Adjoint propagation of error signal through modular recurrent neural networks for biologically plausible learning
- University of Science and Technology of China, China
- China Southern Power Grid, China
Abstract
Biologically plausible learning mechanisms have implications for understanding brain functions and engineering intelligent systems. Inspired by the multi-scale recurrent connectivity in the brain, we introduce an adjoint propagation (AP) framework, in which the error signals arise naturally from recurrent dynamics and propagate concurrently with forward inference signals. AP inherits the modularity of multi-region recurrent neural network (MR-RNN) models and leverages the convergence properties of RNN modules to facilitate fast and scalable training. This framework eliminates the biologically implausible feedback required by the backpropagation (BP) algorithm, and allows concomitant error propagation for multiple tasks through the same RNN. We demonstrate that AP succeeds in training on standard benchmark tasks, achieving accuracies comparable to BP-trained networks while adhering to neurobiological constraints. The training process exhibits robustness, maintaining performance over extended training epochs. Importantly, AP supports flexible resource allocation for multiple cognitive tasks, consistent with observations in neuroscience. This framework bridges artificial and biological learning principles, paving the way for energy-efficient intelligent systems inspired by the brain and offering a mechanistic theory that can guide experimental investigations in neuroscience.
Data availability
All data generated or analysed during this study are included in the manuscript and supporting files. The code of the study is provided via GitHub at https://github.com/Zero0Hero/Adjoint-Propagation-framework.
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Funding
Chinese Academy of Sciences
- Tao Chen
University of Science and Technology of China
- Tao Chen
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Copyright
© 2026, Liu et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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Adjoint propagation of error signal through modular recurrent neural networks for biologically plausible learning
eLife 15:e108237.
https://doi.org/10.7554/eLife.108237
