---
_id: '10635'
abstract:
- lang: eng
text: The brain efficiently performs nonlinear computations through its intricate
networks of spiking neurons, but how this is done remains elusive. While nonlinear
computations can be implemented successfully in spiking neural networks, this
requires supervised training and the resulting connectivity can be hard to interpret.
In contrast, the required connectivity for any computation in the form of a linear
dynamical system can be directly derived and understood with the spike coding
network (SCN) framework. These networks also have biologically realistic activity
patterns and are highly robust to cell death. Here we extend the SCN framework
to directly implement any polynomial dynamical system, without the need for training.
This results in networks requiring a mix of synapse types (fast, slow, and multiplicative),
which we term multiplicative spike coding networks (mSCNs). Using mSCNs, we demonstrate
how to directly derive the required connectivity for several nonlinear dynamical
systems. We also show how to carry out higher-order polynomials with coupled networks
that use only pair-wise multiplicative synapses, and provide expected numbers
of connections for each synapse type. Overall, our work demonstrates a novel method
for implementing nonlinear computations in spiking neural networks, while keeping
the attractive features of standard SCNs (robustness, realistic activity patterns,
and interpretable connectivity). Finally, we discuss the biological plausibility
of our approach, and how the high accuracy and robustness of the approach may
be of interest for neuromorphic computing.
acknowledgement: "A preprint version of this article has been peer-reviewed and recommended
by Peer Community In Neuroscience (DOI link to the recommendation: https://doi.org/10.24072/pci.cneuro.100003).\r\nWe
thank Christian Machens and Nuno Calaim for useful discussions on the project. This
report\r\ncame out of a collaboration started at the CAJAL Advanced Neuroscience
Training Programme in\r\nComputational Neuroscience in Lisbon, Portugal, during
the 2019 summer. The authors would\r\nlike to thank the participants, TAs, lecturers,
and organizers of the summer school. SWK was\r\nsupported by the Simons Collaboration
on the Global Brain (543009). WFP was supported by\r\nFCT (032077). MN was supported
by European Union Horizon 2020 (665385).\r\n"
article_number: e68
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Michele
full_name: Nardin, Michele
id: 30BD0376-F248-11E8-B48F-1D18A9856A87
last_name: Nardin
orcid: 0000-0001-8849-6570
- first_name: James W.
full_name: Phillips, James W.
last_name: Phillips
- first_name: William F.
full_name: Podlaski, William F.
last_name: Podlaski
- first_name: Sander W.
full_name: Keemink, Sander W.
last_name: Keemink
citation:
ama: Nardin M, Phillips JW, Podlaski WF, Keemink SW. Nonlinear computations in spiking
neural networks through multiplicative synapses. Peer Community Journal.
2021;1. doi:10.24072/pcjournal.69
apa: Nardin, M., Phillips, J. W., Podlaski, W. F., & Keemink, S. W. (2021).
Nonlinear computations in spiking neural networks through multiplicative synapses.
Peer Community Journal. Centre Mersenne ; Peer Community In. https://doi.org/10.24072/pcjournal.69
chicago: Nardin, Michele, James W. Phillips, William F. Podlaski, and Sander W.
Keemink. “Nonlinear Computations in Spiking Neural Networks through Multiplicative
Synapses.” Peer Community Journal. Centre Mersenne ; Peer Community In,
2021. https://doi.org/10.24072/pcjournal.69.
ieee: M. Nardin, J. W. Phillips, W. F. Podlaski, and S. W. Keemink, “Nonlinear computations
in spiking neural networks through multiplicative synapses,” Peer Community
Journal, vol. 1. Centre Mersenne ; Peer Community In, 2021.
ista: Nardin M, Phillips JW, Podlaski WF, Keemink SW. 2021. Nonlinear computations
in spiking neural networks through multiplicative synapses. Peer Community Journal.
1, e68.
mla: Nardin, Michele, et al. “Nonlinear Computations in Spiking Neural Networks
through Multiplicative Synapses.” Peer Community Journal, vol. 1, e68,
Centre Mersenne ; Peer Community In, 2021, doi:10.24072/pcjournal.69.
short: M. Nardin, J.W. Phillips, W.F. Podlaski, S.W. Keemink, Peer Community Journal
1 (2021).
date_created: 2022-01-17T11:12:40Z
date_published: 2021-12-15T00:00:00Z
date_updated: 2022-01-17T13:30:01Z
day: '15'
ddc:
- '519'
department:
- _id: GradSch
- _id: JoCs
doi: 10.24072/pcjournal.69
ec_funded: 1
external_id:
arxiv:
- '2009.03857'
file:
- access_level: open_access
checksum: cd9af6b331918608f2e3d1c7940cbf4f
content_type: application/pdf
creator: mnardin
date_created: 2022-01-17T11:15:26Z
date_updated: 2022-01-17T11:15:26Z
file_id: '10636'
file_name: 10_24072_pcjournal_69.pdf
file_size: 3311494
relation: main_file
success: 1
file_date_updated: 2022-01-17T11:15:26Z
has_accepted_license: '1'
intvolume: ' 1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Peer Community Journal
publication_identifier:
eissn:
- 2804-3871
publication_status: published
publisher: Centre Mersenne ; Peer Community In
quality_controlled: '1'
status: public
title: Nonlinear computations in spiking neural networks through multiplicative synapses
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 1
year: '2021'
...