge of chaos', which is thought to be key to the ability of the human brain to tackle complex information processing tasks with high efficiency. The authors demonstrate a controllable regime of chaotic self-oscillations in their devices and simulate a memristor grid that can solve a typical computationally hard task—a travelling salesman problem—with higher accuracy and efficiency than an approach that does not incorporate chaotic elements. Building artificial neural networks with chaotic oscillators based on single electronic devices provides an exciting direction for unconventional analogue computing.
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