Directed Equilibrium Propagation Revisited
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, ye...
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/11/1866 |
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| author | Pedro Costa Pedro A. Santos |
| author_facet | Pedro Costa Pedro A. Santos |
| author_sort | Pedro Costa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6863ee34e4604bcf8b10b415cd591f2d |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6863ee34e4604bcf8b10b415cd591f2d2025-08-20T02:32:57ZengMDPI AGMathematics2227-73902025-06-011311186610.3390/math13111866Directed Equilibrium Propagation RevisitedPedro Costa0Pedro A. Santos1Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, PortugalInstituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, PortugalEquilibrium 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.https://www.mdpi.com/2227-7390/13/11/1866recurrent neural networksequilibrium propagationbiologically plausible algorithms |
| spellingShingle | Pedro Costa Pedro A. Santos Directed Equilibrium Propagation Revisited Mathematics recurrent neural networks equilibrium propagation biologically plausible algorithms |
| title | Directed Equilibrium Propagation Revisited |
| title_full | Directed Equilibrium Propagation Revisited |
| title_fullStr | Directed Equilibrium Propagation Revisited |
| title_full_unstemmed | Directed Equilibrium Propagation Revisited |
| title_short | Directed Equilibrium Propagation Revisited |
| title_sort | directed equilibrium propagation revisited |
| topic | recurrent neural networks equilibrium propagation biologically plausible algorithms |
| url | https://www.mdpi.com/2227-7390/13/11/1866 |
| work_keys_str_mv | AT pedrocosta directedequilibriumpropagationrevisited AT pedroasantos directedequilibriumpropagationrevisited |