# STDP as presynaptic activity times rate of change of postsynaptic activity

arXiv: https://arxiv.org/abs/1509.05936 · HTML: https://mlsanity.com/paper/1509.05936/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2015.

## Built on by (most cited first, 9 of 9)

- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [BSNN: Towards Faster and Better Conversion of Artificial Neural Networks to Spiking Neural Networks with Bistable Neurons](https://mlsanity.com/paper/2105.12917/) (2021)
- [An STDP-Based Supervised Learning Algorithm for Spiking Neural Networks](https://mlsanity.com/paper/2203.03379/) (2022)
- [Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation](https://mlsanity.com/paper/2308.12053/) (2023)
- [Spike Accumulation Forwarding for Effective Training of Spiking Neural Networks](https://mlsanity.com/paper/2310.02772/) (2023)
- [aSTDP: A More Biologically Plausible Learning](https://mlsanity.com/paper/2206.14137/) (2022)
- [Biologically Inspired Spiking Diffusion Model with Adaptive Lateral Selection Mechanism](https://mlsanity.com/paper/2503.23767/) (2025)
- [ADPTNet: Adaptive with Prescriptive Timescales Non-Linear SSM for Sequence Modelling](https://mlsanity.com/paper/2609.34034/) (2026)

## Abstract (arXiv)

We introduce a weight update formula that is expressed only in terms of firing rates and their derivatives and that results in changes consistent with those associated with spike-timing dependent plasticity (STDP) rules and biological observations, even though the explicit timing of spikes is not needed. The new rule changes a synaptic weight in proportion to the product of the presynaptic firing rate and the temporal rate of change of activity on the postsynaptic side. These quantities are interesting for studying theoretical explanation for synaptic changes from a machine learning perspective. In particular, if neural dynamics moved neural activity towards reducing some objective function, then this STDP rule would correspond to stochastic gradient descent on that objective function.