A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks
Tommaso Salvatori, Yuhang Song, Yordan Yordanov, Beren Millidge, Lei Sha, Cornelius Emde, Zhenghua Xu, Rafal Bogacz, Thomas Lukasiewicz
Abstract
Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.
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Cited by top-tier papers8
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- Brain-like Variational InferenceHadi Vafaii, Dekel Galor, Jacob L. YatesNeurIPS 2025 · 7 citations
- Can local learning match self-supervised backpropagation?Wu S. Zihan, Ariane Delrocq, Wulfram Gerstner, Guillaume BellecICML 2026 · 1 citation
- On the Infinite Width and Depth Limits of Predictive Coding NetworksFrancesco Innocenti, El Mehdi Achour, Rafal BogaczICML 2026
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- Big Self-Supervised Models are Strong Semi-Supervised LearnersTing Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi et al.NeurIPS 2020 · 2,611 citations
- Your classifier is secretly an energy based model and you should treat it like oneWill Grathwohl, Kuan-Chieh Wang, Jörn-Henrik Jacobsen, David Duvenaud et al.ICLR 2020 · 643 citations
- Simulating a Primary Visual Cortex at the Front of CNNs Improves Robustness to Image PerturbationsJoel Dapello, Tiago Marques, Martin Schrimpf, Franziska Geiger et al.NeurIPS 2020 · 250 citations
- Can the Brain Do Backpropagation? - Exact Implementation of Backpropagation in Predictive Coding NetworksYuhang Song, Thomas Lukasiewicz, Zhenghua Xu, Rafal BogaczNeurIPS 2020 · 117 citations
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