# Toward Lifelong Learning in Equilibrium Propagation: Sleep-like and Awake Rehearsal for Enhanced Stability

arXiv: https://arxiv.org/abs/2508.14081 · HTML: https://mlsanity.com/paper/2508.14081/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [FearNet: Brain-Inspired Model for Incremental Learning](https://mlsanity.com/paper/1711.10563/) (2017)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Memory Efficient Experience Replay for Streaming Learning](https://mlsanity.com/paper/1809.05922/) (2018)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Continual Learning for Recurrent Neural Networks: an Empirical Evaluation](https://mlsanity.com/paper/2103.07492/) (2021)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [Equivalence of Equilibrium Propagation and Recurrent Backpropagation](https://mlsanity.com/paper/1711.08416/) (2017)
- [EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementations](https://mlsanity.com/paper/2010.07859/) (2020)
- [Meta-Learning Biologically Plausible Plasticity Rules with Random Feedback Pathways](https://mlsanity.com/paper/2210.16414/) (2022)
- [Biologically-inspired neuronal adaptation improves learning in neural networks](https://mlsanity.com/paper/2204.14008/) (2022)
- [Sleep-Like Unsupervised Replay Improves Performance when Data are Limited or Unbalanced](https://mlsanity.com/paper/2402.10956/) (2024)
- [Scaling SNNs Trained Using Equilibrium Propagation to Convolutional Architectures](https://mlsanity.com/paper/2405.02546/) (2024)

## Built on by (most cited first, 5 of 5)

- [Not Just After One: Sleep-Inspired Replay Prevents Catastrophic Forgetting After Sequential Tasks](https://mlsanity.com/paper/2606.08447/) (2026)
- [Heterogeneous Time Constants Improve Stability in Equilibrium Propagation](https://mlsanity.com/paper/2603.03402/) (2026)
- [Dendritic Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2605.08135/) (2026)
- [The Neural Division of Labor: Biologically-Inspired Modular Architectures for Robust Neuromorphic Computing](https://mlsanity.com/paper/2608.08317/) (2026)
- [Replay in the Silent Degrees of Freedom: Continual Learning Without an Offline Phase](https://mlsanity.com/paper/2609.31630/) (2026)

## Abstract (arXiv)

Recurrent neural networks (RNNs) trained using Equilibrium Propagation (EP), a biologically plausible training algorithm, have demonstrated strong performance in various tasks such as image classification and reinforcement learning. However, these networks face a critical challenge in continuous learning: catastrophic forgetting, where previously acquired knowledge is overwritten when new tasks are learned. This limitation contrasts with the human brain's ability to retain and integrate both old and new knowledge, aided by processes like memory consolidation during sleep through the replay of learned information. To address this challenge in RNNs, here we propose a sleep-like replay consolidation (SRC) algorithm for EP-trained RNNs. We found that SRC significantly improves RNN's resilience to catastrophic forgetting in continuous learning scenarios. In class-incremental learning with SRC implemented after each new task training, the EP-trained multilayer RNN model (MRNN-EP) performed significantly better compared to feedforward networks incorporating several well-established regularization techniques. The MRNN-EP performed on par with MRNN trained using Backpropagation Through Time (BPTT) when both were equipped with SRC on MNIST data and surpassed BPTT-based models on the Fashion MNIST, Kuzushiji-MNIST, CIFAR10, and ImageNet datasets. Combining SRC with rehearsal, also known as "awake replay", further boosted the network's ability to retain long-term knowledge while continuing to learn new tasks. Our study reveals the applicability of sleep-like replay techniques to RNNs and highlights the potential for integrating human-like learning behaviors into artificial neural networks (ANNs).