E-prop plasticity examples

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:

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] (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, 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.

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

Tutorial on learning to generate sine waves 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

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

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

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

Tutorial on learning N-MNIST classification with e-prop

Tutorial on learning N-MNIST classification with e-prop