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The high-conductance state enables neural sampling in networks of LIF neurons

The high-conductance state enables neural sampling in networks of LIF neurons Petrovici et al. BMC Neuroscience 2015, 16(Suppl 1):O2 http://www.biomedcentral.com/1471-2202/16/S1/O2 ORAL PRESENTATION Open Access The high-conductance state enables neural sampling in networks of LIF neurons 1* 1 2 1 1 Mihai A Petrovici , Ilja Bytschok , Johannes Bill , Johannes Schemmel , Karlheinz Meier From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 The apparent stochasticity of in-vivo neural circuits has membrane potential before and after refractoriness by long been hypothesized to represent a signature of propagating the PDF of the effective membrane potential ongoing stochastic inference in the brain [1-3]. More from spike to spike within a burst. For the membrane recently, a theoretical framework for neural sampling has potential evolution between bursts, we consider an been proposed, which explains how sample-based infer- Ornstein-Uhlenbeck approximation. We find that our ence can be performed by networks of spiking neurons theoretical prediction of the neural response function closely matches simulation data. Moreover, in the HCS [4,5]. One particular requirement of this approach is that the membrane potential of these neurons satisfies the so- scenario, we show that the neural response function called neural computability condition (NCC), which in becomes symmetric and can be well approximated by a turn leads to a logistic neural response function. logistic function, thereby providing the correct dynamics Analytical approaches to calculating this function have in order to perform neural sampling. Such stochastic fir- been the subject of many theoretical studies. In order to ing units can then be used to sample from arbitrary prob- make the problem tractable, particular assumptions ability distributions over binary random variables regarding the neural or synaptic parameters are usually [4,5,8,9]. We hereby provide not only a normative frame- made [6,7]. However, biologically significant activity work for Bayesian inference in cortex, but also powerful regimes exist which are not covered by these approaches: applications of low-power, accelerated neuromorphic sys- Under strong synaptic bombardment, as is often the case tems to highly relevant machine learning problems. in cortex, the neuron is shifted into a high-conductance state (HCS), which is characterized by a small membrane Acknowledgements time constant. In this regime, synaptic time constants This research was supported by EU grants #269921 (BrainScaleS), #237955 and refractory periods dominate membrane dynamics. (FACETS-ITN), #604102 (Human Brain Project), the Austrian Science Fund FWF #I753-N23 (PNEUMA) and the Manfred Stärk Foundation. The HCS is also particularly interesting from a func- tional point of view. In [5], we have shown that LIF neu- Authors’ details rons that are shifted into a HCS by background synaptic Kirchhoff-Institute for Physics, University of Heidelberg, Heidelberg, Germany. Institute for Theoretical Computer Science, University of Graz, bombardment can attain the correct firing statistics to Graz, Austria. sample from well-defined probability distributions (i.e., satisfy the NCC). In order to calculate the response func- Published: 18 December 2015 tion of neurons in this regime, we are required to con- References sider a new approach. 1. Körding K, Wolpert D: Bayesian integration in sensorimotor learning. The core idea of this approach is to separately consider Nature 2004, 427:244-247. two different “modes” of spiking dynamics: burst spiking 2. Fizser J, Berkes P, Orbán G, Lengyel M: Statistically optimal perception and learning: from behavior to neural representations. Trends in Cognitive and transient quiescence, in which the neuron does not Sciences 2010, 14(3):119-130. spike for longer periods. For the bursting mode, we expli- 3. Friston K, Mattout J, Kilner J: Action understanding and active inference. citly take into consideration the autocorrelation of the Biological Cybernetics 2011, 104(1-2):137-160. 4. Büsing Lars, Bill Johannes, Nessler Bernhard, Maass Wolfgang: Neural dynamics as sampling: A model for stochastic computation in recurrent * Correspondence: mpedro@kip.uni-heidelberg.de networks of spiking neurons. PLoS Computational Biology 2011, 7(11): Kirchhoff-Institute for Physics, University of Heidelberg, Heidelberg, Germany e1002211. Full list of author information is available at the end of the article © 2015 Petrovici et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Petrovici et al. BMC Neuroscience 2015, 16(Suppl 1):O2 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/O2 5. Petrovici MA, Bill J, Bytschok I, Schemmel J, Karlheinz Meier: Stochastic inference with deterministic spiking neurons. arXiv preprint 2013, 1311.3211. 6. Brunel N, Sergi S: Firing Frequency of leaky integrate-and-fire neurons with synaptic current dynamics. Journal of Theoretical Biology 1998, 195(1):87-95. 7. Moreno-Bote R, Parga N: Role of synaptic filtering on the firing response of simple model neurons. Physical Review Letters 2004, 92:028102. 8. Pecevski D, Büsing L, Maass W: Probabilistic inference in general graphical models through sampling in stochastic networks of spiking neurons. PLoS Computational Biology 2011, 7(12):e1002294. 9. Probst D, Petrovici MA, Bytschok I, Bill J, Peceyski D, Schemmel J, Meier K: Probabilistic inference in discrete spaces can be implemented into networks of LIF neurons. Frontiers in Neuroscience 2015, 9:13. doi:10.1186/1471-2202-16-S1-O2 Cite this article as: Petrovici et al.: The high-conductance state enables neural sampling in networks of LIF neurons. BMC Neuroscience 2015 16(Suppl 1):O2. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BMC Neuroscience Springer Journals

The high-conductance state enables neural sampling in networks of LIF neurons

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Petrovici et al.
Subject
Biomedicine; Neurosciences; Neurobiology; Animal Models
eISSN
1471-2202
DOI
10.1186/1471-2202-16-S1-O2
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See Article on Publisher Site

Abstract

Petrovici et al. BMC Neuroscience 2015, 16(Suppl 1):O2 http://www.biomedcentral.com/1471-2202/16/S1/O2 ORAL PRESENTATION Open Access The high-conductance state enables neural sampling in networks of LIF neurons 1* 1 2 1 1 Mihai A Petrovici , Ilja Bytschok , Johannes Bill , Johannes Schemmel , Karlheinz Meier From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 The apparent stochasticity of in-vivo neural circuits has membrane potential before and after refractoriness by long been hypothesized to represent a signature of propagating the PDF of the effective membrane potential ongoing stochastic inference in the brain [1-3]. More from spike to spike within a burst. For the membrane recently, a theoretical framework for neural sampling has potential evolution between bursts, we consider an been proposed, which explains how sample-based infer- Ornstein-Uhlenbeck approximation. We find that our ence can be performed by networks of spiking neurons theoretical prediction of the neural response function closely matches simulation data. Moreover, in the HCS [4,5]. One particular requirement of this approach is that the membrane potential of these neurons satisfies the so- scenario, we show that the neural response function called neural computability condition (NCC), which in becomes symmetric and can be well approximated by a turn leads to a logistic neural response function. logistic function, thereby providing the correct dynamics Analytical approaches to calculating this function have in order to perform neural sampling. Such stochastic fir- been the subject of many theoretical studies. In order to ing units can then be used to sample from arbitrary prob- make the problem tractable, particular assumptions ability distributions over binary random variables regarding the neural or synaptic parameters are usually [4,5,8,9]. We hereby provide not only a normative frame- made [6,7]. However, biologically significant activity work for Bayesian inference in cortex, but also powerful regimes exist which are not covered by these approaches: applications of low-power, accelerated neuromorphic sys- Under strong synaptic bombardment, as is often the case tems to highly relevant machine learning problems. in cortex, the neuron is shifted into a high-conductance state (HCS), which is characterized by a small membrane Acknowledgements time constant. In this regime, synaptic time constants This research was supported by EU grants #269921 (BrainScaleS), #237955 and refractory periods dominate membrane dynamics. (FACETS-ITN), #604102 (Human Brain Project), the Austrian Science Fund FWF #I753-N23 (PNEUMA) and the Manfred Stärk Foundation. The HCS is also particularly interesting from a func- tional point of view. In [5], we have shown that LIF neu- Authors’ details rons that are shifted into a HCS by background synaptic Kirchhoff-Institute for Physics, University of Heidelberg, Heidelberg, Germany. Institute for Theoretical Computer Science, University of Graz, bombardment can attain the correct firing statistics to Graz, Austria. sample from well-defined probability distributions (i.e., satisfy the NCC). In order to calculate the response func- Published: 18 December 2015 tion of neurons in this regime, we are required to con- References sider a new approach. 1. Körding K, Wolpert D: Bayesian integration in sensorimotor learning. The core idea of this approach is to separately consider Nature 2004, 427:244-247. two different “modes” of spiking dynamics: burst spiking 2. Fizser J, Berkes P, Orbán G, Lengyel M: Statistically optimal perception and learning: from behavior to neural representations. Trends in Cognitive and transient quiescence, in which the neuron does not Sciences 2010, 14(3):119-130. spike for longer periods. For the bursting mode, we expli- 3. Friston K, Mattout J, Kilner J: Action understanding and active inference. citly take into consideration the autocorrelation of the Biological Cybernetics 2011, 104(1-2):137-160. 4. Büsing Lars, Bill Johannes, Nessler Bernhard, Maass Wolfgang: Neural dynamics as sampling: A model for stochastic computation in recurrent * Correspondence: mpedro@kip.uni-heidelberg.de networks of spiking neurons. PLoS Computational Biology 2011, 7(11): Kirchhoff-Institute for Physics, University of Heidelberg, Heidelberg, Germany e1002211. Full list of author information is available at the end of the article © 2015 Petrovici et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Petrovici et al. BMC Neuroscience 2015, 16(Suppl 1):O2 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/O2 5. Petrovici MA, Bill J, Bytschok I, Schemmel J, Karlheinz Meier: Stochastic inference with deterministic spiking neurons. arXiv preprint 2013, 1311.3211. 6. Brunel N, Sergi S: Firing Frequency of leaky integrate-and-fire neurons with synaptic current dynamics. Journal of Theoretical Biology 1998, 195(1):87-95. 7. Moreno-Bote R, Parga N: Role of synaptic filtering on the firing response of simple model neurons. Physical Review Letters 2004, 92:028102. 8. Pecevski D, Büsing L, Maass W: Probabilistic inference in general graphical models through sampling in stochastic networks of spiking neurons. PLoS Computational Biology 2011, 7(12):e1002294. 9. Probst D, Petrovici MA, Bytschok I, Bill J, Peceyski D, Schemmel J, Meier K: Probabilistic inference in discrete spaces can be implemented into networks of LIF neurons. Frontiers in Neuroscience 2015, 9:13. doi:10.1186/1471-2202-16-S1-O2 Cite this article as: Petrovici et al.: The high-conductance state enables neural sampling in networks of LIF neurons. BMC Neuroscience 2015 16(Suppl 1):O2. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit

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BMC NeuroscienceSpringer Journals

Published: Dec 18, 2015

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