Mathematical modeling of the processes of signal routing by logic matrix, information encoding and decoding in the biomorphic neuroprocessor

About the author:

Alexander D. Pisarev, Cand. Sci. (Tech.), Associate Professor, Department of Applied and Technical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; Senior Researcher, Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; spcb.doc@utmn.ru, https://orcid.org/0000-0002-5602-3880

Abstract:

At the University of Tyumen, a biomorphic hardware neuroprocessor based on a combined memristor-diode crossbar has been developed. The neuroprocessor implements a biomorphic spiking neural network with a large number of neurons and trainable synaptic connections between them. Large biomorphic neural networks make it possible to reproduce the functionality of the human brain cortical column. This provides new opportunities for information processing tasks by standalone neuroprocessor. When designing and optimizing the operation of the input and output devices, as well as the logic matrix of the neuroprocessor created based on large combined memristor-diode crossbars, physico-mathematical models are needed to simulate their work.

This report presents the physico-mathematical models developed for this neuroprocessor: of the operation of a logic matrix cell built on the basis of simplified electrical models of a memristor and a Zener diode; of the process of the neurons output spikes routing of by the logic matrix to the synapses of other neurons; of processes of information encoding into biomorphic impulses and decoding of neural block output into a binary code. With the help of these models and numerical simulation, the operability of the input and output devices, as well as the logic matrix of the biomorphic neuroprocessor, is shown when processing incoming information. The originality of the models is associated with the specifics of the selected memristor-diode cell of the universal large logic matrix, which, in addition to its main work as a spikes router, is the basis of the electrical circuits of the input and output devices of the neuroprocessor.

For numerical simulation of the operation of large electrical circuits containing memristor-diode crossbars, the original specialized program MDC-SPICE was used.

References:

1. Pisarev A. D., Udovichenko S. Yu. 2021. Biomorphic neuroprocessor based on nanoscale composite memristor-diode crossbar. Moscow: Technosphera, 2021. 228 p. [In Russian]

2. Pisarev A. D., Busygin A. N., Ibrahim A. H. A., Udovichenko S. Yu. 2020. “Simulation of information decoding processes in the output device of the biomorphic neuroprocessor”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 6, no. 4 (24), pp. 179-193. DOI: 10.21684/2411-7978-2020-6-4-179-193 [In Russian]

3. Pisarev A. D. 2019. “Energy efficient biomorphic pulse information coding in electronic neurons for the entrance unit of the neuroprocessor”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 5, no. 3, pp. 186-212. DOI: 10.21684/2411-7978-2019-5-3-186-212 [In Russian]

4. Udovichenko S. Yu, Pisarev A. D., Busygin A. N., Maevsky O. V. 2017. “3D CMOS, memristor nanotechnology for creating logical and memory matrices of neuroprocessor”. Nanoindustry, no. 5 (76), pp. 26-34. DOI: 10.22184/1993-8578.2017.76.5.26.34 [In Russian]

5. Udovichenko S. Yu., Pisarev A. D., Busygin A. N., Bobylev A. N. 2021.
   “Biomorphous neuroprocessor — prototype of a new generation computer being a carrier of artificial intelligence. Part 2”. Nanoindustry, vol. 14, no. 1 (103), pp. 68-79.
   DOI: 10.22184/1993-8578.2021.14.1.68.79 [In Russian]

6. Udovichenko S. Yu, Pisarev A. D., Busygin A. N., Maevsky O. V. 2018. “Neuroprocessor based on combined memristor-diode crossbar”. Nanoindustry, vol. 11, no. 5 (84), pp. 344-355. DOI: 10.22184/1993-8578.2018.84.5.344.355 [In Russian]

7. Biolek D., Di Ventra M., Pershin Yu. V. 2013. “Reliable SPICE simulations of memristors, memcapacitors and meminductors”. Radioengineering, vol. 22, no. 4, pp. 945-968. DOI: 10.48550/arXiv.1307.2717

8. Busygin A. N., Ebrahim A. H., Pisarev A. D., Udovichenko S. Yu. 2021. “Input device for a biomorphic neuroprocessor based on a memristor-diode crossbar for the pulse coding of information”. Nanobiotechnology Reports, vol. 16, no. 6, pp. 798-803. DOI: 10.1134/S2635167621060069

9. Pisarev A. D., Busygin A. N., Udovichenko S. Yu., Maevsky O. V. 2018. “3D memory matrix based on a composite memristor-diode crossbar for a neuromorphic processor”. Microelectronic Engineering, vol. 198, pp. 1-7. DOI: 10.1016/j.mee.2018.06.008

10. Pisarev A. D., Busygin A. N., Udovichenko S. Yu., Maevsky O. V. 2022. “A biomorphic neuroprocessor based on a composite memristor-diode crossbar”. Microelectronics Journal, vol. 102, art. 104827. DOI: 10.1016/j.mejo.2020.104827

11. Pisarev A. D., Busygin A. N., Bobylev A. N., Udovichenko S. Yu. 2019. “Operation principle and fabrication technology of the neuroprocessor input unit on the basis of the memristive logic matrix”. International Journal of Nanotechnology, vol. 16, no. 6-10, pp. 596-601. DOI: 10.1504/IJNT.2019.106630

12. Winters B. D., Shan-Xue Jin, Ledford K. R., Golding N. L. 2017. “Amplitude normalization of dendritic EPSPs at the soma of binaural coincidence detector neurons of the medial superior olive”. Journal of Neuroscience, vol. 37, no. 12, pp. 3138-3149. DOI: 10.1523/JNEUROSCI.3110-16.2017

13. Wong S., Hu C. M. 1991. “SPICE macro model for the simulation of zener diode I-V characteristics”. IEEE Circuits and Devices Magazine, vol. 7, no. 4, pp. 9-12. DOI: 10.1109/101.134564