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Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks

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Abstract

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.

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References

  • Akam, T., Oren, I., Mantoan, L., Ferenczi, E., & Kullmann, D. M. (2012). Oscillatory dynamics in the hippocampus support dentate gyrus-CA3 coupling. Nature Neuroscience, 15(5), 763–768.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Arieli, A., Sterkin, A., Grinvald, A., & Aertsen, A. (1996). Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science, 273(5283), 1868–1871.

    Article  CAS  PubMed  Google Scholar 

  • Bai, Z. (1997). Circular law. The Annals of Probability, 25(1), 494–529.

    Article  Google Scholar 

  • Banerjee, A., Seriv̀s, P., & Pouget, A. (2008). Dynamical constraints on using precise spike timing to compute in recurrent cortical networks. Neural Computation, 20(4), 974–993.

    Article  PubMed  Google Scholar 

  • Barak, O., Sussillo, D., Romo, R., Tsodyks, M., & Abbott, L. F. (2013). From fixed points to chaos: Three models of delayed discrimination. Progress in Neurobiology 103, 10.1016/j.pneurobio.2013.02.002.

  • Bernacchia, A., Seo, H., Lee, D., & Wang, X. J. (2011). A reservoir of time constants for memory traces in cortical neurons. Natural Neuroscience, 14(3), 366–372. doi:10.1038/nn.2752.

    Article  CAS  Google Scholar 

  • Bertschinger, N., & Natschläger, T. (2004). Real-time computation at the edge of chaos in recurrent neural networks. Neural Computation, 16(7), 1413–1436.

    Article  PubMed  Google Scholar 

  • Bonifazi, P., Goldin, M., Picardo, M. A., Jorquera, I., Cattani, A., Bianconi, G., Represa, A., Ben-Ari, Y., & Cossart, R. (2009). GABAergic hub neurons orchestrate synchrony in developing hippocampal networks. Science, 326(5958), 1419–1424.

    Article  CAS  PubMed  Google Scholar 

  • Brin, M., & Stuck, G. (2002). Introduction to dynamical systems: Cambridge University Press.

  • Buhusi, C.V., & Meck, W.H. (2005). What makes us tick? Functional and neural mechanisms of interval timing. Nature Reviews Neuroscience, 6(10), 755–765. doi:10.1038/nrn1764.

    Article  CAS  PubMed  Google Scholar 

  • Buonomano, D. V., & Maass, W. (2009). State-dependent computations: spatiotemporal processing in cortical networks. Nature Reviews Neuroscience, 10(2), 113–125.

    Article  CAS  PubMed  Google Scholar 

  • Buxhoeveden, D. P., & Casanova, M. F. (2002). The minicolumn hypothesis in neuroscience. Brain, 125(5), 935–951.

    Article  PubMed  Google Scholar 

  • Churchland, M. M., & Shenoy, K. V. (2007). Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. Journal of neurophysiology, 97(6), 4235–4257.

    Article  PubMed  Google Scholar 

  • Churchland, M. M., Cunningham, J. P., Kaufman, M. T., Foster, J. D., Nuyujukian, P., Ryu, S. I., & Shenoy, K. V. (2012). Neural population dynamics during reaching. Nature, 487(7405), 51–56. doi:10.1038/nature11129.

    CAS  PubMed  PubMed Central  Google Scholar 

  • De Zeeuw, C. I., Hoebeek, F. E., Bosman, L. W., Schonewille, M., Witter, L., & Koekkoek, S. K. (2011). Spatiotemporal firing patterns in the cerebellum. Nature Reviews Neuroscience, 12(6), 327–344.

    Article  CAS  PubMed  Google Scholar 

  • Enel, P. (2014). Dynamic representation in the prefrontal cortex : insights from comparing reservoir computing and primate neurophysiology: Theses, Université Claude Bernard - Lyon I.

  • Ermentrout, B. (1996). Type I membranes, phase resetting curves, and synchrony. Neural computation, 8(5), 979–1001.

    Article  CAS  PubMed  Google Scholar 

  • Farries, M. A., & Wilson, C. J. (2012). Phase response curves of subthalamic neurons measured with synaptic input and current injection. Journal of Neurophysiology, 108(7), 1822–1837. doi:10.1152/jn.00053.2012.

    Article  PubMed  PubMed Central  Google Scholar 

  • Fiete, I. R., Burak, Y., & Brookings, T. (2008). What grid cells convey about rat location. The Journal of Neuroscience, 28(27), 6858–6871.

    Article  CAS  PubMed  Google Scholar 

  • Froemke, R. C., & Schreiner, C. E. (2015). Synaptic plasticity as a cortical coding scheme. Current opinion in neurobiology, 35, 185–199.

    Article  CAS  PubMed  Google Scholar 

  • Fu, Y., Yu, Y., Paxinos, G., Watson, C., & Rusznák, Z. (2015). Aging-dependent changes in the cellular composition of the mouse brain and spinal cord. Neuroscience, 290(0), 406–420. doi:10.1016/j.neuroscience.2015.01.039.

    Article  CAS  PubMed  Google Scholar 

  • Goel, A., & Buonomano, D. V. (2014). Timing as an intrinsic property of neural networks: evidence from in vivo and in vitro experiments. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1637), 20120,460.

    Article  Google Scholar 

  • Häusler, S., Markram, H., & Maass, W. (2003). Perspectives of the high-dimensional dynamics of neural microcircuits from the point of view of low-dimensional readouts. Complexity, 8(4), 39– 50.

    Article  Google Scholar 

  • Haykin, S. (2002). Adaptive filter theory. Prentice Hall, 2, 478–481.

    Google Scholar 

  • Hoerzer, G. M., Legenstein, R., & Maass, W. (2014). Emergence of complex computational structures from chaotic neural networks through reward-modulated Hebbian learning. Cerebral cortex, 24(3), 677–690.

    Article  PubMed  Google Scholar 

  • Hooper, S. L. (2001). Central Pattern Generators. In eLS: Wiley.

  • Jaeger, H. (2002). Adaptive nonlinear system identification with echo state networks. pp 593–600.

  • Jarvis, S., Rotter, S., & Egert, U. (2010). Extending stability through hierarchical clusters in echo state networks. Frontiers in Neuroinformatics, 4.

  • Joshi, P., & Maass, W. (2005). Movement generation with circuits of spiking neurons. Neural Computation, 17(8), 1715–1738.

    Article  PubMed  Google Scholar 

  • Kahana, M. J. (2006). The cognitive correlates of human brain oscillations. The Journal of Neuroscience, 26 (6), 1669–1672.

    Article  CAS  PubMed  Google Scholar 

  • Keller, C. J., Honey, C. J., Mégevand, P, Entz, L., Ulbert, I., & Mehta, A. D. (2014). Mapping human brain networks with cortico-cortical evoked potentials. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1653), 20130, 528.

    Article  Google Scholar 

  • Laje, R., & Buonomano, D. V. (2013). Robust timing and motor patterns by taming chaos in recurrent neural networks. Natural Neuroscience, 16. doi:10.1038/nn.3405.

  • Lajoie, G., Lin, K. K., & Shea-Brown, E. (2013). Chaos and reliability in balanced spiking networks with temporal drive. Physical Review E, 87(5), 052,901.

    Article  Google Scholar 

  • Lajoie, G., Thivierge, J. P., & Shea-Brown, E. (2014). Structured chaos shapes spike-response noise entropy in balanced neural networks. Frontiers in Computational Neuroscience, 8. doi:10.3389/fncom.2014.00123.

  • Li, X., Zhong, L., Xue, F., & Zhang, A. (2015). A Priori Data-Driven Multi-Clustered Reservoir Generation Algorithm for Echo State Network. PloS One, 10(4).

  • London, M., Roth, A., Beeren, L., Häusser, M., & Latham, P. E. (2010). Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature, 466(7302), 123–127.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lustig, C., Matell, M. S., & Meck, W. H. (2003). Not “just” a coincidence: Frontal-striatal interactions in working memory and interval timing. Memory, 13(3-4), 441–448.

    Google Scholar 

  • Maass, W., Natschläger, T., & Markram, H. (2002). Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation, 14(11), 2531–2560.

    Article  PubMed  Google Scholar 

  • MacKay, W. A. (2005). Wheels of motion: oscillatory potentials in the motor cortex. Motor Cortex in Voluntary Movements: A Distributed System for Distributed Functions, 181–211.

  • Mainen, Z. F., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268 (5216), 1503–1506.

    Article  CAS  PubMed  Google Scholar 

  • Mante, V., Sussillo, D., Shenoy, K. V., & Newsome, W. T. (2013). Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature, 503(7474), 78–84.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Mazurek, M. E., Roitman, J. D., Ditterich, J., & Shadlen, M. N. (2003). A role for neural integrators in perceptual decision making. Cerebral cortex, 13(11), 1257–1269.

    Article  PubMed  Google Scholar 

  • Meunier, D., Lambiotte, R., & Bullmore, E. T. (2010). Modular and hierarchically modular organization of brain networks. Frontiers in neuroscience, 4.

  • Miall, C. (1989). The storage of time intervals using oscillating neurons. Neural Computation, 1(3), 359–371.

    Article  Google Scholar 

  • Molgedey, L., Schuchhardt, J., & Schuster, H. G. (1992). Suppressing chaos in neural networks by noise. Physical Review Letters, 69(26), 3717–3719.

    Article  PubMed  Google Scholar 

  • Mountcastle, V. B. (1997). The columnar organization of the neocortex. Brain, 120(4), 701–722.

    Article  PubMed  Google Scholar 

  • Pakkenberg, B., Pelvig, D., Marner, L., Bundgaard, M. J., Gundersen, H. J. G., Nyengaard, J. R., & Regeur, L. (2003). Aging and the human neocortex. Proceedings of the 6th International Symposium on the Neurobiology and Neuroendocrinology of Aging, 38(1-2), 95–99. doi:10.1016/S0531-5565(02)00151-1.

    Google Scholar 

  • Perin, R., Berger, T. K., & Markram, H. (2011). A synaptic organizing principle for cortical neuronal groups. Proceedings of the National Academy of Sciences, 108(13), 5419–5424.

    Article  CAS  Google Scholar 

  • Perrett, S. P., Ruiz, B. P., & Mauk, M. D. (1993). Cerebellar cortex lesions disrupt learning-dependent timing of conditioned eyelid responses. The Journal of Neuroscience, 13(4), 1708–1718.

    CAS  PubMed  Google Scholar 

  • Rajan, K., Abbott, L., & Sompolinsky, H. (2010). Stimulus-dependent suppression of chaos in recurrent neural networks. Physical Review E, 82(1), 011,903.

    Article  Google Scholar 

  • Romo, R., Brody, C. D., Hernandez, A., & Lemus, L. (1999). Neuronal correlates of parametric working memory in the prefrontal cortex. Nature, 399(6735), 470–473. doi:10.1038/20939.

    Article  CAS  PubMed  Google Scholar 

  • Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage, 52(3), 1059–1069.

    Article  PubMed  Google Scholar 

  • Rubinov, M., Sporns, O., Thivierge, J. P., & Breakspear, M. (2011). Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons. PLoS computational biology, 7(6), e1002,038.

    Article  CAS  Google Scholar 

  • Soderstrand, M. A., Jenkins, W. K., Jullien, G. A., & Taylor, F. J. (Eds.) (1986). Residue Number System Arithmetic: Modern Applications in Digital Signal Processing. NJ, USA: IEEE Press.

  • Sompolinsky, H., Crisanti, A., & Sommers, H. (1988). Chaos in random neural networks. Physical Review Letters, 61(3), 259.

    Article  PubMed  Google Scholar 

  • Sussillo, D., & Abbott, L. F. (2009). Generating Coherent Patterns of Activity from Chaotic Neural Networks. Neuron, 63. doi:10.1016/j.neuron.2009.07.018.

  • Sussillo, D., & Barak, O. (2013). Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural Computation, 25(3), 626–649.

    Article  PubMed  Google Scholar 

  • Sussillo, D., Churchland, M. M., Kaufman, M. T., & Shenoy, K. V. (2015). A neural network that finds a naturalistic solution for the production of muscle activity. Nature Neuroscience, 18(7), 1025–1033.

    Article  CAS  PubMed  Google Scholar 

  • Tiesinga, P., Fellous, J. M., & Sejnowski, T. J. (2008). Regulation of spike timing in visual cortical circuits. Nature Reviews Neuroscience, 9(2), 97–107.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Toledo-Suárez, C., Duarte, R., & Morrison, A. (2014). Liquid computing on and off the edge of chaos with a striatal microcircuit. Frontiers in Computational Neuroscience, 8.

  • Van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274(5293), 1724–1726.

    Article  CAS  PubMed  Google Scholar 

  • Westlye, L. T., Walhovd, K. B., Dale, A. M., Bjørnerud, A., Due-Tønnessen, P., Engvig, A., Grydeland, H., Tamnes, C. K., Østby, Y., & Fjell, A. M. (2009). Life-span changes of the human brain white matter: diffusion tensor imaging (DTI) and volumetry. Cerebral cortex p bhp280.

  • Yamazaki, T., & Tanaka, S. (2007). The cerebellum as a liquid state machine. Neural Networks, 20(3), 290–297.

    Article  PubMed  Google Scholar 

  • Yuste, R., MacLean, J. N., Smith, J., & Lansner, A. (2005). The cortex as a central pattern generator. Nature Reviews Neuroscience, 6(6), 477–483.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

This work was supported by a Discovery grant from the Natural Sciences and Engineering Council of Canada (NSERC Grant No. 210977 and No. 210989), operating funds from the Canadian Institutes of Health Research (CIHR Grant No. 6105509), and the University of Ottawa Brain and Mind Institute (uOBMI), scholarships awarded to PVL from the Ontario Graduate Scholarship (OGS) and the Fonds de recherche Nature et technologies (FQRNT) as well as a FQRNT postdoctoral fellowship, a Bernstein Fellowship and an Innovation Fellowship from the Washington Research Foundation to GL. We would like to thank Eric S. Kuebler and Nareg Berberian for their helpful comments.

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  1. School of Psychology and Center for Neural Dynamics, University of Ottawa, Ottawa, Ontario, Canada

    Philippe Vincent-Lamarre & Jean-Philippe Thivierge

  2. UW Institute for Neuroengineering, University of Washington, Seattle, Washington, US

    Guillaume Lajoie

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  1. Philippe Vincent-Lamarre
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Correspondence to Philippe Vincent-Lamarre.

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Vincent-Lamarre, P., Lajoie, G. & Thivierge, JP. Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks. J Comput Neurosci 41, 305–322 (2016). https://doi.org/10.1007/s10827-016-0619-3

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