Stabilization of Hebbian neural nets by inhibitory learning
type: Item
instance of: scholarly article
title: Stabilization of Hebbian neural nets by inhibitory learning
zbMATH Open document ID: 0552.92007
DOI: 10.1007/BF00336182
author: Paul Easton
author: P. Gordon
published in: Biological Cybernetics
publication date: 1984-01-01T00:00:00Z
review text: Hebbian neural models with simultaneously active pre- and postsynaptic neurons are considered which are stabilized by recurrent inhibition via modifiable inhibitory synapses. A one synapse model which is a system of two differential equations incorporating Hebb's principle is described to introduce the main definitions. Adding to the model first fixed feed- forward inhibition, then dynamic feed-forward and then fixed recurrent one, it is shown that there is no stable steady state solution. With modifiable recurrent inhibition a non-zero solution exists when the input exceeds a certain intensity. When the zero solution is the only one, it is stable, but when the non-zero solution exists it is stable and the zero solution is unstable. The equations are extended to time varying input and to many neuron systems. The linearized equations are tensor invariant under a class of rotations of the state space. The response to stimulation may be derived as a set of independent modes of activity distributed over the net, which may be identified with cell assemblies. Analytic solutions of the three layer system are given.
Mathematics Subject Classification ID: 92Cxx
zbMATH DE Number: 3880490
zbMATH Keywords: stabilization
zbMATH Keywords: inhibitory learning
zbMATH Keywords: continuously infinite set of equivalent solutions
zbMATH Keywords: dynamic recurrent inhibition
zbMATH Keywords: Hebbian neural models
zbMATH Keywords: simultaneously active pre- and postsynaptic neurons
zbMATH Keywords: modifiable inhibitory synapses
zbMATH Keywords: differential equations
zbMATH Keywords: feed-forward inhibition
zbMATH Keywords: dynamic feed-forward
zbMATH Keywords: no stable steady state solution
zbMATH Keywords: modifiable recurrent inhibition
zbMATH Keywords: time varying input
zbMATH Keywords: many neuron systems
zbMATH Keywords: tensor invariant
zbMATH Keywords: rotations of the state space
zbMATH Keywords: Analytic solutions of the three layer system
Wikidata QID: Q52277572
MaRDI profile type: Publication
cites work: Neural theory of association and concept-formation
cites work: A simple neural network generating an interactive memory
cites work: Functional equations in the theory of dynamic programming. XV: Layered functionals and partial differential equations
cites work: A theory for the acquisition and loss of neuron specificity in visual cortex
cites work: On the development of feature detectors in the visual cortex with applications to learning and reaction-diffusion systems
cites work: Q4125819
cites work: Self-organized formation of topologically correct feature maps
cites work: Fast adaptive formation of orthogonalizing filters and associative memory in recurrent networks of neuron-like elements
cites work: A simplified neuron model as a principal component analyzer
cites work: Q5585825
cites work: Formation of topographic maps and columnar microstructures in nerve fields
full work available at URL: https://doi.org/10.1007/bf00336182
OpenAlex ID: W2026627891
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description: scientific article; zbMATH DE number 3880490