Contrastive Hebbian Learning Research Articles

Learning Stiffness Tensors in Self-Activated Solids via a Local Rule.

Mechanical metamaterials are often designed with particular properties for specific load-bearing functions. Alternatively, this study aims to create a class of active lattice metamaterials, dubbed self-activated solids, that can learn desired stiffness tensors from the elastic deformations they experienced, a crucial feature to improve the performance, efficiency, and functionality of materials. Artificial adaptive matters that combine sensory, control, and actuation elements can offer appealing solutions. However, challenges still remain: The designs will rely on accurate off-line and global computations, as well as intricate coordination among individual elements. Here, a simple online and local learning strategy is initiated based on contrastive Hebbian learning to gradually guide self-activated solids to possess sought-after stiffness tensors autonomously and reversibly. During learning, the bond stiffness of the active lattice varies depending only on its local strain. The numerical tests show that the self-activated solid can not only achieve the desired bulk, shear, and coupling moduli but also manifest uni-mode and bi-mode extremal materials by itself after experiencing the corresponding elastic deformations. Further, the self-activated solid can also achieve the desired time-varying moduli when exposed to temporally different loads. The design is applicable to any lattice geometries and is resistant to damage and instabilities. The material design approach and the physical learning strategy suggested can benefit the design of autonomous materials, physical learning machines, and adaptiverobots.

Physical learning of stiffness tensors by self-activated solids

Unlike plastic deformations, elastic deformations usually cannot change mechanical properties of materials under different loading conditions. In this talk, we suggest a class of self-activated solids and derive a local learning rule so that the solid can learn the desired stiffness tensors through repeated elastic deformations it experienced. The local learning rule is inspired by contrastive Hebbian learning, which guides the learning process by modulating the bond stiffness of the solid based on its local stain. Extensive numerical tests are performed to validate the design and learning rule. We show that the self-activated solid can be physically trained to display the desired bulk, shear, and coupling moduli and to manifest uni-mode and bi-mode materials. The solid can also realize time-varying moduli to function as time-modulated materials. The material design and learning strategy introduced are scalable and applicable to arbitrary lattice geometries and other discrete material systems. The study could lead to new physical learning systems, beneficial to autonomous materials, machines, and robots.

Scalable Nanophotonic-Electronic Spiking Neural Networks

Spiking neural networks (SNN) provide a new computational paradigm capable of highly parallelized, real-time processing. Photonic devices are ideal for the design of high-bandwidth, parallel architectures matching the SNN computational paradigm. Furthermore, the co-integration of CMOS and photonic elements combineslow-loss photonic devices with analog electronics for greater flexibility of nonlinear computational elements. We designed and simulated an optoelectronic spiking neuron circuit on a monolithic silicon photonics (SiPh) process that replicates useful spiking behaviors beyond the leaky integrate-and-fire (LIF). Additionally, we explored two learning algorithms with the potential for on-chip learning using Mach-Zehnder Interferometric (MZI) meshes as synaptic interconnects. A variation of Random Backpropagation (RPB) was experimentally demonstrated on-chip and matched the performance of a standard linear regression on a simple classification task. In addition, we applied the Contrastive Hebbian Learning (CHL) rule to a simulated neural network composed of MZI meshes for a random input-output mapping task. The CHL-trained MZI network performed better than random guessing but did not match the performance of the ideal neural network (without the constraints imposed by the MZI meshes). Through these efforts, we demonstrate that co-integrated CMOS and SiPh technologies are well-suited to the design of scalable SNN computing architectures.

Biologically-inspired neuronal adaptation improves learning in neural networks

ABSTRACT Since humans still outperform artificial neural networks on many tasks, drawing inspiration from the brain may help to improve current machine learning algorithms. Contrastive Hebbian learning (CHL) and equilibrium propagation (EP) are biologically plausible algorithms that update weights using only local information (without explicitly calculating gradients) and still achieve performance comparable to conventional backpropagation. In this study, we augmented CHL and EP with Adjusted Adaptation, inspired by the adaptation effect observed in neurons, in which a neuron’s response to a given stimulus is adjusted after a short time. We add this adaptation feature to multilayer perceptrons and convolutional neural networks trained on MNIST and CIFAR-10. Surprisingly, adaptation improved the performance of these networks. We discuss the biological inspiration for this idea and investigate why Neuronal Adaptation could be an important brain mechanism to improve the stability and accuracy of learning.

Comparing the performance of Hebbian against backpropagation learning using convolutional neural networks

In this paper, we investigate Hebbian learning strategies applied to Convolutional Neural Network (CNN) training. We consider two unsupervised learning approaches, Hebbian Winner-Takes-All (HWTA), and Hebbian Principal Component Analysis (HPCA). The Hebbian learning rules are used to train the layers of a CNN in order to extract features that are then used for classification, without requiring backpropagation (backprop). Experimental comparisons are made with state-of-the-art unsupervised (but backprop-based) Variational Auto-Encoder (VAE) training. For completeness,we consider two supervised Hebbian learning variants (Supervised Hebbian Classifiers—SHC, and Contrastive Hebbian Learning—CHL), for training the final classification layer, which are compared to Stochastic Gradient Descent training. We also investigate hybrid learning methodologies, where some network layers are trained following the Hebbian approach, and others are trained by backprop. We tested our approaches on MNIST, CIFAR10, and CIFAR100 datasets. Our results suggest that Hebbian learning is generally suitable for training early feature extraction layers, or to retrain higher network layers in fewer training epochs than backprop. Moreover, our experiments show that Hebbian learning outperforms VAE training, with HPCA performing generally better than HWTA.

Contrastive Hebbian Feedforward Learning for Neural Networks.

This paper addresses the biological plausibility of both backpropagation (BP) and contrastive Hebbian learning (CHL) used in the Boltzmann machines. The main claim of this paper is that CHL is a general learning algorithm that can be used to steer feedforward networks toward desirable outcomes, and steer them away from undesirable outcomes without any need for the specialized feedback circuit of BP or the symmetric connections used by the Boltzmann machines. After adding perturbations during the learning phase to all the neurons in the network, multiple feedforward outcomes are classified into Hebbian and anti-Hebbian sets based on the network predictions. The algorithm is applied to networks when optimizing a loss objective where BP excels and is also applied to networks with stochastic binary outputs where BP cannot be easily applied. The power of the proposed algorithm lies in its simplicity where both learning and gradient estimation through stochastic binary activations are combined into a single local Hebbian rule. We will also show that both Hebbian and anti-Hebbian correlations are evaluated from the readily available signals that are fundamentally different from CHL used in the Boltzmann machines. We will demonstrate that the new learning paradigm where Hebbian/anti-Hebbian correlations are based on correct/incorrect predictions is a powerful concept that separates this paper from other biologically inspired learning algorithms.

Contrastive Hebbian learning with random feedback weights

Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb’s rule and the contrastive divergence algorithm. It operates in two phases, the free phase, where the data are fed to the network, and a clamped phase, where the target signals are clamped to the output layer of the network and the feedback signals are transformed through the transpose synaptic weight matrices. This implies symmetries at the synaptic level, for which there is no evidence in the brain so far. In this work, we propose a new variant of the algorithm, called random contrastive Hebbian learning, which does not rely on any synaptic weights symmetries. Instead, it uses random matrices to transform the feedback signals during the clamped phase, and the neural dynamics are described by first order non-linear differential equations. The algorithm is experimentally verified by solving a Boolean logic task, classification tasks (handwritten digits and letters), and an autoencoding task. This article also shows how the parameters affect learning, especially the random matrices. We use the pseudospectra analysis to investigate further how random matrices impact the learning process. Finally, we discuss the biological plausibility of the proposed algorithm, and how it can give rise to better computational models for learning.

Characteristics of contrastive Hebbian learning with pseudorehearsal for multilayer neural networks on reduction of catastrophic forgetting

Neural networks encounter serious catastrophic forgetting or catastrophic interference when information is learned sequentially. One of the methods which can reduce catastrophic forgetting is pseudorehearsal, in which pseudopatterns are learned with training patterns. This method has shown superior performance for multilayer neural networks trained by the backpropagation algorithm. However, the backpropagation algorithm is biologically implausible because it requires passage of error signals backward from output neurons to input ones. That is, the learning cannot by executed locally. On the other hand, contrastive Hebbian learning (CHL) is a learning method using Hebbian rule for synaptic weight changes. Since Hebbian learning can be performed locally between two neurons and does not need to take into account error information computed at output neurons, it is much more biologically plausible than the backpropagation algorithm. In this paper, we examine characteristics of multilayer neural networks trained by CHL with pseudorehearsal when information is applied sequentially, and how catastrophic forgetting can be reduced.

Characteristics of contrastive Hebbian learning with pseudorehearsal for multilayer neural networks on reduction of catastrophic forgetting

Neural networks encounter serious catastrophic forgetting or catastrophic interference when information is learned sequentially. One of the methods which can reduce catastrophic forgetting is pseudorehearsal, in which pseudopatterns are learned with training patterns. This method has shown superior performance for multilayer neural networks trained by the backpropagation algorithm. However, the backpropagation algorithm is biologically implausible because it requires passage of error signals backward from output neurons to input ones. That is, the learning cannot by executed locally. On the other hand, contrastive Hebbian learning (CHL) is a learning method using Hebbian rule for synaptic weight changes. Since Hebbian learning can be performed locally between two neurons and does not need to take into account error information computed at output neurons, it is much more biologically plausible than the backpropagation algorithm. In this paper, we examine characteristics of multilayer neural networks trained by CHL with pseudorehearsal when information is applied sequentially, and how catastrophic forgetting can be reduced.

Equilibrium Propagation: Bridging the Gap between Energy-Based Models and Backpropagation.

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 while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal “back-propagated” during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task.

How Inhibitory Oscillations Can Train Neural Networks and Punish Competitors

We present a new learning algorithm that leverages oscillations in the strength of neural inhibition to train neural networks. Raising inhibition can be used to identify weak parts of target memories, which are then strengthened. Conversely, lowering inhibition can be used to identify competitors, which are then weakened. To update weights, we apply the Contrastive Hebbian Learning equation to successive time steps of the network. The sign of the weight change equation varies as a function of the phase of the inhibitory oscillation. We show that the learning algorithm can memorize large numbers of correlated input patterns without collapsing and that it shows good generalization to test patterns that do not exactly match studied patterns.

A knowledge-resonance (KRES) model of category learning.

This article introduces a connectionist model of category learning that takes into account the prior knowledge that people bring to new learning situations. In contrast to connectionist learning models that assume a feedforward network and learn by the delta rule or backpropagation, this model, the knowledge-resonance model, or KRES, employs a recurrent network with bidirectional symmetric connection whose weights are updated according to a contrastive Hebbian learning rule. We demonstrate that when prior knowledge is represented in the network, KRES accounts for a considerable range of empirical results regarding the effects of prior knowledge on category learning, including (1) the accelerated learning that occurs in the presence of knowledge, (2) the better learning in the presence of knowledge of category features that are not related to prior knowledge, (3) the reinterpretation of features with ambiguous interpretations in light of error-corrective feedback, and (4) the unlearning of prior knowledge when that knowledge is inappropriate in the context of a particular category.

Equivalence of backpropagation and contrastive Hebbian learning in a layered network.

Backpropagation and contrastive Hebbian learning are two methods of training networks with hidden neurons. Backpropagation computes an error signal for the output neurons and spreads it over the hidden neurons. Contrastive Hebbian learning involves clamping the output neurons at desired values and letting the effect spread through feedback connections over the entire network. To investigate the relationship between these two forms of learning, we consider a special case in which they are identical: a multilayer perceptron with linear output units, to which weak feedback connections have been added. In this case, the change in network state caused by clamping the output neurons turns out to be the same as the error signal spread by backpropagation, except for a scalar prefactor. This suggests that the functionality of backpropagation can be realized alternatively by a Hebbian-type learning algorithm, which is suitable for implementation in biological networks.

Instabilities and Oscillation in the Deterministic Boltzmann Machine

Simulations indicate that the deterministic Boltzmann machine, unlike the stochastic Boltzmann machine from which it is derived, exhibits unstable behavior during contrastive Hebbian learning of nonlinear problems, including oscillation in the learning algorithm and extreme sensitivity to small weight perturbations. Although careful choice of the initial weight magnitudes, the learning rate, and the annealing schedule will produce convergence in most cases, the stability of the resulting solution depends on the parameters in a complex and generally indiscernible way. We show that this unstable behavior is the result of over parameterization (excessive freedom in the weights), which leads to continuous rather than isolated optimal weight solution sets. This allows the weights to drift without correction by the learning algorithm until the free energy landscape changes in such a way that the settling procedure employed finds a different minimum of the free energy function than it did previously and a gross output error occurs. Because all the weight sets in a continuous optimal solution set produce exactly the same network outputs, we define reliability, a measure of the robustness of the network, as a new performance criterion.

TOLERANCE OF ON-CHIP LEARNING TO VARIOUS CIRCUIT INACCURACIES

An investigation is made of the tolerance of various in-circuit learning algorithms to component imprecision and other circuit limitations in artificial neural networks. In contrast with most previous work, the various circuit limitations are treated separately for their effects on learning. Supervised learning mechanisms including backpropagation and contrastive Hebbian learning, and unsupervised soft competitive learning were found to be sufficiently tolerant of those levels of arithmetic inaccuracy, noise, nonlinearity, weight decay, and statistical variation from fabrication that we have experienced in 1.2 μm analog CMOS circuits employing Gilbert multipliers as the primary computational element. These learning circuits also function properly in the presence of offset errors in analog multipliers and adders, provided that the computed weight updates are constrained by the circuitry to be made only when they exceed certain minimum or threshold values. These results may also be relevant for other analog circuit approaches and for compact (low bit rate) digital implementations, although in this case, the minimum weight increment defined by the bit precision could necessitate stochastic updating.

Biologically Plausible Error-Driven Learning Using Local Activation Differences: The Generalized Recirculation Algorithm

The error backpropagation learning algorithm (BP) is generally considered biologically implausible because it does not use locally available, activation-based variables. A version of BP that can be computed locally using bidirectional activation recirculation (Hinton and McClelland 1988) instead of backpropagated error derivatives is more biologically plausible. This paper presents a generalized version of the recirculation algorithm (GeneRec), which overcomes several limitations of the earlier algorithm by using a generic recurrent network with sigmoidal units that can learn arbitrary input/output mappings. However, the contrastive Hebbian learning algorithm (CHL, also known as DBM or mean field learning) also uses local variables to perform error-driven learning in a sigmoidal recurrent network. CHL was derived in a stochastic framework (the Boltzmann machine), but has been extended to the deterministic case in various ways, all of which rely on problematic approximations and assumptions, leading some to conclude that it is fundamentally flawed. This paper shows that CHL can be derived instead from within the BP framework via the GeneRec algorithm. CHL is a symmetry-preserving version of GeneRec that uses a simple approximation to the midpoint or second-order accurate Runge-Kutta method of numerical integration, which explains the generally faster learning speed of CHL compared to BI. Thus, all known fully general error-driven learning algorithms that use local activation-based variables in deterministic networks can be considered variations of the GeneRec algorithm (and indirectly, of the backpropagation algorithm). GeneRec therefore provides a promising framework for thinking about how the brain might perform error-driven learning. To further this goal, an explicit biological mechanism is proposed that would be capable of implementing GeneRec-style learning. This mechanism is consistent with available evidence regarding synaptic modification in neurons in the neocortex and hippocampus, and makes further predictions.