Title: Scaling Equilibrium Propagation: Training a Predictive Coding Network on ImageNet

Abstract:

Equilibrium Propagation (EP) is a physics-inspired training framework that has traditionally been applied to energy-based models, such as coupled phase oscillators, nonlinear resistive networks, and continuous Hopfield networks. Despite its potential, EP’s practical utility has been constrained to relatively modest problem sizes. Similarly, Predictive Coding Networks (PCNs)—another subset of energy-based models grounded in computational neuroscience—have typically relied on specialized training algorithms and have not yet been scaled to large-scale applications.

In this study, we introduce an EP-based training methodology for PCNs that integrates the centered variant of EP with a newly developed equilibration scheme tailored for PCNs. We applied this approach to train a 10-layer convolutional PCN (VGG10) on the full ImageNet dataset. The model achieved a top-5 classification test error rate of 13.23%, a performance closely mirroring the 12.2% error rate of the backpropagation baseline. To the best of our knowledge, this marks the first successful demonstration of both PCNs and EP-based training at the ImageNet scale.

These findings substantially broaden the scalability of both methodologies. They imply that the main obstacles to scaling EP in other physical systems likely stem from the computational characteristics of those systems, rather than from intrinsic limitations within the EP framework itself.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC