# Contribute to balance, wire in accordance: Emergence of backpropagation from a simple, bio-plausible neuroplasticity rule

arXiv: https://arxiv.org/abs/2405.14139 · HTML: https://mlsanity.com/paper/2405.14139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 79 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Equivalence of Equilibrium Propagation and Recurrent Backpropagation](https://mlsanity.com/paper/1711.08416/) (2017)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [Credit Assignment Through Broadcasting a Global Error Vector](https://mlsanity.com/paper/2106.04089/) (2021)
- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)

## Abstract (arXiv)

Backpropagation (BP) has been pivotal in advancing machine learning and remains essential in computational applications and comparative studies of biological and artificial neural networks. Despite its widespread use, the implementation of BP in the brain remains elusive, and its biological plausibility is often questioned due to inherent issues such as the need for symmetry of weights between forward and backward connections, and the requirement of distinct forward and backward phases of computation. Here, we introduce a novel neuroplasticity rule that offers a potential mechanism for implementing BP in the brain. Similar in general form to the classical Hebbian rule, this rule is based on the core principles of maintaining the balance of excitatory and inhibitory inputs as well as on retrograde signaling, and operates over three progressively slower timescales: neural firing, retrograde signaling, and neural plasticity. We hypothesize that each neuron possesses an internal state, termed credit, in addition to its firing rate. After achieving equilibrium in firing rates, neurons receive credits based on their contribution to the E-I balance of postsynaptic neurons through retrograde signaling. As the network's credit distribution stabilizes, connections from those presynaptic neurons are strengthened that significantly contribute to the balance of postsynaptic neurons. We demonstrate mathematically that our learning rule precisely replicates BP in layered neural networks without any approximations. Simulations on artificial neural networks reveal that this rule induces varying community structures in networks, depending on the learning rate. This simple theoretical framework presents a biologically plausible implementation of BP, with testable assumptions and predictions that may be evaluated through biological experiments.