Directed Equilibrium Propagation Revisited

Pedro Costa () and Pedro A. Santos ()
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Pedro Costa: Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal
Pedro A. Santos: Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal

Mathematics, 2025, vol. 13, issue 11, 1-19

Abstract: Equilibrium Propagation (EP) offers a biologically inspired alternative to backpropagation for training recurrent neural networks, but its reliance on symmetric feedback connections and stability limitations hinders practical adoption. The DirEcted EP (DEEP) model relaxes the symmetry constraint, yet suffers from convergence issues and lacks a principled learning guarantee. In this work, we generalize DEEP by incorporating neuronal leakage, providing new convergence criteria for the network’s dynamics. We additionally propose a novel local learning rule closely linked to the objective function’s gradient and establish sufficient conditions for reliable learning in small networks. Our results resolve longstanding stability challenges and bring energy-based learning models closer to biologically plausible and provably effective neural computation.

Keywords: recurrent neural networks; equilibrium propagation; biologically plausible algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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