Abstract
Neuromorphic computing aims at the realization of intelligent systems able to process information similarly to our brain. Brain-inspired computing paradigms have been implemented in crossbar arrays of memristive devices; however, this approach does not emulate the topology and the emergent behaviour of biological neuronal circuits, where the principle of self-organization regulates both structure and function. Here, we report on in materia reservoir computing in a fully memristive architecture based on self-organized nanowire networks. Thanks to the functional synaptic connectivity with nonlinear dynamics and fading memory properties, the designless nanowire complex network acts as a network-wide physical reservoir able to map spatio-temporal inputs into a feature space that can be analysed by a memristive resistive switching memory read-out layer. Computing capabilities, including recognition of spatio-temporal patterns and time-series prediction, show that the emergent memristive behaviour of nanowire networks allows in materia implementation of brain-inspired computing paradigms characterized by a reduced training cost.
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Data availability
The data that support the findings of this study are available on Zenodo (https://doi.org/10.5281/zenodo.5153335). All other data are available from the authors.
Code availability
The codes used to generate datasets of simulations can be accessed on GitHub (https://github.com/MilanoGianluca/Nanowire_Network_Reservoir_Computing).
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Acknowledgements
We acknowledge support by M. Raimondo in helping with SEM measurements. Device fabrication was performed at Nanofacility Piemonte, a facility supported by the Compagnia di San Paolo foundation, and at PoliFAB, the micro- and nanofabrication facility of Politecnico di Milano. Part of this work was supported by the European project MEMQuD, code 20FUN06. This project (EMPIR 20FUN06 MEMQuD) has received funding from the European Metrology Programme for Innovation and Research (EMPIR) cofinanced by the participating states and from the European Union’s Horizon 2020 research and innovation programme. This article received funding from the European Union’s Horizon 2020 research and innovation program (grant agreement no. 824164).
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G.M., D.I. and C.R. generated the idea and designed the experiments. G.M. performed NW network fabrication and characterization. G.P. and G.M. performed multielectrode NW network characterization. S.R. and S.H. performed fabrication and characterization of the ReRAM read-out. G.M. and K.M. developed the NW network model and performed RC simulations. G.M., K.M. and G.P. analysed data. G.M. and C.R. prepared the manuscript. L.B., D.I. and C.R. supervised the research. All authors participated in the discussion of results and revision of the manuscript.
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The device configuration and implementation method of reservoir computing are currently under patent filing (Italian priority application number 102021000019277). Patent applicants: Politecnico di Torino, Politecnico di Milano, Istituto Nazionale di Ricerca Metrologica; Inventors: G.M., G.P., K.M., D.I. and C.R.
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Supplementary Information
Supplementary Figs. 1–34, Tables 1 and 2, Notes 1–11 and references.
Supplementary Video 1
Animation of the spatio-temporal evolution of the conductive path formation and following dissolution in two-terminal configuration with a voltage pulse (2 V, 100 s). The animation with the grid-graph model refers to Fig. 2a. According to the grid-graph model discussed in Supplementary Note 3, short-term conductance dynamics of each edge are modelled through a potentiation–depression rate balance equation. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. During modelling, the left electrode was biased while the right one was kept as a ground.
Supplementary Video 2
Animation of the spatio-temporal evolution of the conductivity map under stimulation in a multi-terminal configuration, with a voltage pulse applied to pad 1 (5 V, 10 ms) while keeping other electrodes at ground. The animation with the grid-graph model refers to Supplementary Fig. 12. The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to pad 4, according to the schematization of the experimental set-up reported in Supplementary Fig. 12b. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. As can be observed, stimulation in the multi-terminal configuration results in the formation of conductive pathways resulting from the voltage distribution across the sample during stimulation.
Supplementary Video 3
Animation of the spatio-temporal evolution of the conductivity map under pattern stimulation. The animation with the grid-graph model refers to Fig. 3 (evolution of the conductivity map) and Supplementary Fig. 17 (evolution of output signal time traces). The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to pad 4, according to the schematization of the experimental set-up reported in Supplementary Fig. 12b. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. As can be observed, the peculiar evolution of the conductivity map depends on the spatial and temporal sequence of inputs.
Supplementary Video 4
Animation of in materia reservoir computing process where a digit pattern (from the MNIST handwritten dataset) is fed into the NW network physical reservoir as a spatio-temporal input, and the final reservoir output is then passed as input to a read-out one-layer fully connected neural network to perform classification. The animation shows the process of binarization and subsequent chopping and merging of the pattern to transform the digit into a spatio-temporal input with 196 pulse streams with four time frames applied to different pads of the sample. Then, the spatio-temporal evolution of the conductivity map and corresponding evolution of the reservoir output after stimulation with the digit ‘6’ according to the grid-graph model are shown. The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to the pad highlighted in Supplementary Fig. 24 of the manuscript, according to the schematization of the experimental set-up reported in the same figure. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. At the end of pattern stimulation, the final reservoir output voltages (at time frame t4) are then passed as input to the read-out one-layer neural network for classification.
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Milano, G., Pedretti, G., Montano, K. et al. In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks. Nat. Mater. 21, 195–202 (2022). https://doi.org/10.1038/s41563-021-01099-9
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DOI: https://doi.org/10.1038/s41563-021-01099-9
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