Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits

Nature Neuroscience volume 24, pages 1010–1019 (2021)Cite this article

Subjects

An Author Correction to this article was published on 02 November 2021

This article has been updated

Abstract

Synaptic plasticity is believed to be a key physiological mechanism for learning. It is well established that it depends on pre- and postsynaptic activity. However, models that rely solely on pre- and postsynaptic activity for synaptic changes have, so far, not been able to account for learning complex tasks that demand credit assignment in hierarchical networks. Here we show that if synaptic plasticity is regulated by high-frequency bursts of spikes, then pyramidal neurons higher in a hierarchical circuit can coordinate the plasticity of lower-level connections. Using simulations and mathematical analyses, we demonstrate that, when paired with short-term synaptic dynamics, regenerative activity in the apical dendrites and synaptic plasticity in feedback pathways, a burst-dependent learning rule can solve challenging tasks that require deep network architectures. Our results demonstrate that well-known properties of dendrites, synapses and synaptic plasticity are sufficient to enable sophisticated learning in hierarchical circuits.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The credit assignment problem for hierarchical networks.
Fig. 2: Burst-dependent plasticity rule.
Fig. 3: Dendrite-dependent bursting combined with short-term plasticity supports the simultaneous propagation of bottom-up and top-down signals.
Fig. 4: Burst-dependent plasticity can solve the credit assignment problem for the XOR task.
Fig. 5: Burst-dependent plasticity of recurrent and feedback connections promotes gradient-based learning by linearizing and aligning feedback.
Fig. 6: Ensemble-level burst-dependent plasticity supports learning in deep networks.

Similar content being viewed by others

Data availability

The MNIST, CIFAR-10 (ref. 76) and ImageNet77 datasets are publicly available from http://yann.lecun.com/exdb/mnist/, https://www.cs.toronto.edu/~kriz/cifar.html and http://www.image-net.org, respectively.

Code availability

The code used in this article is available at https://github.com/apayeur/spikingburstprop and https://github.com/jordan-g/Burstprop.

Change history

References

  1. Hebb, D. O. The Organization of Behavior (Wiley, New York, 1949).

    Google Scholar 

  2. Artola, A., Bröcher, S. & Singer, W. Different voltage dependent thresholds for inducing long-term depression and long-term potentiation in slices of rat visual cortex. Nature 347, 69–72 (1990).

    Article  CAS  PubMed  Google Scholar 

  3. Markram, H., Lübke, J., Frotscher, M. & Sakmann, B. Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275, 213–215 (1997).

    Article  CAS  PubMed  Google Scholar 

  4. Paulsen, O. & Sejnowski, T. J. Natural patterns of activity and long-term synaptic plasticity. Curr. Opin. Neurobiol. 10, 172–180 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Sjöström, P. J., Turrigiano, G. G. & Nelson, S. B. Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32, 1149–1164 (2001).

    Article  PubMed  Google Scholar 

  6. Letzkus, J. J., Kampa, B. M. & Stuart, G. J. Learning rules for spike timing-dependent plasticity depend on dendritic synapse location. J. Neurosci. 26, 10420–10429 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Kampa, B., Letzkus, J. & Stuart, G. Requirement of dendritic calcium spikes for induction of spike-timing-dependent synaptic plasticity. J. Physiol. 574, 283–290 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Sjöström, P. J. & Häusser, M. A cooperative switch determines the sign of synaptic plasticity in distal dendrites of neocortical pyramidal neurons. Neuron 51, 227–238 (2006).

    Article  PubMed  Google Scholar 

  9. Gambino, F. et al. Sensory-evoked LTP driven by dendritic plateau potentials in vivo. Nature 515, 116–119 (2014).

    Article  CAS  PubMed  Google Scholar 

  10. Geun Hee, S. et al. Neuromodulators control the polarity of spike-timing-dependent synaptic plasticity. Neuron 55, 919–929 (2007).

    Article  Google Scholar 

  11. Gerstner, W., Lehmann, M., Liakoni, V., Corneil, D. & Brea, J. Eligibility traces and plasticity on behavioral time scales: experimental support of neoHebbian three-factor learning rules. Front. Neural Circuits 12, 53 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  12. Roelfsema, P. R. & Holtmaat, A. Control of synaptic plasticity in deep cortical networks. Nat. Rev. Neurosci. 19, 166–180 (2018).

    Article  CAS  PubMed  Google Scholar 

  13. Williams, R. J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning 8, 229–256 (1992).

    Article  Google Scholar 

  14. Werfel, J., Xie, X. & Seung, H. S. Learning curves for stochastic gradient descent in linear feedforward networks. Neural Comput. 17, 2699–2718 (2005).

    Article  PubMed  Google Scholar 

  15. Lillicrap, T. P., Santoro, A., Marris, L., Akerman, C. J. & Hinton, G. Backpropagation and the brain. Nat. Rev. Neurosci. 21, 335–346 (2020).

  16. Richards, B. A. et al. A deep learning framework for systems neuroscience. Nat. Neurosci. 22, 1761–1770 (2019).

  17. Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning representations by back-propagating errors. Nature 323, 533–536 (1986).

    Article  Google Scholar 

  18. Larkum, M. E., Zhu, J. & Sakmann, B. A new cellular mechanism for coupling inputs arriving at different cortical layers. Nature 398, 338–341 (1999).

    Article  CAS  PubMed  Google Scholar 

  19. Markram, H., Wang, Y. & Tsodyks, M. Differential signaling via the same axon of neocortical pyramidal neurons. Proc. Natl. Acad. Sci. USA 95, 5323–5328 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Nevian, T. & Sakmann, B. Spine Ca2+ signaling in spike-timing-dependent plasticity. J. Neurosci. 26, 11001–11013 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Froemke, R. C., Tsay, I. A., Raad, M., Long, J. D. & Dan, Y. Contribution of individual spikes in burst-induced long-term synaptic modification. J. Neurophys. 95, 1620–1629 (2006).

    Article  Google Scholar 

  22. Bell, C. C., Caputi, A., Grant, K. & Serrier, J. Storage of a sensory pattern by anti-Hebbian synaptic plasticity in an electric fish. Proc. Natl Acad. Sci. USA 90, 4650–4654 (1993).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Bol, K., Marsat, G., Harvey-Girard, E., Longtin, André & Maler, L. Frequency-tuned cerebellar channels and burst-induced LTD lead to the cancellation of redundant sensory inputs. J. Neurosci. 31, 11028–11038 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Richards, B. A. & Lillicrap, T. P. Dendritic solutions to the credit assignment problem. Curr. Opin. Neurobiol. 54, 28–36 (2019).

    Article  CAS  PubMed  Google Scholar 

  25. Brandalise, F. & Gerber, U. Mossy fiber-evoked subthreshold responses induce timing-dependent plasticity at hippocampal Ca3 recurrent synapses. Proc. Natl Acad. Sci. USA 111, 4303–4308 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Kayser, C., Montemurro, M. A., Logothetis, N. K. & Panzeri, S. Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron 61, 597–608 (2009).

    Article  CAS  PubMed  Google Scholar 

  27. Herzfeld, D. J., Kojima, Y., Soetedjo, R. & Shadmehr, R. Encoding of action by the purkinje cells of the cerebellum. Nature 526, 439–442 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Naud, R. & Sprekeler, H. Sparse bursts optimize information transmission in a multiplexed neural code. Proc. Nat. Acad. Sci. USA 115, 6329–6338 (2018).

  29. Burbank, K. S. Mirrored STDP implements autoencoder learning in a network of spiking neurons. PLoS Comp. Biol. 11, e1004566 (2015).

    Article  Google Scholar 

  30. Akrout, M., Wilson, C., Humphreys, P. C., Lillicrap, T. & Tweed, D. Using weight mirrors to improve feedback alignment. Preprint at arXiv https://arxiv.org/abs/1904.05391 (2019).

  31. Murayama, M. et al. Dendritic encoding of sensory stimuli controlled by deep cortical interneurons. Nature 457, 1137–1141 (2009).

    Article  CAS  PubMed  Google Scholar 

  32. Körding, K. P. & König, P. Supervised and unsupervised learning with two sites of synaptic integration. J. Comput. Neurosci. 11, 207–215 (2001).

    Article  PubMed  Google Scholar 

  33. Granseth, B., Ahlstrand, E. & Lindström, S. Paired pulse facilitation of corticogeniculate epscs in the dorsal lateral geniculate nucleus of the rat investigated in vitro. J. Physiol. 544, 477–486 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Sherman, S. M. Thalamocortical interactions. Curr. Opin. Neurobiol. 22, 575–579 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Meredith, R. M., Floyer-Lea, A. M. & Paulsen, O. Maturation of long-term potentiation induction rules in rodent hippocampus: role of gabaergic inhibition. J. Neurosci. 23, 11142–11146 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Inglebert, Y., Aljadeff, J., Brunel, N. & Debanne, D. Synaptic plasticity rules with physiological calcium levels. Proc. Natl Acad.Sci. USA 117, 33639–33648 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Kampa, B. M. & Stuart, G. J. Calcium spikes in basal dendrites of layer 5 pyramidal neurons during action potential bursts. J. Neurosci. 26, 7424–32 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Doron, G. et al. Perirhinal input to neocortical layer 1 controls learning. Science 370, eaaz3136 (2020).

  39. Mäki-Marttunen, T., Iannella, N., Edwards, A. G., Einevoll, G. & Blackwell, K. T. A unified computational model for cortical post-synaptic plasticity. eLife 9, e55714 (2020).

  40. Bienenstock, E. L., Cooper, L. N. & Munro, P. W. Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci. 2, 32–48 (1982).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Ning-Long, X. et al. Nonlinear dendritic integration of sensory and motor input during an active sensing task. Nature 492, 247–251 (2012).

    Article  Google Scholar 

  42. Felleman, D. J. & van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–47 (1991).

    Article  CAS  PubMed  Google Scholar 

  43. Sacramento, J., Costa, R. C., Bengio, Y. & Senn, W. Dendritic cortical microcircuits approximate the backpropagation algorithm. Adv. Neural Inf. Process. Syst. 31, 8721–8732 (2018).

    Google Scholar 

  44. Bartunov, S. et al. Assessing the scalability of biologically-motivated deep learning algorithms and architectures. Adv. Neural Inf. Process. Syst. 31, 9368–9378 (2018).

    Google Scholar 

  45. Boerlin, M., Machens, C. K. & Denève, S. Predictive coding of dynamical variables in balanced spiking networks. PLoS Comp. Biol. 9, e1003258 (2013).

    Article  Google Scholar 

  46. Petreanu, L., Mao, T., Sternson, S. M. & Svoboda, K. The subcellular organization of neocortical excitatory connections. Nature 457, 1142–1145 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Ren, Si-Qiang, Li, Z., Lin, S., Bergami, M. & Shi, S.-H. Precise long-range microcircuit-to-microcircuit communication connects the frontal and sensory cortices in the mammalian brain. Neuron 104, 385–401.e3 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Golding, N. L., Staff, N. P. & Spruston, N. Dendritic spikes as a mechanism for cooperative long-term potentiation. Nature 418, 326–331 (2002).

    Article  CAS  PubMed  Google Scholar 

  49. Wang, X. et al. Feedforward excitation and inhibition evoke dual modes of firing in the cat’s visual thalamus during naturalistic viewing. Neuron 55, 465–478 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Owen, S. F., Berke, J. D. & Kreitzer, A. C. Fast-spiking interneurons supply feedforward control of bursting, calcium, and plasticity for efficient learning. Cell 172, 683–695 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Zenke, F. & Gerstner, W. Limits to high-speed simulations of spiking neural networks using general-purpose computers. Front. Neuroinf. 8, 76 (2014).

    Article  Google Scholar 

  52. Bittner, K. C., Milstein, A. D., Grienberger, C., Romani, S. & Magee, J. C. Behavioral time scale synaptic plasticity underlies ca1 place fields. Science 357, 1033–1036 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Tremblay, R., Lee, S. & Rudy, B. Gabaergic interneurons in the neocortex: from cellular properties to circuits. Neuron 91, 260–292 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Nigro, M. J., Hashikawa-Yamasaki, Y. & Rudy, B. Diversity and connectivity of layer 5 somatostatin-expressing interneurons in the mouse barrel cortex. J. Neurosci. 38, 1622–1633 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Hilscher, M. M., Leão, R. N., Edwards, S. J., Leão, K. E. & Kullander, K. ChRNA2-Martinotti cells synchronize layer 5 type a pyramidal cells via rebound excitation. PLOS Biol. 15, e200139226 (2017).

  56. Naud, R., Marcille, N., Clopath, C. & Gerstner, W. Firing patterns in the adaptive exponential integrate-and-fire model. Biol. Cybern. 99, 335–347 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  57. Packer, A. M. & Yuste, R. Dense, unspecific connectivity of neocortical parvalbumin-positive interneurons: a canonical microcircuit for inhibition? J. Neurosci. 31, 13260–13271 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. De Kock, C. P. J. & Sakmann, B. High frequency action potential bursts (>100 Hz) in l2/3 and l5b thick tufted neurons in anaesthetized and awake rat primary somatosensory cortex. J. Physiol. 586, 3353–3364 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  59. Womelsdorf, T., Ardid, S., Everling, S. & Valiante, T. A. Burst firing synchronizes prefrontal and anterior cingulate cortex during attentional control. Current Biology 24, 2613–2621 (2014).

    Article  CAS  PubMed  Google Scholar 

  60. Costa, R. P., Sjöström, P. J. & Van Rossum, M. C. W. Probabilistic inference of short-term synaptic plasticity in neocortical microcircuits. Front. Comput. Neurosci. 7, 75 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  61. Samadi, A., Lillicrap, T. P. & Tweed, D. B. Deep learning with dynamic spiking neurons and fixed feedback weights. Neural Comput. 29, 578–602 (2017).

    Article  PubMed  Google Scholar 

  62. Guerguiev, J., Lillicrap, T. P. & Richards, B. A. Towards deep learning with segregated dendrites. eLife 6, e22901 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  63. Lee, D.-H., Zhang, S., Fischer, A. & Bengio, Y. Difference target propagation. In Proc. Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ed. Hutter, F. et al.) 498–515 (Springer, 2015).

  64. Liao, Q., Leibo, J. Z. & Poggio, T. How important is weight symmetry in backpropagation? In Proc. Thirtieth AAAI Conference on Artificial Intelligence (ed. Schuurmans, D. et al.) 1837–1844 (AAAI, 2016).

  65. Xiao, W., Chen, H., Liao, Q. & Poggio, T. Biologically-plausible learning algorithms can scale to large datasets. Preprint at arXiv https://arxiv.org/abs/1811.03567 (2018).

  66. Lillicrap, T. C., Cownden, D., Tweed, D. B. & Akerman, C. J. Random synaptic feedback weights support error backpropagation for deep learning. Nature Commun. 7, 13276 (2016).

  67. Scellier, B. & Bengio. Y. Towards a biologically plausible backprop. Preprint at arXiv https://arxiv.org/abs/1602.05179v5 (2016).

  68. Yali, A. Deep learning with asymmetric connections and Hebbian updates. Front. Comput. Neurosci. https://doi.org/10.3389/fncom.2019.00018 (2019).

  69. Whittington, J. C. R. & Bogacz, R. Theories of error back-propagation in the brain. Trends Cogn. Sci. 23, 235–250 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  70. Mostafa, H., Ramesh, V. & Cauwenberghs, G. Deep supervised learning using local errors. Front. Neurosci. 12, 608 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  71. Nokland, A. Direct feedback alignment provides learning in deep neural networks. Adv. Neural Inf. Process. Syst. 29, 1037–1045 (2016).

    Google Scholar 

  72. Lansdell, B., J., Prakash, P. R. & Kording, K. P. Learning to solve the credit assignment problem. Preprint at arXiv https://arxiv.org/abs/1906.00889v4 (2019).

  73. Pozzi, I., Bohté, S. & Roelfsema, P. A biologically plausible learning rule for deep learning in the brain. Preprint at arXiv https://arxiv.org/abs/1811.01768 (2018).

  74. Laborieux, A. et al. Scaling equilibrium propagation to deep convnets by drastically reducing its gradient estimator bias. Front. Neurosci. 15, 129 (2021).

    Article  Google Scholar 

  75. Kolen, J. F. & Pollack, J. B. Backpropagation without weight transport. In Proc. 1994 IEEE International Conference on Neural Networks (ICNN’94) Vol. 3, 1375–1380 (IEEE, 1994).

  76. Krizhevsky, A., Nair, V. & Hinton, G. Cifar-10 (Canadian Institute for Advanced Research) Technical Report (Univ. Toronto, 2009).

  77. Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K. & Fei-Fei, L. ImageNet: a large-scale hierarchical image database. In Proc. CVPR09 248–255 (IEEE, 2009).

  78. He, K., Zhang, X., Ren, S. & Sun, J. Delving deep into rectifiers: surpassing human-level performance on imagenet classification. In Proc. IEEE International Conference on Computer Vision 1026–1034 (IEEE, 2015).

  79. Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proc. Thirteenth International Conference on Artificial Intelligence and Statistics (ed. Whye Teh, Y. et al.) 249–256 (Society for Artificial Intelligence and Statistics, 2010).

Download references

Acknowledgements

We thank A. Santoro and L. Maler for comments on this manuscript. We also thank M. Hilscher and M.J. Nigro for sharing data about SOM+ neurons. In addition, we thank T. Mesnard for helping with the development of the rate-based model. This work was supported by two NSERC Discovery grants (to R.N., no. 06872 and to B.A.R., no. 04947), a CIHR Project grant (no. RN383647-418955), a Fellowship from the CIFAR Learning in Machines and Brains Program (to B.A.R.), an Ontario Early Researcher Award (to B.A.R., no. ER 17-13-242), a Healthy Brains, Healthy Lives New Investigator Start-up (to B.A.R., no. 2b-NISU-8) the Novartis Research Foundation (to F.Z.).

Author information

Author notes

  1. Alexandre Payeur

    Present address: University of Montréal and Mila, Montréal, QC, Canada

  2. These authors contributed equally: Alexandre Payeur, Jordan Guerguiev.

  3. These authors jointly supervised this work: Blake A. Richards, Richard Naud.

Authors and Affiliations

  1. Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, ON, Canada

    Alexandre Payeur & Richard Naud

  2. Ottawa Brain and Mind Institute, University of Ottawa, Ottawa, ON, Canada

    Alexandre Payeur & Richard Naud

  3. Centre for Neural Dynamics, University of Ottawa, Ottawa, ON, Canada

    Alexandre Payeur & Richard Naud

  4. Department of Biological Sciences, University of Toronto Scarborough, Toronto, ON, Canada

    Jordan Guerguiev

  5. Department of Cell and Systems Biology, University of Toronto, Toronto, ON, Canada

    Jordan Guerguiev

  6. Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland

    Friedemann Zenke

  7. Mila, Montréal, QC, Canada

    Blake A. Richards

  8. Department of Neurology and Neurosurgery, McGill University, Montréal, QC, Canada

    Blake A. Richards

  9. School of Computer Science, McGill University, Montréal, QC, Canada

    Blake A. Richards

  10. Learning in Machines and Brains Program, Canadian Institute for Advanced Research, Toronto, ON, Canada

    Blake A. Richards

  11. Department of Physics, University of Ottawa, Ottawa, ON, Canada

    Richard Naud

Authors
  1. Alexandre Payeur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jordan Guerguiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Friedemann Zenke
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Blake A. Richards
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Richard Naud
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the burst-dependent learning rule. A.P., F.Z. and R.N. designed the spiking simulations. A.P. performed the spiking simulations. J.G. designed the recurrent plasticity rule and performed the numerical experiments on CIFAR-10 and ImageNet. B.A.R. and R.N. wrote the manuscript, with contributions from J.G. and A.P. B.A.R. and R.N. cosupervised the project.

Corresponding authors

Correspondence to Blake A. Richards or Richard Naud.

Ethics declarations

Competing interests

R.N., B.A.R. and A.P. have a provisional patent application for a neuromorphic implementation of the algorithm described in this article. The other authors declare no competing interests.

Additional information

Peer review information Nature Neuroscience thanks Gabriel Kreiman, Panayiota Poirazi and Nelson Spruston for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Effects of population size, randomized examples and absence of hidden-layer plasticity on the XOR task.

a, Comparison of costs for the XOR task. In blue is the cost for the network in Fig. 4 in the main text, but with 2000 neurons per population and slightly different parameter values. The dot-dashed pink line is for when the examples are randomly selected within an epoch. The dotted red line has no plasticity in the hidden layer. The dashed green line is for 400 neurons per population. b-e, Output event rate (ER) after learning. The dashed grey line separates ‘true (1)’ and ‘false (0)’ for the XOR. Only in c is XOR not solved.

Extended Data Fig. 2 Impact of different time scales on the XOR task.

a, Comparison of costs for when the duration of examples T (in s) (dashed green line) and the moving average time constant τavg (in s) (dotted orange line) are changed with respect to the values used in Fig. 4 (solid blue). b, Output event rate (ER) after learning for the three cases in panel a. The dashed grey line separates ‘true (1)’ and ‘false (0)’ for the XOR.

Extended Data Fig. 3 Learning XOR with symmetric feedback pathways.

a, Schematic diagram illustrating the symmetric feedback (⊕ and ⊕). b, Output-layer activity for the XOR task. Note that the XOR task is still solved. Only a single realization is displayed here. (ci-cii) The symmetric feedback yields very similar representations at the hidden layer.

Extended Data Fig. 4 Dynamics of the time-dependent rate model while learning MNIST.

a, Schematic of the network. The enlarged hidden layer population stresses the fact that the burst rate is equal to the event rate times the burst probability, with the event and burst probability nonlinearly integrating the feedforward and feedback signals, respectively. b, Example event rates (i, iii, v) and weights (ii, iv) for two consecutive examples during the first epoch. In (i), the teacher is illustrated as a dashed line. Learning intervals are indicated by light green vertical bars. c, Burst probabilities (i, iii) and differences of burst probabilities (ii, iv) for the same examples as in b.

Extended Data Fig. 5 Network mechanisms regulating the bursting nonlinearity.

All panels display the burst probability of a large population of two-compartment pyramidal neurons as a function of the intensity of the injected dendritic current. The insets illustrate the microcircuit - including the PV-like neurons (disks) and the SOM-like neurons (inverted triangles) - and the parameter that is being modified is indicated by a colored circuit element. Increasing color intensities corresponds to increasing values of the parameter. a, Increasing the strength of inhibitory synapses from SOM neurons onto the pyramidal neurons’ dendrites produces divisive burst probability control. b, Disinhibiting the pyramidal neurons’ dendrites by applying a hyperpolarizing current to the SOM neurons - mimicking inhibition from the VIP neurons - increases the slope. c, Increasing the probability of release onto SOM neurons produces a small divisive gain modulation. d, Increasing the dendritic excitability by increasing the strength of the regenerative dendritic activity produces an additive gain control.

Extended Data Fig. 6 The bursting nonlinearity controls the learning rate.

a, Schematic of the network. Each hidden layer had 500 units. The recurrent weights (Z(1) and Z(2)) and the feedback alignment weights (Y(1) and Y(2)) are explicitly represented. b, Angle between the weight updates W(1) in the standard backpropagation algorithm and in burstprop for the MNIST digit recognition task. The angle is displayed for different values of the slope of the dendritic nonlinearity (β). Results are displayed as the mean +/- standard deviation over 10 realizations with randomly initialized weights.

Extended Data Fig. 7 Linearity of feedback signals degrades with depth in deep convolutional network trained on ImageNet.

Each plot shows the change in burst probability of a unit in hidden layer l, Δpl, as the burst probability at the output layer, p8, is changed by Δp8 (n=1000), along with the Pearson’s correlation coefficient and two-tailed p-value (blue, top), as well as a random sample of 2000 burst probabilities after presentation of an input image (red, bottom).

Extended Data Fig. 8 Learning MNIST with the simplified rate model.

A convolutional network whose architecture is described in Supplementary Table 3 was trained using backprop, feedback alignment, and burstprop. As in Fig. 6a,c, recurrent input was introduced at hidden layers to keep burst probabilities linear with respect to feedback signals.

Extended Data Fig. 9 The variance of the burst probability decreases during learning.

a, Variance of the burst probability as a function of the epoch for the MNIST task, for each layer in a network with 3 hidden layers with 500 units each. b, Variance of the burst probability as a function of the test error, showing that the magnitude of the variance is correlated with the test error.

Supplementary information

Supplementary Information

Supplementary Text, Tables 1–4 and Supplementary Figs. 1 and 2.

Reporting Summary

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Payeur, A., Guerguiev, J., Zenke, F. et al. Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits. Nat Neurosci 24, 1010–1019 (2021). https://doi.org/10.1038/s41593-021-00857-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41593-021-00857-x

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing