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Equilibrium Propagation (EP) is a biologically-inspired algorithm for convergent RNNs with a local learning rule that comes with strong theoretical guarantees. The parameter updates of the neural network during the credit assignment phase…

Neural and Evolutionary Computing · Computer Science 2020-06-09 Axel Laborieux , Maxence Ernoult , Benjamin Scellier , Yoshua Bengio , Julie Grollier , Damien Querlioz

Equilibrium Propagation (EP) is a biologically-inspired counterpart of Backpropagation Through Time (BPTT) which, owing to its strong theoretical guarantees and the locality in space of its learning rule, fosters the design of…

Machine Learning · Computer Science 2021-01-15 Axel Laborieux , Maxence Ernoult , Benjamin Scellier , Yoshua Bengio , Julie Grollier , Damien Querlioz

Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to…

Machine Learning · Computer Science 2026-02-04 Antonino Emanuele Scurria , Dimitri Vanden Abeele , Bortolo Matteo Mognetti , Serge Massar

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the…

Machine Learning · Computer Science 2017-03-30 Benjamin Scellier , Yoshua Bengio

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight…

Machine Learning · Computer Science 2024-04-09 Axel Laborieux , Friedemann Zenke

Equilibrium Propagation (EP) is a supervised learning algorithm that trains network parameters using local neuronal activity. This is in stark contrast to backpropagation, where updating the parameters of the network requires significant…

Machine Learning · Computer Science 2025-04-01 Jonathan Peters , Philippe Talatchian

Equilibrium propagation (EP) is an alternative to backpropagation (BP) that allows the training of deep neural networks with local learning rules. It thus provides a compelling framework for training neuromorphic systems and understanding…

Machine Learning · Computer Science 2022-09-02 Axel Laborieux , Friedemann Zenke

Equilibrium Propagation (EP) is a biologically inspired local learning rule first proposed for convergent recurrent neural networks (CRNNs), in which synaptic updates depend only on neuron states from two distinct phases. EP estimates…

Machine Learning · Computer Science 2026-05-11 Jiaqi Lin , Malyaban Bal , Abhronil Sengupta

Equilibrium Propagation (EP) is a powerful and more bio-plausible alternative to conventional learning frameworks such as backpropagation. The effectiveness of EP stems from the fact that it relies only on local computations and requires…

Neural and Evolutionary Computing · Computer Science 2023-08-23 Malyaban Bal , Abhronil Sengupta

Equilibrium Propagation (EP) is a learning algorithm that bridges Machine Learning and Neuroscience, by computing gradients closely matching those of Backpropagation Through Time (BPTT), but with a learning rule local in space. Given an…

Neural and Evolutionary Computing · Computer Science 2020-05-11 Maxence Ernoult , Julie Grollier , Damien Querlioz , Yoshua Bengio , Benjamin Scellier

Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong…

Machine Learning · Computer Science 2026-03-17 Karol Sajnok , Michał Matuszewski

Equilibrium propagation (EP) is a training framework for energy-based systems, i.e. systems whose physics minimizes an energy function. EP has been explored in various classical physical systems such as resistor networks, elastic networks,…

Quantum Physics · Physics 2024-06-04 Benjamin Scellier

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,…

Machine Learning · Computer Science 2026-04-14 Guillaume Pourcel , Debabrota Basu , Maxence Ernoult , Aditya Gilra

How the brain performs credit assignment is a fundamental unsolved problem in neuroscience. Many `biologically plausible' algorithms have been proposed, which compute gradients that approximate those computed by backpropagation (BP), and…

Machine Learning · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

Equilibrium Propagation (EP) is a biologically inspired alternative algorithm to backpropagation (BP) for training neural networks. It applies to RNNs fed by a static input x that settle to a steady state, such as Hopfield networks. EP is…

Neural and Evolutionary Computing · Computer Science 2020-05-11 Maxence Ernoult , Julie Grollier , Damien Querlioz , Yoshua Bengio , Benjamin Scellier

Equilibrium Propagation (EP) is a biologically inspired learning algorithm for convergent recurrent neural networks, i.e. RNNs that are fed by a static input x and settle to a steady state. Training convergent RNNs consists in adjusting the…

Machine Learning · Computer Science 2019-06-03 Maxence Ernoult , Julie Grollier , Damien Querlioz , Yoshua Bengio , Benjamin Scellier

The search for ``biologically plausible'' learning algorithms has converged on the idea of representing gradients as activity differences. However, most approaches require a high degree of synchronization (distinct phases during learning)…

Machine Learning · Computer Science 2024-12-03 Rasmus Kjær Høier , Christopher Zach

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…

Computation · Statistics 2016-01-12 Guillaume P Dehaene , Simon Barthelmé

Machine learning is a powerful method of extracting meaning from data; unfortunately, current digital hardware is extremely energy-intensive. There is interest in an alternative analog computing implementation that could match the…

Machine Learning · Computer Science 2026-02-17 Jonathan Lin , Aman Desai , Frank Barrows , Francesco Caravelli

Equilibrium Propagation (EP) is an algorithm intrinsically adapted to the training of physical networks, thanks to the local updates of weights given by the internal dynamics of the system. However, the construction of such a hardware…

Neural and Evolutionary Computing · Computer Science 2021-04-20 Jérémie Laydevant , Maxence Ernoult , Damien Querlioz , Julie Grollier
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