# A Taxonomy of Recurrent Learning Rules

arXiv: https://arxiv.org/abs/2207.11439 · HTML: https://mlsanity.com/paper/2207.11439/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 23 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Towards an integration of deep learning and neuroscience](https://mlsanity.com/paper/1606.03813/) (2016)
- [Brain-Inspired Learning on Neuromorphic Substrates](https://mlsanity.com/paper/2010.11931/) (2020)
- [Understanding Synthetic Gradients and Decoupled Neural Interfaces](https://mlsanity.com/paper/1703.00522/) (2017)
- [Biologically inspired alternatives to backpropagation through time for learning in recurrent neural nets](https://mlsanity.com/paper/1901.09049/) (2019)

## Built on by (most cited first, 2 of 2)

- [S-TLLR: STDP-inspired Temporal Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2306.15220/) (2023)
- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)

## Abstract (arXiv)

Backpropagation through time (BPTT) is the de facto standard for training recurrent neural networks (RNNs), but it is non-causal and non-local. Real-time recurrent learning is a causal alternative, but it is highly inefficient. Recently, e-prop was proposed as a causal, local, and efficient practical alternative to these algorithms, providing an approximation of the exact gradient by radically pruning the recurrent dependencies carried over time. Here, we derive RTRL from BPTT using a detailed notation bringing intuition and clarification to how they are connected. Furthermore, we frame e-prop within in the picture, formalising what it approximates. Finally, we derive a family of algorithms of which e-prop is a special case.