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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

Neuromorphic architectures, which incorporate parallel and in-memory processing, are crucial for accelerating artificial neural network (ANN) computations. This work presents a novel memristor-based multi-layer neural network (memristive…

Emerging Technologies · Computer Science 2025-07-29 Santlal Prajapat , Manobendra Nath Mondal , Susmita Sur-Kolay

Convergence of dynamic feedback neural networks (NNs), as the Cohen-Grossberg, Hopfield and cellular NNs, has been for a long time a workhorse of NN theory. Indeed, convergence in the presence of multiple stable equilibrium points (EPs) is…

Systems and Control · Electrical Eng. & Systems 2025-07-29 Mauro Di Marco , Mauro Forti , Luca Pancioni , Giacomo Innocenti , Alberto Tesi

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

Edge devices operating in dynamic environments critically need the ability to continually learn without catastrophic forgetting. The strict resource constraints in these devices pose a major challenge to achieve this, as continual learning…

Systems and Control · Electrical Eng. & Systems 2024-11-12 Fatima Tuz Zohora , Vedant Karia , Nicholas Soures , Dhireesha Kudithipudi

We present a systematic study of memristor based neural networks trained with the hardware-friendly Manhattan update rule, focusing on the trade offs between learning performance and energy consumption. Using realistic models of…

Mesoscale and Nanoscale Physics · Physics 2025-11-07 Walter Quiñonez , María José Sánchez , Diego Rubi

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

Memristive neural networks (MNNs), which use memristors as neurons or synapses, have become a hot research topic recently. However, most memristors are not compatible with mainstream integrated circuit technology and their stabilities in…

Emerging Technologies · Computer Science 2019-01-03 Zhiri Tang , Ruohua Zhu , Peng Lin , Jin He , Hao Wang , Qijun Huang , Sheng Chang , Qiming Ma

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

Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range…

Machine Learning · Statistics 2017-07-19 Cory Merkel

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 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

Recent years have seen a rapid rise of artificial neural networks being employed in a number of cognitive tasks. The ever-increasing computing requirements of these structures have contributed to a desire for novel technologies and…

Emerging Technologies · Computer Science 2022-05-06 Dovydas Joksas , Erwei Wang , Nikolaos Barmpatsalos , Wing H. Ng , Anthony J. Kenyon , George A. Constantinides , Adnan Mehonic

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

Machine learning has recently developed novel approaches, mimicking the synapses of the human brain to achieve similarly efficient learning strategies. Such an approach retains the universality of standard methods, while attempting to…

Asymmetric nonlinear weight update is considered as one of the major obstacles for realizing hardware neural networks based on analog resistive synapses because it significantly compromises the online training capability. This paper…

Deep learning has made remarkable progress in various tasks, surpassing human performance in some cases. However, one drawback of neural networks is catastrophic forgetting, where a network trained on one task forgets the solution when…

Neural and Evolutionary Computing · Computer Science 2024-01-04 Simone D'Agostino , Filippo Moro , Tifenn Hirtzlin , Julien Arcamone , Niccolò Castellani , Damien Querlioz , Melika Payvand , Elisa Vianello

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

Applications of Binary Neural Networks (BNNs) are promising for embedded systems with hard constraints on computing power. Contrary to conventional neural networks with the floating-point datatype, BNNs use binarized weights and activations…

Emerging Technologies · Computer Science 2022-11-14 Mahdi Zahedi , Taha Shahroodi , Stephan Wong , Said Hamdioui

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
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