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Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits

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

This article has been updated


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.

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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.

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Data availability

The MNIST, CIFAR-10 (ref. 76) and ImageNet77 datasets are publicly available from, and, respectively.

Code availability

The code used in this article is available at and

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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.).

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Authors and Affiliations



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.

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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.

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Peer review informationNature 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.

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Payeur, A., Guerguiev, J., Zenke, F. et al. Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits. Nat Neurosci 24, 1010–1019 (2021).

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