eprop_synapse – Synapse type for e-prop plasticity
==================================================

Description
+++++++++++

``eprop_synapse`` is an implementation of a connector model to create synapses between postsynaptic
neurons :math:`j` and presynaptic neurons and :math:`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:

 * :doc:`eprop_iaf<../models/eprop_iaf/>`
 * :doc:`eprop_iaf_adapt<../models/eprop_iaf_adapt/>`
 * :doc:`eprop_readout<../models/eprop_readout/>`
 * :doc:`eprop_learning_signal_connection<../models/eprop_learning_signal_connection/>`

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

 * :doc:`weight_optimizer<../models/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
   :ref:`precise spike timing <sim_precise_spike_times>` into
   account. When calculating the weight update, the precise spike time part
   of the timestamp is ignored.

Parameters
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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   :math:`d_{ji}`                1.0 Dendritic delay
``weight``    pA   :math:`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   :math:`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
:doc:`supervised regression and classification tasks <../auto_examples/eprop_plasticity/index>`
reproducing among others the original proof-of-concept tasks in [1]_.

Transmits
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SpikeEvent, DSSpikeEvent

References
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.. [1] 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
+++++++++++++++++++++++++

.. listexamples:: eprop_synapse