arXiv Machine Learning June 3, 2026 By Tugdual Kerjan, Rasmus H{\o}ier, Benjamin Scellier

Training a Predictive Coding Network on ImageNet using Equilibrium Propagation

Read the original on arXiv Machine Learning →

arXiv:2606. 03584v1 Announce Type: new Abstract: Equilibrium Propagation (EP) is a physics-based training framework that has primarily been employed in energy-based models, including continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

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On the Infinite Width and Depth Limits of Predictive Coding Networks

arXiv:2602. 07697v3 Announce Type: replace-cross Abstract: Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights.

By Francesco Innocenti, El Mehdi Achour, Rafal Bogacz

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Jun 9

ePC: Fast and Deep Predictive Coding in Digital Simulation

arXiv:2505. 20137v5 Announce Type: replace-cross Abstract: Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy.

By C\'edric Goemaere, Gaspard Oliviers, Rafal Bogacz, Thomas Demeester

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Jun 9

Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning

arXiv:2606. 09112v1 Announce Type: cross Abstract: The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks.

By Chen-Rui Fan, Bo Lu, Xing-Yu Wu, Tie-Jun Wang, Chuan Wang

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Optimizing Energy-based Neural Network Training with Coherent Ising Machine

arXiv:2606. 09117v1 Announce Type: cross Abstract: While Ising machines serve as advanced physical solvers for the Ising model,enabling applications in combinatorial optimization and neural network training,their scalability for large-scale neural networks remains constrained by hardware connectivity limitations and suboptimal training methodologies.

By Chen-Rui Fan, Bo Lu, Zhi-Hong Zhang, Run-Qing Zhang, Jing-Wei Wen, Chuan Wang

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Error Highways: Scaling Predictive Coding to Very Deep Networks

Predictive coding networks (PCNs) offer a biologically-plausible, local-learning alternative to back-propagation of errors (backprop). Nevertheless, they have remained largely confined to shallow architectures and evaluated on simple machine intelligence benchmarks.

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RepNet: Tackling spectral bias in deep neural networks via parameter reparameterization

arXiv:2606. 16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.

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Related stories

On the Infinite Width and Depth Limits of Predictive Coding Networks

ePC: Fast and Deep Predictive Coding in Digital Simulation

Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning

Optimizing Energy-based Neural Network Training with Coherent Ising Machine

Error Highways: Scaling Predictive Coding to Very Deep Networks

RepNet: Tackling spectral bias in deep neural networks via parameter reparameterization