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In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is…

We present a novel stochastic Hebb-like learning rule for neural networks. This learning rule is stochastic with respect to the selection of the time points when a synaptic modification is induced by pre- and postsynaptic activation.…

Neural network models offer a theoretical testbed for the study of learning at the cellular level. The only experimentally verified learning rule, Hebb's rule, is extremely limited in its ability to train networks to perform complex tasks.…

On the basis of the general form for the energy needed to adapt the connection strengths of a network in which learning takes place, a local learning rule is found for the changes of the weights. This biologically realizable learning rule…

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…

In this paper, we introduce a new type of generalized neural network where neurons and synapses maintain multiple states. We show that classical gradient-based backpropagation in neural networks can be seen as a special case of a two-state…

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…

Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…

We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this…

Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Neural networks with synaptic weights constructed according to the weighted Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of noise(finite temperature), when the number of stored patterns is finite and in the…

Recurrent Bistable Gradient Networks are attractor based neural networks characterized by bistable dynamics of each single neuron. Coupled together using linear interaction determined by the interconnection weights, these networks do not…

Lateral inhibition models coupled with Hebbian plasticity have been shown to learn factorised causal representations of input stimuli, for instance, oriented edges are learned from natural images. Currently, these models require the…

Hebbian and anti-Hebbian plasticity are widely observed in the biological brain, yet their theoretical understanding remains limited. In this work, we find that when a learning method is regularized with L2 weight decay, its learning signal…

Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability…

As well known, Hebb's learning traces its origin in Pavlov's Classical Conditioning, however, while the former has been extensively modelled in the past decades (e.g., by Hopfield model and countless variations on theme), as for the latter…

Recurrent neural networks in the chaotic regime exhibit complex dynamics reminiscent of high-level cortical activity during behavioral tasks. However, existing training methods for such networks are either biologically implausible, or…

We study some features of learning models based on "delayed" and undifferentiated reinforcement and realized by simple algorithms which may be considered of a very elementary nature. We show that a modification of the Hebb-rule works well…

Bayesian inference provides a principled framework for understanding brain function, while neural activity in the brain is inherently spike-based. This paper bridges these two perspectives by designing spiking neural networks that simulate…