A VGG10 predictive coding network is trained on ImageNet via equilibrium propagation to 13.23% top-5 error, close to the 12.2% backpropagation baseline, marking the first such demonstration at this scale.
Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Equilibrium Propagation (EP) is a learning algorithm for training Energy-based Models (EBMs) on static inputs which leverages the variational description of their fixed points. Extending EP to time-varying inputs is a challenging problem, as the variational description must apply to the entire system trajectory rather than just fixed points, and careful consideration of boundary conditions becomes essential. In this work, we present Generalized Lagrangian Equilibrium Propagation (GLEP), which extends the variational formulation of EP to time-varying inputs. We demonstrate that GLEP yields different learning algorithms depending on the boundary conditions of the system, many of which are impractical for implementation. We then show that Hamiltonian Echo Learning (HEL) -- which includes the recently proposed Recurrent HEL (RHEL) and the earlier known Hamiltonian Echo Backpropagation (HEB) algorithms -- can be derived as a special case of GLEP. Notably, HEL is the only instance of GLEP we found that inherits the properties that make EP a desirable alternative to backpropagation for hardware implementations: it operates in a "forward-only" manner (i.e. using the same system for both inference and learning), it scales efficiently (requiring only two or more passes through the system regardless of model size), and enables local learning.
fields
cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Extends equilibrium propagation to skew-gradient Fitzhugh-Nagumo systems and derives an explicit layer-wise Hamiltonian recurrence for inference in deep residual topologies.
citing papers explorer
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Training a Predictive Coding Network on ImageNet using Equilibrium Propagation
A VGG10 predictive coding network is trained on ImageNet via equilibrium propagation to 13.23% top-5 error, close to the 12.2% backpropagation baseline, marking the first such demonstration at this scale.
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Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
Extends equilibrium propagation to skew-gradient Fitzhugh-Nagumo systems and derives an explicit layer-wise Hamiltonian recurrence for inference in deep residual topologies.