# Biologically-plausible backpropagation through arbitrary timespans via local neuromodulators

arXiv: https://arxiv.org/abs/2206.01338 · HTML: https://mlsanity.com/paper/2206.01338/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2022.

## Built on by (most cited first, 7 of 7)

- [Brain-inspired learning in artificial neural networks: a review](https://mlsanity.com/paper/2305.11252/) (2023)
- [How connectivity structure shapes rich and lazy learning in neural circuits](https://mlsanity.com/paper/2310.08513/) (2023)
- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)
- [A Neuro-mimetic Realization of the Common Model of Cognition via Hebbian Learning and Free Energy Minimization](https://mlsanity.com/paper/2310.15177/) (2023)
- [Can Biologically Plausible Temporal Credit Assignment Rules Match BPTT for Neural Similarity? E-prop as an Example](https://mlsanity.com/paper/2506.06904/) (2025)
- [CATFormer: When Continual Learning Meets Spiking Transformers With Dynamic Thresholds](https://mlsanity.com/paper/2603.15184/) (2026)
- [Flexible inference for animal learning rules using neural networks](https://mlsanity.com/paper/2509.04661/) (2025)

## Abstract (arXiv)

The spectacular successes of recurrent neural network models where key parameters are adjusted via backpropagation-based gradient descent have inspired much thought as to how biological neuronal networks might solve the corresponding synaptic credit assignment problem. There is so far little agreement, however, as to how biological networks could implement the necessary backpropagation through time, given widely recognized constraints of biological synaptic network signaling architectures. Here, we propose that extra-synaptic diffusion of local neuromodulators such as neuropeptides may afford an effective mode of backpropagation lying within the bounds of biological plausibility. Going beyond existing temporal truncation-based gradient approximations, our approximate gradient-based update rule, ModProp, propagates credit information through arbitrary time steps. ModProp suggests that modulatory signals can act on receiving cells by convolving their eligibility traces via causal, time-invariant and synapse-type-specific filter taps. Our mathematical analysis of ModProp learning, together with simulation results on benchmark temporal tasks, demonstrate the advantage of ModProp over existing biologically-plausible temporal credit assignment rules. These results suggest a potential neuronal mechanism for signaling credit information related to recurrent interactions over a longer time horizon. Finally, we derive an in-silico implementation of ModProp that could serve as a low-complexity and causal alternative to backpropagation through time.