On neurodynamics with limiter function and linsker's developmental model

Authors:
Jianfeng Feng;Hong Pan;Vwani P. Roychowdhury
Affiliations:
Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907--1285 USA;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907--1285 USA
Venue:
Neural Computation
Year:
1996

Citing 8
Cited 6

The :20Brain-state-in-a-box" Neural model is a gradient descent algorithm

Journal of Mathematical Psychology
Self-Organization in a Perceptual Network

Computer
Analysis of Linsker's simulations of Hebbian rules

Neural Computation
Neural and automata networks: dynamical behavior and applications

Neural and automata networks: dynamical behavior and applications
Stability and optimization analyses of the generalized brain-state-in-a-box neural network model

Journal of Mathematical Psychology
The role of constraints in Hebbian learning

Neural Computation
Derivation of linear hebbian equations from a nonlinear hebbian model of synaptic plasticity

Neural Computation
Review:

Neural Computation

Lyapunov functions for neural nets with nondifferentiable input-output characteristics

Neural Computation
Fixed-point attractor analysis for a class of neurodynamics

Neural Computation
Dynamical Stability Conditions for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions

Neural Computation
Switching analysis of 2-D neural networks with nonsaturating linear threshold transfer functions

Neurocomputing
A Winner-Take-All Neural Networks of N Linear Threshold Neurons without Self-Excitatory Connections

Neural Processing Letters
Learning in a higher-order simple perceptron

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

The limiter function is used in many learning and retrieval models as the constraint controlling the magnitude of the weight or state vectors. In this paper, we developed a new method to relate the set of saturated fixed points to the set of system parameters of the models that use the limiter function, and then, as a case study, applied this method to Linsker's Hebbian learning network. We derived a necessary and sufficient condition to test whether a given saturated weight or state vector is stable or not for any given set of system parameters, and used this condition to determine the whole regime in the parameter space over which the given state is stable. This approach allows us to investigate the relative stability of the major receptive fields reported in Linsker's simulations, and to demonstrate the crucial role played by the synaptic density functions.