Modeling the Learning of a Spiking Neural Network with Synaptic Delays

    Received 16 January 2019; accepted 04 July 2019

    2019, Vol. 15, no. 3, pp.  365-380

    Author(s): Migalev A. S., Gotovtsev P. M.

    This paper addresses the spiking (or pulsed) neural network model with synaptic time delays at dendrites. This model allows one to change the action potential generation time more precisely with the same input activity pattern. The action potential time control principle proposed previously by several researchers has been implemented in the model considered. In the neuron model the required excitatory and inhibitory presynaptic potentials are formed by weight coefficients with synaptic delays. Various neural network architectures with a long-term plasticity model are investigated. The applicability of the spike-timing-dependent plasticity based learning rule (STDP) to a neuron model with synaptic delays is considered for a more accurate positioning of action potential time. Several learning protocols with a reinforcement signal and induced activity using varieties of functions of weight change (bipolar STDP and Ricker wavelet) are used. Modeling of a single-layer neural network with the reinforcement signal modulating the weight change function amplitude has shown a limited range of available output activity. This limitation can be bypassed using the induced activity of the output neuron layer during learning. This modification of the learning protocol allows reproducing more complex output activity, including for multiple layered networks. The ability to construct desired activity on the network output on the basis of a multichannel input activity pattern was tested on single and multiple layered networks. Induced activity during learning for networks with feedback connections allows one to synchronize multichannel input spike trains with required network output. The application of the weight change function leads to association of input and output activity by the network. When the induced activity is turned off, this association, configuration on the required output, remains. Increasing the number of layers and reducing feedback connection leads to weakening of this effect, so that additional mechanisms are required to synchronize the whole network.
    Keywords: pulsed neural network model, spiking neural network model, synaptic plasticity, synchronization, induced activity, time delayed synapses
    Citation: Migalev A. S., Gotovtsev P. M., Modeling the Learning of a Spiking Neural Network with Synaptic Delays, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 3, pp.  365-380
    DOI:10.20537/nd190313


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    References
    [1] Brooks, R. A., “From Earwigs to Humans”, Robot. Auton. Syst., 20:2–4 (1997), 291–304  crossref
    [2] Brooks, R. A., Breazeal, C., Marjanović, M., Scassalatti, B. and Williamson, M. M., “The Cog Project: Building a Humanoid Robot”, Computation for Metaphors, Analogy, and Agents (CMAA, 1998), Lecture Notes in Comput. Sci., 1562, ed. Ch. L. Nehaniv, Springer, Berlin, 1999, 52–87  crossref
    [3] Adams, B., Breazeal, C., Brooks, R. A., and Scassalatti, B., “Humanoid Robots: A New Kind of Tool”, IEEE Intell. Syst., 15:4 (2000), 25–31  crossref
    [4] Asada, M., Hosoda, K., Kuniyoshi, Y., Ishiguro, H., Inui, T., Yoshikawa, Y., Ogino, M., and Yoshida, C., “Cognitive Developmental Robotics: A Survey”, IEEE Trans. Auton. Mental Develop., 1:1 (2009), 12–34  crossref  mathscinet
    [5] Kawato, M., “From “Understanding the Brain by Creating the Brain” towards Manipulative Neuroscience”, Philos. Trans. R. Soc. Lond. B Biol. Sci., 363 (2008), 2201–2214  crossref
    [6] Morimoto, J. and Kawato, M., “Creating the Brain and Interacting with the Brain: An Integrated Approach to Understanding the Brain”, J. R. Soc. Interface, 12:104 (2015), 1–15  crossref
    [7] D'Angelo, E., Mapelli, L., Casellato, C., Garrido, J. A., Luque, N., Monaco, J., Prestori, F., Pedrocchi, A., and Ros, E., “Distributed Circuit Plasticity: New Clues for the Cerebellar Mechanisms of Learning”, Cerebellum, 15:2 (2016), 139–151  crossref
    [8] Casellato, C., Antonietti, A., Garrido, J. A., Ferrigno, G., D'Angelo, E., and Pedrocchi, A., “Distributed Cerebellar Plasticity Implements Generalized Multiple-Scale Memory Components in Real-Robot Sensimotor Tasks”, Front. Comput. Neuroscie., 9:24 (2015), 1–9
    [9] Ijspeert, A. J., Crespi, A., Ryczko, D., and Cabelguen, J.-M., “From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model”, Science, 315:5817 (2007), 1416–1420  crossref  adsnasa
    [10] Migalev, A. S., “Searching Algorithm for Sound Wave Transform in to Spike Sequence”, Neuroinformatics-2017: Proc. of the 19th Conf. on Artificial Neural Networks: P. 1, National Research Nuclear University MEPhI, Moscow, 2017, 60–70 (Russian)
    [11] Schrauwen, B. and Van Campenhout, J., “BSA, a Fast and Accurate Spike Train Encoding Scheme”, Proc. of the Internat. Joint Conf. on Neural Networks (Portland, Ore., 2003), 2825–2830
    [12] Rieke, F., Warland, D., de Ruyter van Steveninck, R. R., and Bialek, W., Spikes: Exploring the Neural Code, MIT, Cambridge, Mass., 1999, 416 pp.  mathscinet
    [13] Bialek, W., Rieke, F., de Ruyter van Steveninck, R., and Warland, D., “Reading a Neural Code”, Science, 252:5014 (1991), 1854–1857  crossref  adsnasa
    [14] Bialek, W. and Rieke, F., “Reliability and Information Transmission in Spiking Neurons”, Trends Neurosci., 15:11 (1992), 428–434  crossref
    [15] Gonzalez-Bellido, P. T., Peng, H., Yang, J., Georgopoulos, A. P., and Olberg, R. M., “Eight Pairs of Descending Visual Neurons in the Dragonfly Give Wing Motor Centers Accurate Population Vector of Prey Direction”, Proc. Natl. Acad. Sci. USA, 110:2 (2013), 696–701  crossref  adsnasa
    [16] Maas, W. and Bishop, C. M., Pulsed Neural Networks, MIT, Cambridge, Mass., 2001, 377 pp.
    [17] Schwemmer, M. A., Fairhall, A. L., Denéve, S., and Shea-Brown, E. T., “Constructing Precisely Computing Networks with Biophysical Spiking Neurons”, J. Neurosci., 28:35 (2015), 10112–10134  crossref  mathscinet  elib
    [18] Mel, B. W., “Structural Plasticity at the Axodendritic Interface: Some Functional Implications”, Modeling Neural Development, ed. A. Van Ooyen, MIT, Cambridge, Mass., 2003, 273–290
    [19] Case, R. D., Humphries, M., and Gutkin, B., “Passive Dendrites Enable Single Neurons to Compute Linearly Non-Separable Functions”, PLoS Comput. Biol., 9:2 (2013), 1–15  mathscinet
    [20] Migliore, M., Messineo, L., and Ferrante, M., “Dendritic $I_k$ Selectivly Blocks Temporal Summation of Unsynchronized Distal Inputs in CA1 Pyramidal Neurons”, J. Comput. Neurosci., 1:16 (2004), 5–13  crossref
    [21] Sinyavskiy, O. Yu. and Kobrin, A. I., “Reinforcement Learning of a Spiking Neural Network in the Task of Control of an Agent in a Virtual Discrete Environment”, Nelin. Dinam., 7:4 (2011), 859–875 (Russian)  mathnet  crossref
    [22] Gerstner, W., Spiking Neuron Models: Single Neurons, Populations, Plasticity, MIT, Cambridge, Mass., 2002, 496 pp.  mathscinet
    [23] Migalev, A. S., “Application of Custom Synaptic Plasticity Model on Spiking Neural Networks”, Neuroinformatics-2018: Proc. of the 21st Internat. Conf. on Artificial Neural Networks: P. 2, National Research Nuclear University MEPhI, Moscow, 2018, 154–161 (Russian)
    [24] Thiele, J. C., Bichler, O., and Dupret, A., “Event-Based, Timescale Invariant Unsupervised Online Deep Learning with STDP”, Front. Comput. Neurosci., 12 (2018), 1–13  crossref
    [25] Tavanaei, A., Masquelier, T., and Maida, A., “Representation Learning Using Event-Based STDP”, Neural Netw., 9:2 (2018), 1–15
    [26] Diehl, P. U. and Cook, M., “Event-Based, Timescale Invariant Unsupervised Online Deep Learning with STDP”, Front. Comput. Neuroscie., 12 (2018), 1–13
    [27] Demin, V. A. and Nekhaev, D. V., “Spiking Neural Networks Learning Based on a Neuron Activity Maximizing Principle”, Neuroinformatics-2018: Proc. of the 21st Internat. Conf. on Artificial Neural Networks: P. 2, National Research Nuclear University MEPhI, Moscow, 2018, 54–64 (Russian)  mathscinet
    [28] Demin, V. A. and Nekhaev, D. V., “Recurrent Spiking Neural Network Learning Based on a Competitive Maximization of Neuronal Activity”, Front. Neuroinform., 12 (2018), 1–13  crossref
    [29] Zappacosta, S., Mannella, F., Mirolli, M., and Baldassarre, G., “General Differential Hebbian Learning: Capturing Temporal Relations between Events in Neural Networks and the Brain”, PLoS Comput. Biol., 14:8 (2018), 1–30  crossref
    [30] Zhang, J.-C., Lau, P.-M., and Bi, G.-Q., “Gain in Sensitivity and Loss in Temporal Contrast of STDP by Dopaminergic Modulation at Hippocampal Synapses”, Proc. Natl. Acad. Sci. USA, 106:31 (2009), 13028–13033  crossref  adsnasa
    [31] Izhikevich, E. M., “Solving the Distal Reward Problem through Linkage of STDP and Dopamine Signaling”, Cereb. Cortex, 17:10 (2007), 2443–2452  crossref  elib
    [32] Kuśmierz, Ł., Isomura, T., and Toyoizumi, T., “Learning with Three Factors: Modulating Hebbian Plasticity with Errors”, Curr. Opin. Neurobiol., 2017, no. 46, 170–177
    [33] Gerstner, W., Lehmann, M., Liakoni, V., Corneil, D., and Brea, J., “Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules”, Front. Neural Circuits, 12 (2018), 053, 16 pp.  crossref
    [34] Cui, Y., Paillé, V., Xu, H., Genet, S., Delord, B., Fino, E., Berry, H., and Venance, L., “Endocannabinoids Mediate Bidirectional Striatal Spike-Timing-Dependent Plasticity”, J. Physiol., 593:13 (2018), 2833–2849  crossref
    [35] Quartz, S. R., “Modeling the Neural Basis of Cognitive Development”, Modeling Neural Development, ed. A. Van Ooyen, MIT, Cambridge, Mass., 2003, 291–313
    [36] Izhikevich, E. M., “Polychronization: Computation with Spikes”, Neural Comput., 18:2 (2006), 245–282  crossref  mathscinet  zmath  elib



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