Nonlinear computations in spiking neural networks through multiplicative synapses
M. Nardin, J.W. Phillips, W.F. Podlaski, S.W. Keemink, ArXiv (n.d.).
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Author
Nardin, MicheleIST Austria
;
Phillips, James W;
Podlaski, William F;
Keemink, Sander W

Department
Abstract
The brain performs many nonlinear computations through intricate spiking
neural networks (SNNs). How neural network dynamics relate to arbitrary
computations under these constraints is still an open question. As a strong
constraint, these networks are hypothesized to be robust to perturbations and
use minimal energy. The theory of Spike Coding Networks (SCNs) derives the
required connectivity and dynamics for both information representation and
linear dynamical systems from first principles, and achieves robustness and
efficiency. Nonlinear dynamical systems have thus far only been implemented in
SCNs by filtering neural inputs through sets of nonlinear dendritic basis
functions. While this approach works well, it relies on providing a rich enough
basis set as well as supervised training of the connectivity weights. Another
way to implement nonlinear computations is through multiplicatively interacting
synapses. However, there is currently no principled way to implement such
synapses in SCNs. Here, we extend the core SCN derivations to implement
polynomial dynamical systems, from which also the need for such
multiplicatively interacting synapses arises. We demonstrate our approach with
a highly accurate Lorenz attractor implementation, as well as a second-order
approximation of a double pendulum. We additionally demonstrate how to
implement higher-order polynomials using sequential networks with only
pair-wise synapses. Finally, we derive upper bounds and expected numbers of
connections based on the sparsity of the underlying representation. Overall,
our work provides an alternative way to directly implement nonlinear
computations in spike coding networks, and expands our understanding about the
potential functions of multiplicative synapses. Furthermore, due to the high
accuracy and low energy usage of our approach, this work may be of interest for
neuromorphic computing.
Publishing Year
Date Published
2020-09-08
Journal Title
arXiv
Acknowledgement
We thank Christian Machens for useful discussions on the project. This report came out
of a collaboration started at the CAJAL Advanced Neuroscience Training Programme in
Computational Neuroscience in Lisbon, Portugal, during the 2019 summer. The authors
would like to thank the participants, TAs, lecturers, and organizers of the summer school.
SWK was supported by the Simons Collaboration on the Global Brain (543009). WFP was
supported by FCT (032077). MN was supported by European Union Horizon 2020 (665385).
Article Number
2009.03857
IST-REx-ID
Cite this
Nardin M, Phillips JW, Podlaski WF, Keemink SW. Nonlinear computations in spiking neural networks through multiplicative synapses. arXiv.
Nardin, M., Phillips, J. W., Podlaski, W. F., & Keemink, S. W. (n.d.). Nonlinear computations in spiking neural networks through multiplicative synapses. arXiv.
Nardin, Michele, James W Phillips, William F Podlaski, and Sander W Keemink. “Nonlinear Computations in Spiking Neural Networks through Multiplicative Synapses.” ArXiv, n.d.
M. Nardin, J. W. Phillips, W. F. Podlaski, and S. W. Keemink, “Nonlinear computations in spiking neural networks through multiplicative synapses,” arXiv. .
Nardin M, Phillips JW, Podlaski WF, Keemink SW. Nonlinear computations in spiking neural networks through multiplicative synapses. arXiv, 2009.03857.
Nardin, Michele, et al. “Nonlinear Computations in Spiking Neural Networks through Multiplicative Synapses.” ArXiv, 2009.03857.
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