eprop_synapse – Synapse type for e-prop plasticity

Description

eprop_synapse is an implementation of a connector model to create synapses between postsynaptic neurons \(j\) and presynaptic neurons and \(i\) for eligibility propagation (e-prop) plasticity.

E-prop plasticity was originally introduced and implemented in TensorFlow in [1].

The e-prop synapse triggers the calculation of the gradient at each spike over an interval that begins at the previous spike and ends at a cutoff specified by the user or the current spike, depending on which of the two time points is earlier. The gradient calculation is specific to the post-synaptic neuron and thus defined there.

Eventually, it optimizes the weight with the specified optimizer.

E-prop synapses require archiving of continuous quantities. Therefore e-prop synapses can only be connected to neuron models that are capable of archiving. So far, compatible models are eprop_iaf, eprop_iaf_psc_delta, eprop_iaf_psc_delta_adapt, eprop_iaf_adapt, and eprop_readout.

For more information on e-prop plasticity, see the documentation on the other e-prop models:

• eprop_iaf

• eprop_iaf_adapt

• eprop_readout

• eprop_learning_signal_connection

For more information on the optimizers, see the documentation of the weight optimizer:

• weight_optimizer

Details on the event-based NEST implementation of e-prop can be found in [2].

Warning

This synaptic plasticity rule does not take precise spike timing into account. When calculating the weight update, the precise spike time part of the timestamp is ignored.

Parameters

The following parameters can be set in the status dictionary.

Common e-prop synapse parameters
Parameter	Unit	Math equivalent	Default	Description
optimizer			{}	Dictionary of optimizer parameters

Individual synapse parameters
Parameter	Unit	Math equivalent	Default	Description
delay	ms	\(d_{ji}\)	1.0	Dendritic delay
weight	pA	\(W_{ji}\)	1.0	Initial value of synaptic weight

Recordables

The following variables can be recorded.

Synapse recordables
State variable	Unit	Math equivalent	Initial value	Description
weight	pA	\(B_{jk}\)	1.0	Synaptic weight

Usage

This model can only be used in combination with the other e-prop models and the network architecture requires specific wiring, input, and output. The usage is demonstrated in several supervised regression and classification tasks reproducing among others the original proof-of-concept tasks in [1].

Transmits

SpikeEvent, DSSpikeEvent

References

[1] (1,2)

Bellec G, Scherr F, Subramoney F, Hajek E, Salaj D, Legenstein R, Maass W (2020). A solution to the learning dilemma for recurrent networks of spiking neurons. Nature Communications, 11:3625. https://doi.org/10.1038/s41467-020-17236-y

[2]

Korcsak-Gorzo A, Stapmanns J, Espinoza Valverde JA, Plesser HE, Dahmen D, Bolten M, Van Albada SJ, Diesmann M. Event-based implementation of eligibility propagation (in preparation)

See also

Examples using this model

• Tutorial on learning N-MNIST classification with e-prop

• Tutorial on learning to accumulate evidence with e-prop after Bellec et al. (2020)

• Tutorial on learning to generate a lemniscate with e-prop after Bellec et al. (2020)

• Tutorial on learning to generate handwritten text with e-prop after Bellec et al. (2020)

• Tutorial on learning to generate sine waves with e-prop

• Tutorial on learning to generate sine waves with e-prop after Bellec et al. (2020)