scholarly journals Stochastic neural networks with the weighted Hebb rule

1994 ◽  
Vol 191 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
Caren Marzban ◽  
Raju Viswanathan
Keyword(s):  
Neural Networks ◽  
Stochastic Neural Networks ◽  
Hebb Rule

Reward-Modulated Hebbian Learning of Decision Making

2010 ◽  
Vol 22 (6) ◽  
pp. 1399-1444 ◽  
Author(s):  
Michael Pfeiffer ◽  
Bernhard Nessler ◽  
Rodney J. Douglas ◽  
Wolfgang Maass
Keyword(s):  
Decision Making ◽  
Hebbian Learning ◽  
Learning Rule ◽  
Final Decision ◽  
Bayesian Decision ◽  
Decision Stage ◽  
Fast Learning ◽  
Hebb Rule ◽  
Adaptive Processes ◽  
Perceptron Learning

We introduce a framework for decision making in which the learning of decision making is reduced to its simplest and biologically most plausible form: Hebbian learning on a linear neuron. We cast our Bayesian-Hebb learning rule as reinforcement learning in which certain decisions are rewarded and prove that each synaptic weight will on average converge exponentially fast to the log-odd of receiving a reward when its pre- and postsynaptic neurons are active. In our simple architecture, a particular action is selected from the set of candidate actions by a winner-take-all operation. The global reward assigned to this action then modulates the update of each synapse. Apart from this global reward signal, our reward-modulated Bayesian Hebb rule is a pure Hebb update that depends only on the coactivation of the pre- and postsynaptic neurons, not on the weighted sum of all presynaptic inputs to the postsynaptic neuron as in the perceptron learning rule or the Rescorla-Wagner rule. This simple approach to action-selection learning requires that information about sensory inputs be presented to the Bayesian decision stage in a suitably preprocessed form resulting from other adaptive processes (acting on a larger timescale) that detect salient dependencies among input features. Hence our proposed framework for fast learning of decisions also provides interesting new hypotheses regarding neural nodes and computational goals of cortical areas that provide input to the final decision stage.

scholarly journals STOCHASTIC PSEUDOSPIN NEURAL NETWORK WITH TRIDIAGONAL SYNAPTIC CONNECTIONS

2021 ◽  
pp. 114-122
Author(s):  
R. М. Peleshchak ◽  
V. V. Lytvyn ◽  
О. І. Cherniak ◽  
І. R. Peleshchak ◽  
М. V. Doroshenko
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Connection Matrix ◽  
Synaptic Connections ◽  
Hessenberg Matrix ◽  
Tuning Time ◽  
Hebb Rule ◽  
The Matrix ◽  
Dipole Glass ◽  
Fully Connected

Context. To reduce the computational resource time in the problems of diagnosing and recognizing distorted images based on a fully connected stochastic pseudospin neural network, it becomes necessary to thin out synaptic connections between neurons, which is solved using the method of diagonalizing the matrix of synaptic connections without losing interaction between all neurons in the network. Objective. To create an architecture of a stochastic pseudo-spin neural network with diagonal synaptic connections without loosing the interaction between all the neurons in the layer to reduce its learning time. Method. The paper uses the Hausholder method, the method of compressing input images based on the diagonalization of the matrix of synaptic connections and the computer mathematics system MATLAB for converting a fully connected neural network into a tridiagonal form with hidden synaptic connections between all neurons. Results. We developed a model of a stochastic neural network architecture with sparse renormalized synaptic connections that take into account deleted synaptic connections. Based on the transformation of the synaptic connection matrix of a fully connected neural network into a Hessenberg matrix with tridiagonal synaptic connections, we proposed a renormalized local Hebb rule. Using the computer mathematics system “WolframMathematica 11.3”, we calculated, as a function of the number of neurons N, the relative tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network. Conclusions. We found that with an increase in the number of neurons, the tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network, decreases according to a hyperbolic law. Depending on the direction of pseudospin neurons, we proposed a classification of a renormalized neural network with a ferromagnetic structure, an antiferromagnetic structure, and a dipole glass.

scholarly journals The Hebb Rule for Synaptic Plasticity: Algorithms and Implementations

1989 ◽  
pp. 94-103 ◽  
Author(s):  
Terrence J. Sejnowski ◽  
Gerald Tesauro
Keyword(s):  
Synaptic Plasticity ◽  
Hebb Rule

On Learning Perceptrons with Binary Weights

1993 ◽  
Vol 5 (5) ◽  
pp. 767-782 ◽  
Author(s):  
Mostefa Golea ◽  
Mario Marchand
Keyword(s):  
Learning Curve ◽  
Uniform Distribution ◽  
Pac Learning ◽  
Sample Complexity ◽  
Average Case Analysis ◽  
Average Case ◽  
Hebb Rule ◽  
Product Distributions ◽  
Training Examples ◽  
Learning Analysis

We present an algorithm that PAC learns any perceptron with binary weights and arbitrary threshold under the family of product distributions. The sample complexity of this algorithm is of O[(n/ε)4 ln(n/δ)] and its running time increases only linearly with the number of training examples. The algorithm does not try to find an hypothesis that agrees with all of the training examples; rather, it constructs a binary perceptron based on various probabilistic estimates obtained from the training examples. We show that, under the restricted case of the uniform distribution and zero threshold, the algorithm reduces to the well known clipped Hebb rule. We calculate exactly the average generalization rate (i.e., the learning curve) of the algorithm, under the uniform distribution, in the limit of an infinite number of dimensions. We find that the error rate decreases exponentially as a function of the number of training examples. Hence, the average case analysis gives a sample complexity of O[n ln(1/ε)], a large improvement over the PAC learning analysis. The analytical expression of the learning curve is in excellent agreement with the extensive numerical simulations. In addition, the algorithm is very robust with respect to classification noise.

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