.. _sphx_glr_auto_examples_eprop_plasticity:

E-prop plasticity examples
==========================

.. image:: eprop_supervised_regression_sine-waves.png

Eligibility propagation (e-prop) [1]_ is a three-factor learning rule for spiking neural networks that approximates the
performance of backpropagation through time (BPTT). A complete e-prop model comprises a recurrent neuron model, a
readout neuron model, a synapse model, and a learning signal connection. Two such models are provided: the original
formulation by Bellec et al. (2020) [1]_ and an extended variant with additional biological features [2]_. The e-prop models are related as follows:

.. image:: eprop_model_relationships.png

We provide tutorials to reproduce the supervised regression task for generating temporal patterns and the supervised
classification task from the original TensorFlow implementation [3]_. In addition, we provide two tutorials on
supervised regression for generating two-dimensional temporal patterns and on supervised classification of neuromorphic
MNIST [4]_.

References
----------

.. [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, Espinoza Valverde JA, Stapmanns J, Plesser HE, Dahmen D,
       Bolten M, van Albada SJ, Diesmann M (2025). Event-driven eligibility
       propagation in large sparse networks: efficiency shaped by biological
       realism. arXiv:2511.21674. https://doi.org/10.48550/arXiv.2511.21674

.. [3] https://github.com/IGITUGraz/eligibility_propagation/blob/master/Figure_3_and_S7_e_prop_tutorials/

.. [4] Orchard, G., Jayawant, A., Cohen, G. K., & Thakor, N. (2015). Converting static image datasets to
       spiking neuromorphic datasets using saccades. Frontiers in neuroscience, 9, 159859.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a regression model using supervised e-prop plasticity to generate sine waves">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_regression_sine-waves_bsshslm_2020_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_regression_sine-waves_bsshslm_2020`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning to generate sine waves with e-prop after Bellec et al. (2020)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a regression model using supervised e-prop plasticity to generate sine waves">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_regression_sine-waves_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_regression_sine-waves`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning to generate sine waves with e-prop</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a regression model using supervised e-prop plasticity to generate a lemniscate">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_regression_lemniscate_bsshslm_2020_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_regression_lemniscate_bsshslm_2020`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning to generate a lemniscate with e-prop after Bellec et al. (2020)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a regression model using supervised e-prop plasticity to generate handwritten text">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_regression_handwriting_bsshslm_2020_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_regression_handwriting_bsshslm_2020`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning to generate handwritten text with e-prop after Bellec et al. (2020)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a classification model using supervised e-prop plasticity to accumulate evidence.">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_classification_evidence-accumulation_bsshslm_2020_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_classification_evidence-accumulation_bsshslm_2020`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning to accumulate evidence with e-prop after Bellec et al. (2020)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Training a classification model using supervised e-prop plasticity to classify the Neuromorphic MNIST (N-MNIST) dataset.">

.. only:: html

  .. image:: /auto_examples/eprop_plasticity/images/thumb/sphx_glr_eprop_supervised_classification_neuromorphic_mnist_thumb.png
    :alt:

  :doc:`/auto_examples/eprop_plasticity/eprop_supervised_classification_neuromorphic_mnist`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tutorial on learning N-MNIST classification with e-prop</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/eprop_plasticity/eprop_supervised_regression_sine-waves_bsshslm_2020
   /auto_examples/eprop_plasticity/eprop_supervised_regression_sine-waves
   /auto_examples/eprop_plasticity/eprop_supervised_regression_lemniscate_bsshslm_2020
   /auto_examples/eprop_plasticity/eprop_supervised_regression_handwriting_bsshslm_2020
   /auto_examples/eprop_plasticity/eprop_supervised_classification_evidence-accumulation_bsshslm_2020
   /auto_examples/eprop_plasticity/eprop_supervised_classification_neuromorphic_mnist