Neural Processing Letters

, Volume 44, Issue 1, pp 103–124

Computation by Time

Article
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Abstract

Over the last years, the amount of research performed in the field of spiking neural networks has been growing steadily. Spiking neurons are modeled to approximate the complex dynamic behavior of biological neurons. They communicate via discrete impulses called spikes with the actual information being encoded in the timing of these spikes. As already pointed out by Maass in his paper on the third generation of neural network models, this renders time a central factor for neural computation. In this paper, we investigate at different levels of granularity how absolute time and relative timing enable new ways of biologically inspired neural information processing. At the lowest level of single spiking neurons, we give an overview of coding schemes and learning techniques which rely on precisely timed neural spikes. A high-level perspective is provided in the second part of the paper which focuses on the role of time at the network level. The third aspect of time considered in this work is related to the interfacing of neural networks with real-time systems. In this context, we discuss how the concepts of computation by time can be implemented in computer simulations and on specialized neuromorphic hardware. The contributions of this paper are twofold: first, we show how the exact modeling of time in spiking neural networks serves as an important basis for powerful computation based on neurobiological principles. Second, by presenting a range of diverse learning techniques, we prove the biologically plausible applicability of spiking neural networks to real world problems like pattern recognition and path planning.

Keywords

Spiking neural network Neurobiological learning Reservoir computing Hierarchical learning Neural coding  Neuromorphic hardware 

References

  1. 1.
    Benjamin BV, Peiran Gao, McQuinn E, Choudhary S, Chandrasekaran AR, Bussat JM, Alvarez-Icaza R, Arthur JV, Merolla PA, Boahen K (2014) Neurogrid: a mixed-analog-digital multichip system for large-scale neural simulations. Proc IEEE 102(5):699–716CrossRefGoogle Scholar
  2. 2.
    Bi G, Poo M (2001) Synaptic modification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24(1):139–166CrossRefGoogle Scholar
  3. 3.
    Bohte SM (2004) The evidence for neural information processing with precise spike-times: a survey: natural computing. Nat Comput 3(2):195–206MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bohte SM, Kok JN, La Poutré H (2002) Error-backpropagation in temporally encoded networks of spiking neurons. Neurocomputing 48(1–4):17–37CrossRefMATHGoogle Scholar
  5. 5.
    Bohte SM, La Poutre H, Kok JN (2002) Unsupervised clustering with spiking neurons by sparse temporal coding and multilayer RBF networks. Neural Netw IEEE Trans 13(2):426–435CrossRefGoogle Scholar
  6. 6.
    Brea J, Senn W, Pfister JP (2013) Matching recall and storage in sequence learning with spiking neural networks. J Neurosci 33(23):9565–9575CrossRefGoogle Scholar
  7. 7.
    Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8(3):183–208CrossRefMATHGoogle Scholar
  8. 8.
    Carnell A, Richardson D (2005) Linear algebra for time series of spikes. In: Proceedings of ESANN, pp 363–368Google Scholar
  9. 9.
    Carnevale N, Hines M (2015) NEURON for empirically-based simulations of neurons and networks of neurons: project homepage. http://www.neuron.yale.edu/neuron/
  10. 10.
    Cyr A, Boukadoum M, Thériault F (2014) Operant conditioning: a minimal components requirement in artificial spiking neurons designed for bio-inspired Robot’s controller. Front Neurorobot 8(21)Google Scholar
  11. 11.
    Diamond MC (2001) Response of the brain to enrichment. Anais da Academia Brasileira de Ciências 73:211–220CrossRefGoogle Scholar
  12. 12.
    Farries MA, Fairhall AL (2007) Reinforcement learning with modulated spike timing-dependent synaptic plasticity. J Neurophys 98(6):3648–3665CrossRefGoogle Scholar
  13. 13.
    Floreano D, Mattiussi C (2001) Evolution of spiking neural controllers for autonomous vision-based robots. In: Goos G, Hartmanis J, van Leeuwen J, Gomi T (eds) Evolutionary robotics, vol 2217., From intelligent robotics to artificial life, lecture notes in computer scienceSpringer, Berlin, pp 38–61Google Scholar
  14. 14.
    Florian RV (2005) A reinforcement learning algorithm for spiking neural networks. In: Proceedings of the seventh international symposium on symbolic and numeric algorithms for scientific computing, SYNASC ’05. IEEE Computer Society, Washington, DC, USAGoogle Scholar
  15. 15.
    Frémaux N, Sprekeler H, Gerstner W (2013) Reinforcement learning using a continuous time actor-critic framework with spiking neurons. PLoS Comput Biol 9(4):e1003,024MathSciNetCrossRefGoogle Scholar
  16. 16.
    Furber S, Brown A (2009) Biologically-inspired massively-parallel architectures - computing beyond a million processors. In: Application of concurrency to system design, 2009 (ACSD ’09). Ninth international conference on, pp 3–12Google Scholar
  17. 17.
    Furber SB, Lester DR, Plana LA, Garside JD, Painkras E, Temple S, Brown AD (2013) Overview of the spinnaker system architecture. Comput IEEE Trans 62(12):2454–2467MathSciNetCrossRefGoogle Scholar
  18. 18.
    Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595):76–78CrossRefGoogle Scholar
  19. 19.
    Gerstner W, Kistler WM (2002) Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  20. 20.
    Gewaltig MO, Morrison A, Plesser HE (2012) NEST by example: an introduction to the neural simulation tool NEST. In: Le Novère N (ed) Computational systems neurobiology. Springer, The Netherlands, pp 533–558CrossRefGoogle Scholar
  21. 21.
    Goodman Dan FM, Brette R (2009) The brian simulator. Front Neurosci 3(2):192CrossRefGoogle Scholar
  22. 22.
    Grüning A, Bohte SM (2014) Spiking neural networks: principles and challenges. In: ESANN 2014. 22nd European symposium on artificial neural networks, computational intelligence and machine learning. Bruges, April 23–25, 2014. i6doc.com, Louvain-La-NeuveGoogle Scholar
  23. 23.
    Gütig R (2014) To spike, or when to spike? Theor Comput Neurosci 25:134–139Google Scholar
  24. 24.
    Gütig R, Sompolinsky H (2006) The tempotron: a neuron that learns spike timing-based decisions. Nat Neurosci 9(3):420–428CrossRefGoogle Scholar
  25. 25.
    Hebb DO (1949) The organization of behavior: a neuropsychological theory. Wiley, New YorkGoogle Scholar
  26. 26.
    Hihi SE, Bengio Y (1996) Hierarchical recurrent neural networks for long-term dependencies. In: Touretzky DS, Mozer MC, Hasselmo ME (eds) Advances in neural information processing systems 8. MIT Press, Cambridge, pp 493–499Google Scholar
  27. 27.
    Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544CrossRefGoogle Scholar
  28. 28.
    Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4(2):251–257CrossRefGoogle Scholar
  29. 29.
    Izhikevich EM (2003) Simple model of spiking neurons. Neural Netw IEEE Trans 14(6):1569–1572MathSciNetCrossRefGoogle Scholar
  30. 30.
    Izhikevich EM (2007) Solving the distal reward problem through linkage of STDP and dopamine signaling. Cereb Cortex 17(10):2443–2452CrossRefGoogle Scholar
  31. 31.
    Jin X, Lujan M, Plana LA, Davies S, Temple S, Furber SB (2010) Modeling spiking neural networks on spinnaker. Comput Sci Eng 12(5):91–97CrossRefGoogle Scholar
  32. 32.
    Jin X, Rast A, Galluppi F, Khan M, Furber S (2009) Implementing learning on the spinnaker universal neural chip multiprocessor. In: Leung C, Lee M, Chan J (eds) Neural information processing, vol 5863., Lecture notes in computer scienceSpringer, Berlin, pp 425–432CrossRefGoogle Scholar
  33. 33.
    Kandel ER, Siegelbaum SA (2013) Cellular mechanisms of implicit memory storage and the biological basis of individuality. In: Kandel ER, Schwartz JH, Jessel TM, Siegelbaum SA, Hudspeth AJ (eds) Principles of neural science. McGraw-Hill, New York, pp 1461–1486Google Scholar
  34. 34.
    Kandel ER, Siegelbaum SA (2013) Synaptic integration in the central nervous system. In: Kandel ER, Schwartz JH, Jessel TM, Siegelbaum SA, Hudspeth AJ (eds) Principles of neural science. McGraw-Hill, New York, pp 210–235Google Scholar
  35. 35.
    Koester J, Siegelbaum SA (2013) Propagated signaling: the action potential. In: Kandel ER, Schwartz JH, Jessel TM, Siegelbaum SA, Hudspeth AJ (eds) Principles of neural science. McGraw-Hill, New York, pp 148–176Google Scholar
  36. 36.
    Krichmar J (2008) Neurorobotics. Scholarpedia 3(3):1365CrossRefGoogle Scholar
  37. 37.
    Krichmar J (2015) CARLsim: GPU-accelerated spiking neural network simulator: project homepage. http://www.socsci.uci.edu/~jkrichma/CARLsim/index.html
  38. 38.
    LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444CrossRefGoogle Scholar
  39. 39.
    Legenstein R, Naeger C, Maass W (2005) What can a neuron learn with spike-timing-dependent plasticity? Neural Comput 17(11):2337–2382MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Legenstein R, Pecevski D, Maass W (2008) A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback. PLoS Comput Biol 4(10):e1000,180MathSciNetCrossRefGoogle Scholar
  41. 41.
    Lukoševičius M, Jaeger H (2009) Reservoir computing approaches to recurrent neural network training. Comput Sci Rev 3(3):127–149CrossRefMATHGoogle Scholar
  42. 42.
    Maass W (1997) Networks of spiking neurons: the third generation of neural network models. Neural Netw 10(9):1659–1671CrossRefGoogle Scholar
  43. 43.
    Maass W, Jaeger H, Steil J, Dominey PF, Schrauwen B (2015) Web portal for reservoir computing. http://organic.elis.ugent.be/
  44. 44.
    Maass W, Natschläger T, Markram H (2002) Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput 14(11):2531–2560CrossRefMATHGoogle Scholar
  45. 45.
    Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275(5297):213–215CrossRefGoogle Scholar
  46. 46.
    Masquelier T, Thorpe SJ (2007) Unsupervised learning of visual features through spike timing dependent plasticity. PLoS Comput Biol 3(2):e31CrossRefGoogle Scholar
  47. 47.
    McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133MathSciNetCrossRefMATHGoogle Scholar
  48. 48.
    Memmesheimer RM, Rubin R, Ölveczky BP, Sompolinsky H (2014) Learning precisely timed spikes. Neuron 82(4):925–938CrossRefGoogle Scholar
  49. 49.
    Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98(6):459–478MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Natschläger T, Ruf B (1998) Spatial and temporal pattern analysis via spiking neurons. Network 9(3):319–332CrossRefMATHGoogle Scholar
  51. 51.
    NEST Initiative (2015) NEST: project homepage. http://www.nest-initiative.org/
  52. 52.
    Nichols C, McDaid LJ, Siddique NH (2010) Case study on a self-organizing spiking neural network for robot navigation. Int J Neural Syst 20(06):501–508CrossRefGoogle Scholar
  53. 53.
    Norton D, Ventura D (2006) Preparing more effective liquid state machines using hebbian learning. In: Neural networks, 2006. IJCNN ’06. International joint conference on, pp 4243–4248Google Scholar
  54. 54.
    Pfister JP (2006) Triplets of spikes in a model of spike timing-dependent plasticity. J Neurosci 26(38):9673–9682CrossRefGoogle Scholar
  55. 55.
    Ponulak F, Hopfield JJ (2013) Rapid, parallel path planning by propagating wavefronts of spiking neural activity. Front Comput Neurosci 7:98CrossRefGoogle Scholar
  56. 56.
    Ponulak F, Kasiński A (2009) Supervised learning in spiking neural networks with ReSuMe: sequence learning, classification, and spike shifting. Neural Comput 22(2):467–510MathSciNetCrossRefMATHGoogle Scholar
  57. 57.
    Ponulak F, Kasinski A (2011) Introduction to spiking neural networks: information processing, learning and applications. Acta Neurobiol Exp 71(4):409–433Google Scholar
  58. 58.
    Ros E, Carrillo R, Ortigosa EM, Barbour B, Agís R (2006) Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics. Neural Comput 18(12):2959–2993CrossRefMATHGoogle Scholar
  59. 59.
    Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 65(6):386–408MathSciNetCrossRefGoogle Scholar
  60. 60.
    Schemmel J, Brüderle D, Grübl A, Hock M, Meier K, Millner S (2010) A wafer-scale neuromorphic hardware system for large-scale neural modeling. In: Circuits and systems (ISCAS), proceedings of 2010 IEEE international symposium on, pp 1947–1950Google Scholar
  61. 61.
    Schemmel J, Grubl A, Hartmann S, Kononov A, Mayr C, Meier K, Millner S, Partzsch J, Schiefer S, Scholze S, Schuffny R, Schwartz M (2012) Live demonstration: a scaled-down version of the BrainScaleS wafer-scale neuromorphic system. In: Circuits and systems (ISCAS), 2012 IEEE international symposium on, p 702Google Scholar
  62. 62.
    Schliebs S, Kasabov N (2014) Computational modeling with spiking neural networks. In: Kasabov N (ed) Springer handbook of bio-/neuroinformatics. Springer, Berlin, pp 625–646CrossRefGoogle Scholar
  63. 63.
    Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117CrossRefGoogle Scholar
  64. 64.
    Senn W, Pfister JP (2014) Reinforcement learning in cortical networks. In: Jaeger D, Jung R (eds) Encyclopedia of computational neuroscience. Springer, New York, pp 1–9Google Scholar
  65. 65.
    Sjöström PJ, Turrigiano GG, Nelson SB (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32(6):1149–1164CrossRefGoogle Scholar
  66. 66.
    Sporea I, Grüning A (2012) Supervised learning in multilayer spiking neural networks. Neural Comput 25(2):473–509MathSciNetCrossRefMATHGoogle Scholar
  67. 67.
    Sutton RS, Precup D, Singh S (1999) Between MDPs and semi-MDPs: a framework for temporal abstraction in reinforcement learning. Artif Intell 112(1–2):181–211MathSciNetCrossRefMATHGoogle Scholar
  68. 68.
    Tani J (2014) Self-organization and compositionality in cognitive brains: a neurorobotics study. Proc IEEE 102(4):586–605CrossRefGoogle Scholar
  69. 69.
    The Human Brain Project (2015) Project homepage. https://www.humanbrainproject.eu
  70. 70.
    Walter F, Röhrbein F, Knoll A (2015) Neuromorphic implementations of neurobiological learning algorithms for spiking neural networks. Neural NetwGoogle Scholar
  71. 71.
    Werbos PJ (1990) Backpropagation through time: what it does and how to do it. Proc IEEE 78(10):1550–1560CrossRefGoogle Scholar
  72. 72.
    Wysoski S, Benuskova L, Kasabov N (2006) On-line learning with structural adaptation in a network of spiking neurons for visual pattern recognition. In: Kollias S, Stafylopatis A, Duch W, Oja E (eds) Artificial neural networks—ICANN 2006, vol 4131., Lecture notes in computer scienceSpringer, Berlin, pp 61–70CrossRefGoogle Scholar
  73. 73.
    Xu Y, Zeng X, Zhong S (2013) A new supervised learning algorithm for spiking neurons. Neural Comput 25(6):1472–1511MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Florian Walter
    • 1
  • Florian Röhrbein
    • 1
  • Alois Knoll
    • 1
  1. 1.Institut für Informatik VITechnische Universität MünchenGarching bei MünchenGermany

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