# Cortical credit assignment by Hebbian, neuromodulatory and inhibitory plasticity

arXiv: https://arxiv.org/abs/1911.00307 · HTML: https://mlsanity.com/paper/1911.00307/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

## Built on by (most cited first, 8 of 8)

- [Reverse Differentiation via Predictive Coding](https://mlsanity.com/paper/2103.04689/) (2021)
- [On the relationship between predictive coding and backpropagation](https://mlsanity.com/paper/2106.13082/) (2021)
- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networks](https://mlsanity.com/paper/2103.03725/) (2021)
- [Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules](https://mlsanity.com/paper/2206.00823/) (2022)
- [Three-Factor Learning in Spiking Neural Networks: An Overview of Methods and Trends from a Machine Learning Perspective](https://mlsanity.com/paper/2504.05341/) (2025)
- [Can Biologically Plausible Temporal Credit Assignment Rules Match BPTT for Neural Similarity? E-prop as an Example](https://mlsanity.com/paper/2506.06904/) (2025)
- [A Computational Model of Learning and Memory Using Structurally Dynamic Cellular Automata](https://mlsanity.com/paper/2501.06192/) (2024)

## Abstract (arXiv)

The cortex learns to make associations between stimuli and spiking activity which supports behaviour. It does this by adjusting synaptic weights. The complexity of these transformations implies that synapses have to change without access to the full error information, a problem typically referred to as "credit-assignment". However, it remains unknown how the cortex solves this problem. We propose that a combination of plasticity rules, 1) Hebbian, 2) acetylcholine-dependent and 3) noradrenaline-dependent excitatory plasticity, together with 4) inhibitory plasticity restoring E/I balance, effectively solves the credit assignment problem. We derive conditions under-which a neuron model can learn a number of associations approaching its theoretical capacity. We confirm our predictions regarding acetylcholine-dependent and inhibitory plasticity by reanalysing experimental data. Our work suggests that detailed cortical E/I balance reduces the dimensionality of the problem of associating inputs with outputs, thereby allowing imperfect "supervision" by neuromodulatory systems to guide learning effectively.