Equilibrium Propagation

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Lock-in EP: An In-Situ Training Algorithm for Oscillatory Hardware
Oct 5, 2026Sowjanya Tammali, Wilkie Olin-AmmentorpEquilibrium Propagation On-Device Training
Computer Science, Missouri University of Science and Technology, 500 West 15th Street, Rolla, 65409, MO, USA. · Mathematics & Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, 60439, IL, USA.
Conservation laws determine what physical learning remembers
Jul 30, 2026Bijaya DangolEquilibrium Propagation Neural Network Training Dynamics
1Independent researcher
A Conservation Law for Equilibrium Propagation and Coupled Learning
Jun 13, 2026Joshua A. McGinnis, Adam G. Kline, Yoichiro MoriEquilibrium Propagation Neural Network Training Dynamics
Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA · Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA, USA · Department of Biology, University of Pennsylvania, Philadelphia, PA, USA
Coercivity and Local Convergence of Physical Learning in Linear Circuits
Jun 13, 2026Joshua A. McGinnis, Xinbo Li, Yoichiro MoriEquilibrium Propagation Optimization Convergence Analysis
Department of Mathematics, University of Pennsylvania, Philadelphia.
Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines
Jun 11, 2026Dimitri Vanden Abeele, Daniele Veraldi, Davide Pierangeli +2Equilibrium Propagation Energy-Efficient ML
Laboratoire d’Information Quantique C.P. 224, Université Libre de Bruxelles (ULB), Brussels, Belgium · Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy
Perturbative Contrastive Physical Learning
Jun 8, 2026Kyungeun Kim, Amanuel Anteneh, Israel Klich +2Equilibrium Propagation Contrastive Learning
Department of Mathematics, University of British Columbia, Vancouver, BC Canada · Department of Physics, University of Virginia, 382 McCormick Rd, Charlottesville, VA 22903, USA · Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany +2
Optimizing Energy-based Neural Network Training with Coherent Ising Machine
Jun 8, 2026Chen-Rui Fan, Bo Lu, Zhi-Hong Zhang +3Equilibrium Propagation Neural Network Optimization
School of Artiﬁcial Intelligence, Beijing Normal University, Beijing, 100875, China. · Laboratory for Advanced Computing and Intelligence Engineering, Information Engineering University, Zhengzhou, 450001, China. · China Mobile (Suzhou) Software Technology Company Limited, Suzhou, 215163, China.
Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning
Jun 8, 2026Chen-Rui Fan, Bo Lu, Xing-Yu Wu +2Equilibrium Propagation Hopfield Networks
School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China · Laboratory for Advanced Computing and Intelligence Engineering, Information Engineering University, Zhengzhou 450001, China · School of Physical Science and Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
Training a Predictive Coding Network on ImageNet using Equilibrium Propagation
Jun 2, 2026Tugdual Kerjan, Rasmus Høier, Benjamin ScellierEquilibrium Propagation Predictive Coding
Rain AI
Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
May 20, 2026Jack KendallEquilibrium Propagation Dynamical Systems
Zyphra · San Francisco, CA
Neuromorphic Reinforcement Learning for Quadruped Locomotion Control on Uneven Terrain
May 10, 2026Zhuangyu Han, Abhronil SenguptaEquilibrium Propagation Terrain-Aware Robot Locomotion
School of Electrical Engineering and Computer Science Penn State University University Park, PA 16802
Dendritic Neural Networks with Equilibrium Propagation
May 1, 2026Yoshimasa KuboEquilibrium Propagation Neural Network Training Dynamics
Department of Computer Science Lakehead University Thunder Bay, Canada
Symmetric Equilibrium Propagation for Thermodynamic Diffusion Training
Apr 26, 2026Aditi DeEquilibrium Propagation Thermodynamic Computing

Oct 5, 2026, cs.LGJ/K move · Enter open · S save

Lock-in EP: An In-Situ Training Algorithm for Oscillatory Hardware

Sowjanya Tammali, Wilkie Olin-Ammentorp

Computer Science, Missouri University of Science and Technology, 500 West 15th Street, Rolla, 65409, MO, USA. · Mathematics & Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, 60439, IL, USA.

Equilibrium Propagation On-Device Training Oscillatory Neural Networks

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Analog hardware platforms offer the potential to reduce energy consumption over digital architectures, but in order to succeed, large-scale analog systems must also be able to operate with or recover from the variability of their components. Towards this goal, we derive and demonstrate the lock-in equilibrium propagation (LIEP) training method. LIEP provides local gradient information for each component in an oscillatory network without separate forward and backward sweeps, potentially allowing for in-situ learning capabilities on analog oscillatory hardware platforms. We demonstrate that LIEP can be used both for ab-initio training as well as recovering performance when pre-trained parameters are perturbed. We show that LIEP can be formulated as a three-factor update rule, and suggest that although the method is currently only validated on shallow networks, alternate architectures may allow it to extend to deep and large-scale networks addressing complex tasks.

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