Solutions of the BCM learning rule in a network of lateral interacting nonlinear neurons
Network Computation in Neural SystemsPublished 1 May 1999
Gastone Castellani, Nathan Intrator, Harel Z. Shouval, Leroy L. Cooper
Citations31
SJR quartileQ4
SJR score0.33
SNIP0.56
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The new formalism permits analysis of a laterally connected network of nonlinear neurons and allows explicit calculation of the fixed points under various network conditions and shows that the stable fixed points, in terms of the postsynaptic activity, are not altered by the lateral connectivity or nonlinearity.
Abstract
We introduce a new method for obtaining the fixed points for neurons that follow the BCM learning rule. The new formalism, which is based on the objective function formulation, permits analysis of a laterally connected network of nonlinear neurons and allows explicit calculation of the fixed points under various network conditions. We show that the stable fixed points, in terms of the postsynaptic activity, are not altered by the lateral connectivity or nonlinearity. We show that the lateral connectivity alters the probability of attaining different states in a network of interacting neurons. We further show the exact alteration in presynaptic weights as a result of the neuronal nonlinearity.
Keywords
Computer ScienceNeurosciencePhysics and Astronomy
Journal of NeuroscienceTheory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex
2,950 Citations1982EL Bienenstock, L N Cooper +1 more
The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework and a synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete.
Proceedings of the National Academy of SciencesHomosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade.
1,692 Citations1992Serena M. Dudek, Mark F. Bear
The data suggest that synaptic depression can be triggered by prolonged NMDA receptor activation that is below the threshold for inducing synaptic potentiation, and it is proposed that this mechanism is important for the modifications of hippocampal response properties that underlie some forms of learning and memory.
NatureExperience-dependent modification of synaptic plasticity in visual cortex
635 Citations1996Alfredo Kirkwood, Marc G. Rioult +1 more
In visual cortex of light-deprived rats that LTP is enhanced and LTD diminished over a range of stimulation frequencies, and that these effects can be reversed by as little as two days of light exposure, support the idea that a variable synaptic-modification threshold allows synaptic weights in neural networks to achieve a stable equilibrium.
ScienceCommon Forms of Synaptic Plasticity in the Hippocampus and Neocortex in Vitro
483 Citations1993Alfredo Kirkwood, Serena M. Dudek +3 more
Results provide strong support for the view that common principles may govern experience-dependent synaptic plasticity in CA1 and throughout the superficial layers of the mammalian neocortex.
Philosophical Transactions of the Royal Society B Biological SciencesGenerative models for discovering sparse distributed representations
228 Citations1997Geoffrey E. Hinton, Zoubin Ghahramani
A hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network that learns to extract sparse, distributed, hierarchical representations is described.
Neural NetworksObjective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions
220 Citations1992Nathan Intrator, Leon N. Cooper
An objective function formulation of the Bienenstock, Cooper, and Munro (BCM) theory of visual cortical plasticity is presented that permits the connection between the unsupervised BCM learning procedure and various statistical methods, in particular, that of Projection Pursuit.
Journal of NeurophysiologySynaptic plasticity in visual cortex: comparison of theory with experiment
116 Citations1991Eugene E. Clothiaux, Mark F. Bear +1 more
The aim of this work was to assess whether a form of synaptic modification based on the theory of Bienenstock, Cooper, and Munro (BCM) can, with a fixed set of parameters, reproduce both the kinetics and equilibrium states of experience-dependent modifications cortex.
Proceedings of the National Academy of SciencesFormation of receptive fields in realistic visual environments according to the Bienenstock, Cooper, and Munro (BCM) theory.
91 Citations1994Chi-Tat Law, Leon N. Cooper
Journal of Theoretical BiologyLocalized memories in idiotypic networks
89 Citations1990Gérard Weisbuch, Rob J. de Boer +1 more
It is demonstrated that, for a considerable range of parameters, both models account for the existence of localized memory-states in which only the Ab1 and the Ab2 clones are activated and the clones of the Ab3 level remain virgin.
IEEE Transactions on Signal ProcessingClassification of underwater mammals using feature extraction based on time-frequency analysis and BCM theory
67 Citations1998Q. Huynh, Leon N. Cooper +2 more
The improved results suggest that nonlinear feature extraction from wavelet representations outperforms different linear choices of basis functions.
Pattern Recognition LettersFace recognition using a hybrid supervised/unsupervised neural network
66 Citations1996Nathan Intrator, D. Reisfeld +1 more
Neural ComputationReceptive Field Formation in Natural Scene Environments: Comparison of Single-Cell Learning Rules
60 Citations1998Brian S. Blais, Nathan Intrator +2 more
It is demonstrated that receptive fields developed using learning rules include kurtosis and skewness maximization, the quadratic form of the Bienenstock-Cooper-Munro learning rule, and single-cell independent component analysis depend on a small portion of the distribution.
Vision ResearchBCM network develops orientation selectivity and ocular dominance in natural scene environment
41 Citations1997Harel Z. Shouval, Nathan Intratorj +1 more
It is shown that for the BCM rule a natural image environment with binocular cortical misalignment is sufficient for producing networks with orientation-selective cells and ocular dominance columns.
Neural ComputationEffect of Binocular Cortical Misalignment on Ocular Dominance and Orientation Selectivity
40 Citations1996Harel Z. Shouval, Nathan Intrator +2 more
It is shown that binocular misalignment affects principal component analysis (PCA) and Bienenstock, Cooper, and Munro (BCM) learning in different ways, with binocular neurons emerging in every case for the BCM learning rule.
Proceedings of the National Academy of SciencesMean-field theory of a neural network.
26 Citations1988L N Cooper, Christopher L. Scofield
Investigation of the evolution of a cell in this mean-field network indicates that many of the results on existence and stability of fixed points that have been obtained previously in the single-cell theory can be successfully generalized here.
Munich Personal RePEc Archive (Ludwig Maximilian University of Munich)Three-Dimensional Object Recognition Using an Unsupervised Neural Network: Understanding the Distinguishing Features
15 Citations1991Nathan Intrator, Bülthoff Gold Ji +2 more
Results of an initial study replicating recent psychophysical experiments demonstrated the utility of the proposed method for feature extraction and the authors describe further experiments designed to analyze the nature of the extracted features and their relevance to the theory and psychophysics of object recognition.
International Journal of Bifurcation and ChaosStable State Analysis of an Immune Network Model
7 Citations1998Gastone Castellani, Claudio Giberti +2 more
The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases.