# EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementations

arXiv: https://arxiv.org/abs/2010.07859 · HTML: https://mlsanity.com/paper/2010.07859/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 30 of 31)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Training an Ising Machine with Equilibrium Propagation](https://mlsanity.com/paper/2305.18321/) (2023)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [Agnostic Physics-Driven Deep Learning](https://mlsanity.com/paper/2205.15021/) (2022)
- [Training Dynamical Binary Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2103.08953/) (2021)
- [Equilibrium Propagation: the Quantum and the Thermal Cases](https://mlsanity.com/paper/2405.08467/) (2024)
- [Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems](https://mlsanity.com/paper/2406.00879/) (2024)
- [Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity](https://mlsanity.com/paper/2406.06482/) (2024)
- [SPIDE: A Purely Spike-based Method for Training Feedback Spiking Neural Networks](https://mlsanity.com/paper/2302.00232/) (2023)
- [A Review of Neuroscience-Inspired Machine Learning](https://mlsanity.com/paper/2403.18929/) (2024)
- [Equilibrium Propagation for Learning in Lagrangian Dynamical Systems](https://mlsanity.com/paper/2505.07363/) (2025)
- [Sequence Learning Using Equilibrium Propagation](https://mlsanity.com/paper/2209.09626/) (2022)
- [Toward Lifelong Learning in Equilibrium Propagation: Sleep-like and Awake Rehearsal for Enhanced Stability](https://mlsanity.com/paper/2508.14081/) (2025)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)
- [Near-Equilibrium Propagation training in nonlinear wave systems](https://mlsanity.com/paper/2510.16084/) (2025)
- [Equilibrium Propagation for Non-Conservative Systems](https://mlsanity.com/paper/2602.03670/) (2026)
- [Deep Unsupervised Learning Using Spike-Timing-Dependent Plasticity](https://mlsanity.com/paper/2307.04054/) (2023)
- [Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation](https://mlsanity.com/paper/2308.12053/) (2023)
- [Unsupervised End-to-End Training with a Self-Defined Target](https://mlsanity.com/paper/2403.12116/) (2024)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2101.05536/) (2021)
- [Harnessing uncertainty when learning through Equilibrium Propagation in neural networks](https://mlsanity.com/paper/2503.22810/) (2025)
- [Scalable Equilibrium Propagation via Intermediate Error Signals for Deep Convolutional CRNNs](https://mlsanity.com/paper/2508.15989/) (2025)
- [Dendritic Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2605.08135/) (2026)
- [Neuromorphic Reinforcement Learning for Quadruped Locomotion Control on Uneven Terrain](https://mlsanity.com/paper/2605.09595/) (2026)
- [Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model](https://mlsanity.com/paper/2605.21568/) (2026)

## Abstract (arXiv)

Finding spike-based learning algorithms that can be implemented within the local constraints of neuromorphic systems, while achieving high accuracy, remains a formidable challenge. Equilibrium Propagation is a promising alternative to backpropagation as it only involves local computations, but hardware-oriented studies have so far focused on rate-based networks. In this work, we develop a spiking neural network algorithm called EqSpike, compatible with neuromorphic systems, which learns by Equilibrium Propagation. Through simulations, we obtain a test recognition accuracy of 97.6% on MNIST, similar to rate-based Equilibrium Propagation, and comparing favourably to alternative learning techniques for spiking neural networks. We show that EqSpike implemented in silicon neuromorphic technology could reduce the energy consumption of inference and training respectively by three orders and two orders of magnitude compared to GPUs. Finally, we also show that during learning, EqSpike weight updates exhibit a form of Spike Timing Dependent Plasticity, highlighting a possible connection with biology.