Toward Practical Equilibrium Propagation Braininspired Recurrent Neural Network With Feedback Regulation And Residual Connections

# Toward Practical Equilibrium Propagation: Brain-inspired Recurrent Neural Network with Feedback Regulation and Residual Connections

**arXiv ID:** 2508.11659
**Authors:** Zhuo Liu, Tao Chen
**Published:** 2025-08-05T15:07:50Z
**Abstract:**
Brain-like intelligent systems need brain-like learning methods. Equilibrium Propagation (EP) is a biologically plausible learning framework with strong potential for brain-inspired computing hardware. However, existing im-plementations of EP suffer from instability and prohibi-tively high computational costs. Inspired by the structure and dynamics of the brain, we propose a biologically plau-sible Feedback-regulated REsidual recurrent neural network (FRE-RNN) and study its learning performance in EP framework. Feedback regulation enables rapid convergence by reducing the spectral radius. The improvement in con-vergence property reduces the computational cost and train-ing time of EP by orders of magnitude, delivering perfor-mance on par with backpropagation (BP) in benchmark tasks. Meanwhile, residual connections with brain-inspired topologies help alleviate the vanishing gradient problem that arises when feedback pathways are weak in deep RNNs. Our approach substantially enhances the applicabil-ity and practicality of EP in large-scale networks that un-derpin artificial intelligence. The techniques developed here also offer guidance to implementing in-situ learning in physical neural networks.

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## References

- [arXiv:2508.11659](http://arxiv.org/abs/2508.11659v2)