Skip to main content
Log in

A model for complex sequence learning and reproduction in neural populations

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Temporal patterns of activity which repeat above chance level in the brains of vertebrates and in the mammalian neocortex have been reported experimentally. This temporal structure is thought to subserve functions such as movement, speech, and generation of rhythms. Several studies aim to explain how particular sequences of activity are learned, stored, and reproduced. The learning of sequences is usually conceived as the creation of an excitation pathway within a homogeneous neuronal population, but models embodying the autonomous function of such a learning mechanism are fraught with concerns about stability, robustness, and biological plausibility. We present two related computational models capable of learning and reproducing sequences which come from external stimuli. Both models assume that there exist populations of densely interconnected excitatory neurons, and that plasticity can occur at the population level. The first model uses temporally asymmetric Hebbian plasticity to create excitation pathways between populations in response to activation from an external source. The transition of the activity from one population to the next is permitted by the interplay of excitatory and inhibitory populations, which results in oscillatory behavior that seems to agree with experimental findings in the mammalian neocortex. The second model contains two layers, each one like the network used in the first model, with unidirectional excitatory connections from the first to the second layer experiencing Hebbian plasticity. Input sequences presented in the second layer become associated with the ongoing first layer activity, so that this activity can later elicit the the presented sequence in the absence of input. We explore the dynamics of these models, and discuss their potential implications, particularly to working memory, oscillations, and rhythm generation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abbott, L. F., & Blum, K. I.(1996). Functional significance of long-term potentiation for sequence learning and prediction. Cerebral Cortex, 6(3), 406–416.

    Article  PubMed  CAS  Google Scholar 

  • Abeles, M. (1991). Corticonics: Neural circuits of the cerebral cortex. New York: Cambridge University Press.

    Book  Google Scholar 

  • Amari, S. I. (1972). Learning patterns and pattern sequences by self-organizing nets of threshold elements. IEEE Transactions on Computers, c-21(11), 1197–1206.

    Article  Google Scholar 

  • Brenowitz, E. A., Margoliash, D., & Nordeen, K. W. (1997). An introduction to birdsong and the avian song system. Journal of Neurobiology, 33(5), 495–500.

    Article  PubMed  CAS  Google Scholar 

  • Buonomano, D. V. (2003). Timing of neural responses in cortical organotypic slices. Proceedings of the National Academy of Sciences of the United States of America 100(8), 4897–4902.

    Article  PubMed  CAS  Google Scholar 

  • Buzsáki, G., & Draguhn A. (2004). Neuronal oscillations in cortical networks. Science, 304, 1926–1929.

    Article  PubMed  Google Scholar 

  • Caianiello, E., de Luca, A., & Ricciardi, L. (1967). Reverberations and control of neural networks. Kybernetik, 4, 10–18.

    Article  PubMed  CAS  Google Scholar 

  • Cariani, P. A. (2004). Temporal codes and computations for sensory representation and scene analysis. IEEE Transactions on Neural Networks/IEEE Neural Networks Council, 15(5), 1100–1111.

    Article  Google Scholar 

  • Carr, C. E. (1993). Processing of temporal information in the brain. Annual Review of Neuroscience, 16, 226–243.

    Article  Google Scholar 

  • Chang, W., & Jin, D. (2009). Spike propagation in driven chain networks with dominant global inhibition. Physical Review E, 79(5), 1–5.

    Article  Google Scholar 

  • Compte, A., Constantinidis, C., Tegner, J., Raghavachari, S., Chafee, M. V., Goldman-Rakic, P. S., et al. (2003). Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. Journal of Neurophysiology, 90(5), 3441–3454.

    Article  PubMed  Google Scholar 

  • De Zeeuw, C. I., Hoebeek, F. E., Bosman, L. W. J., Schonewille, M., Witter, L., & Koekkoek, S. K. (2011). Spatiotemporal firing patterns in the cerebellum. Nature Reviews Neuroscience, 12, 327–344.

    Article  PubMed  Google Scholar 

  • Diesmann, M., Gewaltig, M. O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402(6761), 529–533.

    Article  PubMed  CAS  Google Scholar 

  • Doursat, R., & Bienenstock, E.(2006). Neocortical self-structuration as a basis for learning. In 5th International Conference on Development and Learning (ICDL 2006) (pp. 1–6).

  • Durstewitz, D., Seamans, J. K., & Sejnowski, T. J. (2000). Neurocomputational models of working memory. Nature Neuroscience, 3, 1184–1191.

    Article  PubMed  CAS  Google Scholar 

  • Elman, J. L. (1990). Finding structure in time. Cognitive Science, 14(2), 179–211.

    Article  Google Scholar 

  • Fiete, I. R., Senn, W., Wang, C. Z. H., & Hahnloser, R. H. R. (2010). Spike-time-dependent plasticity and heterosynaptic competition organize networks to produce long scale-free sequences of neural activity. Neuron, 65(4), 563–576.

    Article  PubMed  CAS  Google Scholar 

  • Freund, T., & Buzsáki, G. (1998). Interneurons of the hippocampus. Hippocampus, 6(4), 347–470.

    Article  Google Scholar 

  • Fries, P. (2005). A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence. Trends in Cognitive Sciences, 9(10), 474–480.

    Article  PubMed  Google Scholar 

  • Funahashi, S. (2006). Prefrontal cortex and working memory processes. Neuroscience, 139(1), 251–261.

    Article  PubMed  CAS  Google Scholar 

  • Fuster, J. M., & Alexander, G. E. (1971). Neuron activity related to short-term memory. Science, 173(3997), 652–654.

    Article  PubMed  CAS  Google Scholar 

  • Goldman, M. S. (2009). Memory without feedback in a neural network. Neuron, 61(4), 621–634.

    Article  PubMed  CAS  Google Scholar 

  • Gutkin, B. S., Laing, C. R., Colby, C. L., Chow, C. C., & Ermentrout, G. B. (2001). Turning on and off with excitation: The role of spike-timing asynchrony and synchrony in sustained neural activity. Journal of Computational Neuroscience, 11, 121–134.

    Article  PubMed  CAS  Google Scholar 

  • Guyon, I., Personnaz, L., Nadal, J., & Dreyfus, G. (1988). Storage and retrieval of complex sequences in neural networks. Physical Review A, 38(12), 6365–6372.

    Article  PubMed  Google Scholar 

  • Hájos, N., Pálhalmi, J., Mann, E. O., Németh, B., Paulsen, O., & Freund, T. F. (2004). Spike timing of distinct types of GABAergic interneuron during hippocampal gamma oscillations in vitro. The Journal of Neuroscience: The official journal of the Society for Neuroscience, 24(41), 9127–9137.

    Article  Google Scholar 

  • Hanuschkin, A., Diesmann, M., & Morrison, A. (2010). A reafferent model of song syntax generation in the Bengalese finch. BMC Neuroscience, 11(Suppl 1), 33.

    Article  Google Scholar 

  • Horn, D., Levy, N., & Ruppin, E. (2000). Distributed synchrony in an attractor of spiking neurons. Neurocomputing, 32–33, 409–414.

    Article  Google Scholar 

  • Horn, D., & Usher, M. (1992). Oscillatory model of short term memory. In J. Moody (Ed.), Advances in neural information processing systems (Vol. 4). Morgan Kaufmann.

  • Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., et al. (2004). Synfire chains and cortical songs: Temporal modules of cortical activity. Science, 304(5670), 559–564.

    Article  PubMed  CAS  Google Scholar 

  • Itskov, V., Curto, C., Pastalkova, E., & Buzsáki, G. (2011). Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus. The Journal of Neuroscience, 31(8), 2828–2834.

    Article  PubMed  CAS  Google Scholar 

  • Izhikevich, E. M. (2006). Polychronization: Computation with spikes. Neural Computation, 18(2), 245–282.

    Article  PubMed  Google Scholar 

  • Jensen, O. (2006). Maintenance of multiple working memory items by temporal segmentation. Neuroscience, 139(1), 237–249.

    Article  PubMed  CAS  Google Scholar 

  • Jordan, M. (1986). Attractor dynamics and parallelism in a connectionist sequential machine. In: Proceedings of the eighth annual conference of the cognitive science society (pp. 531–546). Hillsdale: Lawrence Erlbaum Associates, Inc.

    Google Scholar 

  • Jun, J. K. & Jin, D. Z. (2007). Development of neural circuitry for precise temporal sequences through spontaneous activity, axon remodeling, and synaptic plasticity. PLoS ONE, 2(1), e723.

    Article  PubMed  Google Scholar 

  • Karbowski, J., & Ermentrout, G. (2002). Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Physical Review E, 65(3), 1–5.

    Article  Google Scholar 

  • Karmarkar, U. R., & Buonomano, D. V. (2007). Timing in the absence of clocks: Encoding time in neural network states. Neuron, 53(3), 427–438. http://www.ncbi.nlm.nih.gov/pubmed/17270738.

    Article  PubMed  CAS  Google Scholar 

  • Kunkel, S., Diesmann, M., & Morrison, A. (2011). Limits to the development of feed-forward structures in large recurrent neuronal networks. Front Comput Neurosci, 4, 160.

    PubMed  Google Scholar 

  • Kleinfeld, D., & Sompolinsky, H. (1988). Associative neural network model for the generation of temporal patterns: Theory and application to central pattern generators. Biophysical Journal, 54, 1039–1051.

    Article  PubMed  CAS  Google Scholar 

  • Lisman, J., & Buzsáki, G. (2008). A neural coding scheme formed by the combined function of gamma and theta oscillations. Schizophrenia Bulletin 34(5), 974–980.

    Article  PubMed  Google Scholar 

  • Lisman, J. E., & Idiart, M.A. (1995). Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science, 267(5203), 1512–1515.

    Article  PubMed  CAS  Google Scholar 

  • Liu, J. K., & Buonomano, D. V. (2009). Embedding multiple trajectories in simulated recurrent neural networks in a self-organizing manner. The Journal of neuroscience: The official journal of the Society for Neuroscience, 29(42), 13,172–13,181.

    Article  CAS  Google Scholar 

  • Luczak, A., Barthó, P., & Harris, K. D. (2009). Spontaneous events outline the realm of possible sensory responses in neocortical populations. Neuron, 62(3), 413–425.

    Article  PubMed  CAS  Google Scholar 

  • Luczak, A., Barthó, P., Marguet, S. L., Buzsáki, G., & Harris, K. D. (2007). Sequential structure of neocortical spontaneous activity in vivo. Proceedings of the National Academy of Sciences of the United States of America, 104(1), 347–352.

    Article  PubMed  CAS  Google Scholar 

  • Mauk, M. D., & Buonomano, D. V. (2004). The neural basis of temporal processing. Annual Review of Neuroscience, 27, 307–340.

    Article  PubMed  CAS  Google Scholar 

  • Meskenaite, V. (1997). Calretinin-immunoreactive local circuit neurons in area 17 of the cynomolgus monkey, Macaca fascicularis. The Journal of Comparative Neurology, 379(1), 113–32.

    Article  PubMed  CAS  Google Scholar 

  • Minai, A., & Levy, W. (1993). Sequence learning in a single trial. In INNS World congress neural networks II (Vol. 2, pp. 505–508).

  • Morrison, A., Aertsen, A., & Diesmann, M. (2007). Spike-timing-dependent plasticity in balanced random networks. Neural Computation, 19(6), 1437–1467.

    Article  PubMed  Google Scholar 

  • Mountcastle, V. B. (1997). The columnar organization of the neocortex. Brain: A Journal of Neurology, 120, 701–722.

    Article  Google Scholar 

  • Nádasdy, Z., Hirase, H., Czurkó, a., Csicsvari, J., & Buzsáki, G. (1999). Replay and time compression of recurring spike sequences in the hippocampus. The Journal of neuroscience: The Official Journal of the Society for Neuroscience, 19(21), 9497–9507.

    Google Scholar 

  • Nakamura, K., Mikami, A., & Kubota, K. (1992). Oscillatory neuronal activity related to visual short-term memory in monkey temporal pole. NeuroReport, 3(1), 117–120.

    Article  PubMed  CAS  Google Scholar 

  • Pastalkova, E., Itskov, V., Amarasingham, A., & Buzsáki, G. (2008). Internally generated cell assembly sequences in the rat hippocampus. Science, 321(5894), 1322–1327.

    Article  PubMed  CAS  Google Scholar 

  • Pesaran, B., Pezaris, J. S., Sahani, M., Mitra, P. P., & Andersen, R. A. (2002). Temporal structure in neuronal activity during working memory in macaque parietal cortex. Nature Neuroscience, 5(8), 805–811.

    Article  PubMed  CAS  Google Scholar 

  • Prut, Y., Vaadia, E., Bergman, H., Haalman, I., Slovin, H., & Abeles, M. (1998). Spatiotemporal structure of cortical activity: Properties and behavioral relevance. Journal of Neurophysiology, 79(6), 2857–2874.

    PubMed  CAS  Google Scholar 

  • Romo, R., Brody, C. D., Hernández, A., & Lemus, L. (1999). Neuronal correlates of parametric working memory in the prefrontal cortex. Nature, 399(6735), 470–473.

    Article  PubMed  CAS  Google Scholar 

  • van Rossum, M. C. W., Turrigiano, G. G., & Nelson, S. B. (2002). Fast propagation of firing rates through layered networks of noisy neurons.The Journal of Neuroscience: The official Journal of the Society for Neuroscience, 22(5), 1956–1966.

    Google Scholar 

  • Shaw, G., Silverman, D., Pearson, J. C. (1985). Model of cortical organization embodying a basis for a theory of information processing and memory recall. Proceedings of the National Academy of Sciences of the United States of America, 82, 2364–2368.

    Article  PubMed  CAS  Google Scholar 

  • Sompolinsky, H., & Kanter, I. (1986). Temporal association in asymmetric neural networks. Physical Review Letters, 57(22), 2861–2864.

    Article  PubMed  Google Scholar 

  • Song, S., Sjöström, P. J., Reigl, M., Nelson, S., & Chklovskii, D. B. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biology, 3(3), e68.

    Article  PubMed  Google Scholar 

  • Sun, R., & Giles, C. (2001). Sequence learning: From recognition and prediction to sequential decision making. IEEE Intelligent Systems, 16(4), 67–70.

    Article  Google Scholar 

  • Suri, R. E., & Sejnowski, T. J. (2002). Spike propagation synchronized by temporally asymmetric Hebbian learning. Biological Cybernetics, 87(5–6), 440–445.

    Article  PubMed  Google Scholar 

  • Sussillo, D., & Abbott, L. F. (2009). Generating coherent patterns of activity from chaotic neural networks. Neuron, 63(4), 544–557.

    Article  PubMed  CAS  Google Scholar 

  • Szatmáry, B., & Izhikevich, E. M. (2010). Spike-timing theory of working memory. PLoS Computational Biology, 6(8), e1000,879.

    Article  Google Scholar 

  • Tallon-Baudry, C., Bertrand, O., & Fischer, C. (2001). Oscillatory synchrony between human extrastriate areas during visual short-term memory maintenance. The Journal of Neuroscience: The official Journal of the Society for Neuroscience, 21(20), Rc177.

    Google Scholar 

  • Tang, A., Jackson, D., Hobbs, J., Chen, W., Smith, J. L., Patel, H., et al. (2008). A maximum entropy model applied to spatial and temporal correlations from cortical networks in vitro. The Journal of Neuroscience: The official Journal of the Society for Neuroscience, 28(2), 505–518.

    Article  CAS  Google Scholar 

  • Thiagarajan, T. C., Lebedev, M. A., Nicolelis, M. A., & Plenz, D. (2010). Coherence potentials: loss-less, all-or-none network events in the cortex. PLoS Biology 8(1), e1000,278.

    Article  Google Scholar 

  • Vogels, T. P., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. The Journal of Neuroscience: The official Journal of the Society for Neuroscience, 25(46), 10,786–10,795.

    Article  CAS  Google Scholar 

  • Wang, D., & Arbib, M. (1990). Complex temporal sequence learning based on short-term memory. Proceedings of the IEEE, 78(9), 1536–1543.

    Article  Google Scholar 

  • Wang, L. (1999). Multi-associative neural networks and their applications to learning and retrieving complex spatio-temporal sequences. IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics: A Publication of the IEEE Systems, Man, and Cybernetics Society, 29(1), 73–82.

    Article  CAS  Google Scholar 

  • Wang, X. J. (2001). Synaptic reverberation underlying mnemonic persistent activity. Trends in Neurosciences, 24(8), 455–63.

    Article  PubMed  CAS  Google Scholar 

  • Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12(1), 1–24.

    Article  PubMed  CAS  Google Scholar 

  • Yamashita, Y., Takahasi, M., Okumura, T., Ikebuchi, M., Yamada, H., Suzuki, M., et al. (2008). Developmental learning of complex syntactical song in the Bengalese finch: A neural network model. Neural Networks: The official Journal of the International Neural Network Society, 21(9), 1224–1231.

    Article  Google Scholar 

  • Yamazaki, T., & Tanaka, S. (2007). The cerebellum as a liquid state machine. Neural Networks: The Official Journal of the International Neural Network Society, 20(3), 290–297.

    Article  Google Scholar 

  • Yoshioka, M., Scarpetta, S., & Marinaro, M. (2007). Spike-timing-dependent synaptic plasticity to learn spatiotemporal patterns in recurrent neural networks. In M. D. S. E. A. J (Ed.), ICANN 2007, Part I, LNCS 4668 (Vol. 1, pp. 757–766). Berlin Heidelberg: Springer.

Download references

Acknowledgements

Sergio Oscar Verduzco-Flores was supported by a grant from the Mind Research Institute. Mark Bodner received support from the Gerard Foundation. Bard Ermentrout was supported by NSF grant DMS0817131.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sergio Oscar Verduzco-Flores.

Additional information

Action Editor: Carson C. Chow

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(PDF 519 KB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Verduzco-Flores, S.O., Bodner, M. & Ermentrout, B. A model for complex sequence learning and reproduction in neural populations. J Comput Neurosci 32, 403–423 (2012). https://doi.org/10.1007/s10827-011-0360-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-011-0360-x

Keywords

Navigation