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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 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 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

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

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 biologically plausible local learning algorithm initially developed for convergent recurrent neural networks (RNNs), where weight updates rely solely on the connecting neuron states across two phases. The…

Neural and Evolutionary Computing · Computer Science 2024-07-04 Jiaqi Lin , Malyaban Bal , Abhronil Sengupta

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

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 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 plausible alternative to backpropagation (BP), but its effectiveness can degrade in deeper and more challenging learning settings. In parallel, dendritic neural networks have demonstrated…

Machine Learning · Computer Science 2026-05-12 Yoshimasa Kubo

Binary Neural Networks (BNNs), which constrain both weights and activations to binary values, offer substantial reductions in computational complexity, memory footprint, and energy consumption. These advantages make them particularly well…

Machine Learning · Computer Science 2026-02-18 Luca Colombo , Fabrizio Pittorino , Daniele Zambon , Carlo Baldassi , Manuel Roveri , Cesare Alippi

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

Brain-like intelligent systems need brain-like learning methods. Equilibrium Propagation (EP) is a biologically plausible learning framework with strong potential for brain-inspired computing hardware. However, existing im-plementations of…

Neural and Evolutionary Computing · Computer Science 2026-05-08 Zhuo Liu , Tao Chen

Spiking Neural Networks (SNNs) promise energy-efficient, sparse, biologically inspired computation. Training them with Backpropagation Through Time (BPTT) and surrogate gradients achieves strong performance but remains biologically…

Emerging Technologies · Computer Science 2025-11-17 Jiaqi Lin , Yi Jiang , Abhronil Sengupta

Physical systems that naturally perform energy descent offer a direct route to accelerating machine learning. Oscillator Ising Machines (OIMs) exemplify this idea: their GHz-frequency dynamics mirror both the optimization of energy-based…

Machine Learning · Computer Science 2025-11-18 Alex Gower

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

We introduce a principled method to train end-to-end analog neural networks by stochastic gradient descent. In these analog neural networks, the weights to be adjusted are implemented by the conductances of programmable resistive devices…

Neural and Evolutionary Computing · Computer Science 2020-06-11 Jack Kendall , Ross Pantone , Kalpana Manickavasagam , Yoshua Bengio , Benjamin Scellier

Metalearning of deep neural network (DNN) architectures and hyperparameters has become an increasingly important area of research. At the same time, network regularization has been recognized as a crucial dimension to effective training of…

Neural and Evolutionary Computing · Computer Science 2021-07-22 Jason Liang , Santiago Gonzalez , Hormoz Shahrzad , Risto Miikkulainen
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