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, backpropagation, is considered biologically implausible. We contribute to the topic of biologically plausible neuronal learning by building upon and extending the equilibrium propagation learning framework. Specifically, we introduce: a new neuronal dynamics and learning rule for arbitrary network architectures; a sparsity-inducing method able to prune irrelevant connections; a dynamical-systems characterization of the models, using Lyapunov theory.
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 corresponds to the configuration where the prediction is made. In the second phase, Equilibrium Propagation relaxes to another nearby fixed point corresponding to smaller prediction error, whereas Recurrent Backpropagation uses a side network to compute error derivatives iteratively. In this work we establish a close connection between these two algorithms. We sh…
Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；École Normale Supérieure de Paris（巴黎高等师范学院）
The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists. Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of neurons would need to communicate through symmetric bidirectional connections. We present a simple two-phase learning procedure for fixed point recurrent networks that addresses both these issues. In our model, neurons perform leaky integration and synaptic weights are updated through a local mechanism. Our learning method generalizes Equilibrium Propagatio…
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Unité Mixte de Physique（联合物理实验室）；Thales（泰雷兹集团）；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；Canadian Institute for Advanced Research（加拿大高等研究院）；Google（谷歌）
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 energy-efficient hardware dedicated to learning. In practice, however, EP does not scale to visual tasks harder than MNIST. In this work, we show that a bias in the gradient estimate of EP, inherent in the use of finite nudging, is responsible for this phenomenon and that cancelling it allows training deep ConvNets by EP, including architectures with distinct forward and…
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-based GCNs have achieved impressive results in many graph related analytics tasks. However, spectral-based models cannot directly work on directed graphs. In this paper, we propose an improved spectral-based GCN for the directed graph by leveraging redefined Laplacians to improve it…
Université de Montréal（蒙特利尔大学）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）
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 target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence whi…
Rain Neuromorphics（Rain神经形态公司）；Mila, Université de Montréal（蒙特利尔大学米拉研究所）；Canadian Institute for Advanced Research（加拿大高等研究院）；Google（谷歌）
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 such as memristors [Chua, 1971], and the nonlinear transfer functions (or `activation functions') are implemented by nonlinear components such as diodes. We show mathematically that a class of analog neural networks (called nonlinear resistive networks) are energy-based models: they possess an energy function as a consequence of Kirchhoff's laws governing elec…
Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines
Laboratoire d’Information Quantique, Université Libre de Bruxelles (ULB)（量子信息实验室，布鲁塞尔自由大学）；Dipartimento di Fisica, Sapienza Università di Roma（物理学系，萨皮恩扎罗马大学）
Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning
School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；Laboratory for Advanced Computing and Intelligence Engineering, Information Engineering University（信息工程大学先进计算与智能工程实验室）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）
Friedrich Miescher Institute for Biomedical Research（弗里德里希·米歇尔生物医学研究所）；University of Basel（巴塞尔大学）
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 learning in neurobiology. However, EP requires infinitesimal teaching signals, thereby limiting its applicability in noisy physical systems. Moreover, the algorithm requires separate temporal phases and has not been applied to large-scale problems. Here we address these issues by extending EP to holomorphic networks. We show analytically that this extension n…
Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
University of Groningen（格罗宁根大学）；Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 - CRIStAL（里尔大学、法国国家信息与自动化研究所、法国国家科学研究中心、中央理工-里尔高等电力学院，UMR 9189 - CRIStAL）；Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究中心）；The University of Sheffield（谢菲尔德大学）
Predicting fading channels is a classical problem with a vast array of applications, including as an enabler of artificial intelligence (AI)-based proactive resource allocation for cellular networks. Under the assumption that the fading channel follows a stationary complex Gaussian process, as for Rayleigh and Rician fading models, the optimal predictor is linear, and it can be directly computed from the Doppler spectrum via standard linear minimum mean squared error (LMMSE) estimation. However, in practice, the Doppler spectrum is unknown, and the predictor has only access to a limited time s…
MRC Brain Networks Dynamics Unit（英国医学研究理事会脑网络动力学部门）；University of Oxford（牛津大学）
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 which operate in ways that more closely satisfy the constraints imposed by neural circuitry. Many such algorithms utilize the framework of energy-based models (EBMs), in which all free variables in the model are optimized to minimize a global energy function. However, in the literature, these algorithms exist in isolation and no unified theory exists linking t…
StochEP: Stochastic Equilibrium Propagation for Spiking Convergent Recurrent Neural Networks
School of Electrical Engineering and Computer Science（电气工程与计算机科学学院）；The Pennsylvania State University（宾夕法尼亚州立大学）；University Park（大学公园）；PA 16802, USA（宾夕法尼亚州16802, 美国）
Central China Normal University（华中师范大学）；Eötvös Loránd University（厄特沃什·罗兰大学）；Center for Energy Research（能源研究中心）；Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
The latest advances of statistical physics have shown remarkable performance of machine learning in identifying phase transitions. In this paper, we apply domain adversarial neural network (DANN) based on transfer learning to studying non-equilibrium and equilibrium phase transition models, which are percolation model and directed percolation (DP) model, respectively. With the DANN, only a small fraction of input configurations (2d images) needs to be labeled, which is automatically chosen, in order to capture the critical point. To learn the DP model, the method is refined by an iterative pro…
How to Train Your Resistive Network: Generalized Equilibrium Propagation and Analytical Learning
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA（明希德电气与计算机工程系，南加州大学，洛杉矶，加利福尼亚州，美国）；Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA（非线性研究中心，洛斯阿拉莫斯国家实验室，洛斯阿拉莫斯，新墨西哥州，美国）；Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA（理论部（T4），洛斯阿拉莫斯国家实验室，洛斯阿拉莫斯，新墨西哥州，美国）；CAI-3, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA（CAI-3，洛斯阿拉莫斯国家实验室，洛斯阿拉莫斯，新墨西哥州，美国）；University of California, Berkeley, Berkeley, CA, 94720, USA（加州大学伯克利分校，伯克利，加利福尼亚州，美国）；Department of Physics, University of Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy（物理学系，比萨大学，布鲁诺·蓬泰科罗夫大道3号，比萨，意大利）
