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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

Recurrent Backpropagation and Equilibrium Propagation are supervised learning algorithms for fixed point recurrent neural networks which differ in their second phase. In the first phase, both algorithms converge to a fixed point which…

Machine Learning · Computer Science 2018-05-24 Benjamin Scellier , Yoshua Bengio

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

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure --…

Machine Learning · Statistics 2021-12-24 Ganlin Song , Ruitu Xu , John Lafferty

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

This study investigates how weight decay affects the update behavior of individual neurons in deep neural networks through a combination of applied analysis and experimentation. Weight decay can cause the expected magnitude and angular…

Machine Learning · Computer Science 2024-06-04 Atli Kosson , Bettina Messmer , Martin Jaggi

Artificial neural networks, one of the most successful approaches to supervised learning, were originally inspired by their biological counterparts. However, the most successful learning algorithm for artificial neural networks,…

Machine Learning · Computer Science 2020-06-18 Matilde Tristany Farinha , Sérgio Pequito , Pedro A. Santos , Mário A. T. Figueiredo

Traditional backpropagation of error, though a highly successful algorithm for learning in artificial neural network models, includes features which are biologically implausible for learning in real neural circuits. An alternative called…

Machine Learning · Computer Science 2020-11-06 Nasir Ahmad , Marcel A. J. van Gerven , Luca Ambrogioni

Standard neural network based on general back propagation learning using delta method or gradient descent method has some great faults like poor optimization of error-weight objective function, low learning rate, instability .This paper…

Neural and Evolutionary Computing · Computer Science 2012-12-20 Mriganka Chakraborty , Arka Ghosh

The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…

Neural and Evolutionary Computing · Computer Science 2018-05-01 Hongyin Luo , Jie Fu , James Glass

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

We present a global algorithm for training multilayer neural networks in this Letter. The algorithm is focused on controlling the local fields of neurons induced by the input of samples by random adaptations of the synaptic weights. Unlike…

Biological Physics · Physics 2007-05-23 Hong Zhao , Tao Jin

Equilibrium propagation has been proposed as a biologically plausible alternative to the backpropagation algorithm. The local nature of gradient computations, combined with the use of convergent RNNs to reach equilibrium states, make this…

Neural and Evolutionary Computing · Computer Science 2026-03-19 Sankar Vinayak Elayedam , Gopalakrishnan Srinivasan

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

Of all the vector fields surrounding the minima of recurrent learning setups, the gradient field with its exploding and vanishing updates appears a poor choice for optimization, offering little beyond efficient computability. We seek to…

Machine Learning · Computer Science 2024-05-06 Patrick Schnell , Nils Thuerey

Ongoing studies have identified similarities between neural representations in biological networks and in deep artificial neural networks. This has led to renewed interest in developing analogies between the backpropagation learning…

Neural and Evolutionary Computing · Computer Science 2019-06-11 Theodore H. Moskovitz , Ashok Litwin-Kumar , L. F. Abbott

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

We consider artificial neurons which will update their weight coefficients with an internal rule based on backpropagation, rather than using it as an external training procedure. To achieve this we include the backpropagation error estimate…

Neural and Evolutionary Computing · Computer Science 2018-08-07 M. N. Nazarov

The brain processes information through many layers of neurons. This deep architecture is representationally powerful, but it complicates learning by making it hard to identify the responsible neurons when a mistake is made. In machine…

Neurons and Cognition · Quantitative Biology 2014-11-04 Timothy P. Lillicrap , Daniel Cownden , Douglas B. Tweed , Colin J. Akerman
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