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We consider artificial neurons which will update their weight coefficientswith an internal rule based on backpropagation, rather than using it as anexternal training procedure. To achieve this we include the backpropagationerror estimate as a separate entity in all the neuron models and perform itsexchange along the synaptic connections. In addition to this we add somespecial type of neurons with reference inputs, which will serve as a basesource of error estimates for the whole network. Finally, we introduce atraining control signal for all the neurons, which can enable the correction ofweights and the exchange of error estimates. For recurrent neural networks wealso demonstrate how to integrate backpropagation through time into theirformalism with the help of some stack memory for reference inputs and externaldata inputs of neurons. Also, for widely used neural networks, such as longshort-term memory, radial basis function networks, multilayer perceptrons andconvolutional neural networks, we demonstrate their alternative descriptionwithin the framework of our new formalism.

Neural networks with dynamical coefficients and adjustable connections on the basis of integrated backpropagation